GEOMORFOLOGIA SÍSMICA TRIDIMENSIONAL DO PALEOCARSTE...
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UNIVERSIDADE ESTADUAL DE CAMPINAS FACULDADE DE ENGENHARIA MECÂNICA E INSTITUTO DE GEOCIÊNCIAS MATEUS BASSO GEOMORFOLOGIA SÍSMICA TRIDIMENSIONAL DO PALEOCARSTE DA FORMAÇÃO MACAÉ, BACIA DE CAMPOS, BRASIL CAMPINAS 2017
Transcript of GEOMORFOLOGIA SÍSMICA TRIDIMENSIONAL DO PALEOCARSTE...
UNIVERSIDADE ESTADUAL DE CAMPINAS
FACULDADE DE ENGENHARIA MECÂNICA
E INSTITUTO DE GEOCIÊNCIAS
MATEUS BASSO
GEOMORFOLOGIA SÍSMICA
TRIDIMENSIONAL DO PALEOCARSTE DA
FORMAÇÃO MACAÉ, BACIA DE CAMPOS,
BRASIL
CAMPINAS
2017
DEDICATÓRIA
Aos meus pais, Maria Neide e Antônio Carlos,
à minha avó Odila,
e à minha cachorra Teca.
AGRADECIMENTOS
Gostaria de agradecer primeiramente à minha família, pois me apoiaram em
todos os momentos durante essa jornada. Principalmente à minha mãe Maria Neide, ao
meu pai Antônio Carlos e à minha avó Odila por todo o incentivo e amor incondicional.
Agradeço também à minha amada namorada Francine, companheira e amiga por
dividir comigo todos os momentos.
Obrigado aos meus grandes amigos da turma de geologia 010, principalmente
aos geoamigos Tales, Vinicius e Ester por ajudarem a tornar a vida mais leve.
Sou grato ao meu orientador Alexandre Campane Vidal, pela oportunidade de
realizar esse mestrado, pela orientação e dedicação não apenas como orientador, mas
também como amigo.
Agradeço aos queridos amigos pesquisadores do CEPETRO: Aline, Guilherme,
Leandro, Bruno e principalmente aos coautores Michelle, Luis e Ulisses sem os quais os
trabalhos aqui apresentados não teriam sido possíveis.
Reitero um agradecimento especial a Michelle Kuroda, por todo o tempo
disponibilizado para me ajudar e esclarecer as infindáveis dúvidas, muito obrigado pela
sua paciência, atenção e por todos os conselhos.
Por fim, agradeço à Statoil pela oportunidade de participar deste projeto e por
todo o suporte oferecido. Obrigado à Juliana Bueno pelo apoio durante o
desenvolvimento desta pesquisa.
“Tudo o que temos de decidir é o que fazer com o tempo que nos é dado”
Gandalf
RESUMO
Dissertação de Mestrado
Mateus Basso
Esta dissertação visa o estudo e a caracterização geomorfológica do horizonte paleocárstico
correspondente ao topo da Formação Macaé (Albiano-Cenomaniano), que consiste nos
depósitos da megassequência de plataforma carbonática rasa da Bacia de Campos, litoral sudeste do Brasil. Os carbonatos da Formação Macaé sofreram intensa carstificação durante um
período de exposição subárea de 10 a 15 milhões de anos, o que levou a criação de uma
geomorfologia única marcada por feições erosivas profundas e um sistema de drenagem bem desenvolvido com alto grau de conexão com a hidrologia de subsuperfície. O processo de
carstificação definido pela alta solubilidade das rochas carbonáticas e pela criação de porosidade
secundária, acarretou o surgimento de sistemas de cavernas que passaram por processos colapsíveis durante a evolução do soterramento. O entendimento do sistema altamente
heterogêneo criado pela carstificação só é possível graças a utilização da sísmica tridimensional.
O horizonte carstificado corresponde a um forte refletor sísmico que uma vez mapeado permite
o estudo geomorfológico do paleohorizonte. No entanto, o processo de interpretação das feições cársticas não é trivial, uma vez que estas apresentam muitas vezes baixa continuidade espacial e
respostas sísmicas sutis. Nesse sentido o entendimento deste sistema deve se dar de maneira
multidisciplinar, através do uso de técnicas de processamento sísmicos e de atributos que facilitem e aumentem a precisão do processo interpretativo. Este trabalho apresenta um artigo
principal cujo enfoque é o entendimento do sistema cárstico sob o ponto de vista geológico e
geomorfológico, porém diferentes técnicas de processamento foram utilizadas, dentre elas a classificação multiatributo não supervisionada por meio do Self-Organizing Map (SOM) bem
como a técnica de gradiente por fatorização QR. Para o maior detalhamento destes dois
métodos, se encontram em anexo dois artigos escritos em segunda autoria. Como resultado final
foi possível constatar a ocorrência de diversas feições cársticas na área de estudo tais como vales, canyons, ravinas, dolinas e sistemas de cavernas. Em adição foi possível também
entender como se deu a variação espacial do processo de carstificação por meio da identificação
de áreas com desenvolvimento cárstico preferencial.
Palavras chaves: Caracterização de Reservatórios; Paleocarste; Geomorfologia Sísmica 3D,
Atributos Sísmicos.
ABSTRACT
Masters Degree
Mateus Basso
This research aims at the study and geomorphological characterization of the paleocarstic
horizon corresponding to the Macaé Formation top (Albian-Cenomanian), which consists of the
shallow platform carbonate megassequence deposits of the Campos Basin, southeast coast of
Brazil. The Macaé Formation carbonates underwent intense karsification during a subarea
exposure period of 10 to 15 million years, which led to the creation of a unique geomorphology
marked by deep erosive features and a well-developed drainage system with a high degree of
connectivity with the subsurface hydrology. The karsification process defined by the high
solubility of the carbonate rocks and by the creation of secondary porosity, led to the creation of
cave systems that underwent collapsible processes during the burial evolution. The
understanding of the highly heterogeneous system created by karsification is only possible
through the use of three-dimensional seismic. The karsified horizon corresponds to a strong
seismic reflector that once mapped allows the geomorphological study of the paleohorizon.
However, the process of interpretation of the karst features is not trivial, since these often
present low spatial continuity and subtle seismic responses. In this sense the understanding of
this system must be done in a multidisciplinary way, through the use of seismic processing
techniques and attributes that facilitate and increase the accuracy of the interpretive process.
This work presents a main article whose focus is understanding of the karst system from a
geological and geomorphological point of view, but different processing techniques were also
used, among them the unsupervised multi-attribute classification through the Self-Organizing
Map (SOM) as well the QR factorization gradient technique. For the greater detail of these two
methods, two articles written in second authorship are attached. As a final result, it was possible
to verify the occurrence of several karst features in the study area such as valleys, canyons,
ravines, sinkholes and cave systems. In addition, it was also possible to understand how occur
the spatial variation of the karsification process by identifying areas with enhanced karst
development.
Keywords: Reservoir Characterization; Paleokarst; 3D Seismic Geomorphology; Seismic
Attributes
SUMÁRIO
Introdução ....................................................................................................... 16
Referências Bibliográficas ............................................................................... 17
Artigo 1: Three- Dimensional Seismic Geomorphology of the Macaé Formation
Paleokarst, Campos Basin, Brazil ............................................................................... 18
ABSTRACT .................................................................................................. 19
INTRODUCTION ......................................................................................... 19
MATERIAL AND METHOD .......................................................................... 20
GEOLOGIC SETTINGS ............................................................................... 22
THEORETICAL FOUNDAMENTATION – EPIGENIC KARST AND
PALEOKARST ........................................................................................................ 23
RESULTS AND DISCUSSION ..................................................................... 25
Surface Geomorphology and Drainage Patterns ...................................... 25
Endokarstic Features ................................................................................ 30
Caves Systems ............................................................................................................. 30
Coalesced Collapsed-Caves Systems ............................................................................ 33
Spatial distribution of karstification ............................................................................. 34
CONCLUSION ............................................................................................. 36
ACKNOWLEDGMENT ................................................................................. 37
REFERENCES ............................................................................................ 37
Considerações finais ....................................................................................... 40
Anexo A, Artigo 2: A Fast Approach for Unsupervised Karst Feature
Identification Using GPU ............................................................................................. 42
ABSTRACT .................................................................................................. 43
INTRODUCTION ......................................................................................... 43
OVERVIEW OF KARST FEATURES ........................................................... 44
THE SELF-ORGANIZING MAP ................................................................... 45
GRAPHICAL HARDWARE UNIT (GPU) AND CUDA ................................... 46
GPU PARALLEL IMPLEMENTATION .......................................................... 47
METHODOLOGY......................................................................................... 48
CASE OF STUDY: MACAÉ FORMATION ................................................... 51
EXPERIMENTS AND DISCUSSION ............................................................ 51
CONCLUSION ............................................................................................. 54
ACKNOWLEDGMENT ................................................................................. 54
REFERENCES ............................................................................................ 54
Anexo B, Artigo 3: High amplitude anomalies identification by QR factorization
gradient technique ...................................................................................................... 58
ABSTRACT .................................................................................................. 59
INTRODUCTION ......................................................................................... 59
MATERIAL AND METHOD .......................................................................... 60
Geologic Settings and Dataset ................................................................. 60
Vertical QR gradient technique ................................................................. 61
Seismic attributes ..................................................................................... 62
APPLICATION AND RESULTS ................................................................... 62
Karst features ........................................................................................... 62
Igneous Intrusions .................................................................................... 67
CONCLUSIONS........................................................................................... 70
ACKNOWLEDGEMENTS ............................................................................ 71
REFERENCES ............................................................................................ 71
Índice de Figuras
Artigo 1: Three-Dimensional Seismic Geomorphology of the Macaé Formation Paleokarst,
Campos Basin, Brazil
Figure 1: Location of the Campos Basin on the Southeastern Brazilian continental margin. Areas in pink and orange indicate, respectively, basin onshore and offshore segments; areas in green correspond to main oil fields (modified from Cardoso and Hamza, 2014). ...................... 22
Figure 2: The Campos Basin stratigraphy and tectono-stratigraphic evolution. The Macaé Formation from the shallow carbonate megasequence is highlighted in red. (Modified from Mohriak et al., 2008). .............................................................................................................. 23
Figure 3: Block diagram of an epigenic karst terrain, including the main features observed in the exokarstic, epikarstic and endokarstic domains. ...................................................................... 24
Figure 4: (A) Relief map of the paleokarst corresponding to the top of the Macaé Fm, indicating main identified karstic features. Dotted line of wider spacing indicates the limit between highlands and lowlands zones. Dotted line of shorter spacing limits a region of high noise levels and lower confidence to interpretation. (B) Schematic map delimiting the valleys in blue, a canyon in green, ravines in Orange and sinkholes in pink. ....................................................... 26
Figure 5: SW – NE seismic sections indicating the relationship between valley A (A), the canyon (B), and complex structural systems. On the left, non-interpreted images and on the right the interpretation of main faults associated with the fluviokarstic features. The pink arrow indicates an apparent paleochannel in the valley A ................................................................................ 27
Figure 6: (A) A relief map of the NE region of the study area, indicating the circular depression occurrence (black circles), dotted line designates the limit between lowlands and highlands. (B) Image resultant from spectral decomposition and posterior color composition to frequencies of 20, 40 and 65 Hz. (C) Result of thr attribute similarity used in the paleokarstic horizon. (D) Isopach map due to thickness variation in the Macaé Fm. The red arrows indicate examples of circular closed depressions, whose occurrence is variably better demarcated by the different images. ................................................................................................................................... 28
Figure 7: The 3D result of an unsupervised multi-attribute classification by means of the Self-Organizing Map (SOM) combining the attributes most positive and most negative curvature, envelop weighted frequency, amplitude second derivative and isopach map. The red arrows point to various sinkholes. ....................................................................................................... 29
Figure 8: Depth (m) vs width (m) of circular features mainly associated with sinkholes. There is an increasing depth tendency according to the diameters of the depressions; however, this behavior is less clear, when it comes to small depressions. ..................................................... 29
Figure 9: Seismic interpretation of two sinkholes (A and B), possibly associated to paleocaves collapse. On the left, images exhibit non-interpreted features in seismic section. On the right, images are structurally interpreted, indicating suprastratal (SD) and intrastratal (ID) deformation zones. Green line corresponds to the top of the Macaé Fm. top............................................... 30
Figure 10: Comparative chart of different attributes and techniques used to identify SBRs. (A) Indicates possible SBRs in seismic section, green line indicates the top of the Macaé Fm. (B), (C), (D) correspond to RMSA, signal envelop and energy, respectively. (E) Results from the amplitude filter obtained in conventional seismic data, and (F) corresponds to the QR factorization gradient technique. .............................................................................................. 31
Figure 11: Comparison between the bright spots found in the study area and the ones produced as a result of the physical experiment conducted by Xu et al. (2016). In (A) SBRs different variations related to the cave diameters and in (B) the different responses associated with changes in form and distribution of the caves. (After Xu et al. 2016). ....................................... 33
Figure 12: Example of coalesced, collapsed-caves systems in seismic section SW-NE. (A) Non-interpreted image indicating bright spots, and (B) interpreted image indicating normal (N) and reverse (R) faulting. SD and ID correspond respectively to the supra and intrastratal deformation zones................................................................................................................... 34
Figure 13: Analysis of the northeasernt region subvolume in (A) three-dimensional model of the distribution of bright spots related to karst features obtained with QR vertical gradient amplitude difference technique and (B) plan visualization of the 3D model superimposed with the paleokarst horizon. Dotted áreas indicate regions with the highest concentration of karst features................................................................................................................................... 35
Figure 14: Depth (m) of the bright spots in relation to paleokarst horizon. Four main ranges of depth were identified, group 1 represent the oldest caves and group 5 the youngest. The purple line indicates the maximum depth reached by the Canyon (Cmd). ........................................... 36
Anexo A, Artigo 2: Graphical Hardware applied in karst identification Figure A. 1: Block diagram of an epigenic karst terrain, including the main features observed in
exokarstic, epikarstic and endokarstic domains. ...................................................................... 44
Figure A. 2: Memory architecture in a CUDA-enabled GPU (Extracted from Kirk and Hwu,
2010). ..................................................................................................................................... 47
Figure A. 3: Main workflow. ..................................................................................................... 49
Figure A. 4: The set of five attributes shown at the Macaé top: (a) most positive and (b) most
negative curvatures, (c) amplitude second derivative, (d) envelope-weighted frequency and (e)
isopach map. .......................................................................................................................... 49
Figure A. 5: Top of the Macaé formation and some of the identified geological features in the
amplitude data: ravines (green arrows), a wide and sinuous canyon (red arrow) and sinkholes
(pink arrows). .......................................................................................................................... 51
Figure A. 6: Maps of distribution: (a) U-matrix, (b) ampltiude second derivative, (c) most
negative and (d) most positive curvature, (e) envelope weighted frequency, (f) isopach
distribution maps, and (g) labeled neuron map. ....................................................................... 52
Figure A. 7: Classification result showing in red several geomorphologic features on the Macaé
seismic horizon ....................................................................................................................... 53
Figure A. 8: Classification result in details. (a) ravines (green arrows) and sinkholes (pink
arrows), and (b) canyon (red arrow). ....................................................................................... 53
Anexo B, Artigo 3: High amplitude anomalies identification by QR factorization gradient
technique
Figure B. 1: Time slice showing the two study areas. In A, the polygon in which the high-amplitudes are predominantly associated with karst features, and in B, the polygon associated with igneous intrusions and the sections used to illustrate the results. ..................................... 60
Figure B. 2: a) Amplitude of section AA’, used to illustrate gradient results to highlight karsts. The attributes calculated were: b) Hilbert’s Transform; c) Energy, and d) Input, the Energy minus Hilbert. The yellow circles represent the karst feature highlighted in all figures. .............. 63
Figure B. 3: a) LSF results obtained for the Macaé Formation section. b) Horizontal LSF. c) Vertical LSF. d) Final LSF. The top of the Macaé Formation highlighted in a) is also well seen in other images. The yellow circles represent the karst feature, highlighted in all figures, despite of the noise. After Maoshan et al. (2011). .................................................................................... 64
Figure B. 4: (a) QR factorization results obtained for the Macaé Formation section. b) Horizontal QR. c) Vertical QR. d) Final QR. The top of the Macaé Formation highlighted in a) is also well seen in other images, as proposed by Maoshan et al (2011), but with less noise. The yellow circles represent the karst feature highlighted in all figures. ..................................................... 65
Figure B. 5: Zoom of the karst features and regions without karst features. a) The original amplitude and the associated karst feature and areas without karst features below. b) Vertical LSF. c) Final LSF. d) Vertical QR. Note the homogeneity and better karst delineation of the proposed QR factorization method in d. ................................................................................... 66
Figure B. 6: In blue, geobodies of karst features defined by QR factorization gradient difference technique, after selecting the interval between the Macaé top and bottom horizons. For the correct imaging of the volume, the seismic anomaly associated with the Macaé top horizon was removed.................................................................................................................................. 67
Figure B. 7: a) Amplitude of section BB’, used to illustrate the gradient results to highlight igneous intrusions. b) Hilbert’s transform. c) Energy. d) Input used for both methods. e) Vertical LSF. f) Vertical QR factorization. The yellow box highlights the igneous intrusion. Note the benefit of applying the QR method, which could eliminate most of the noise, evidencing the desired amplitude anomaly. ..................................................................................................... 69
Figure B. 8: Final result of vertical QR factorization gradient applied to igneous intrusion in 3D identification. In blue the seismic body of the highlighted igneous intrusion illustrated by Fig. B. 7 f. ............................................................................................................................................. 70
Índice de Tabelas
Artigo 1: Three-Dimensional Seismic Geomorphology of the Macaé Formation Paleokarst,
Campos Basin, Brazil
Table 1: The main seismic attributes and processing techniques, their description and application on karst interpretation. ........................................................................................... 21
Table 2: Morphometric data of fluviokarstic features ................................................................ 26
Anexo A, Artigo 2: Graphical Hardware applied in karst identification
Table A. 1: Structure dimensions used in the application. ........................................................ 47
Table A. 2: Parameters used to setup the SOM algorithm. ....................................................... 50
Table A. 3: Additional parameters for the parallel implementation. ........................................... 50
Table A. 4: Computing time comparison .................................................................................. 54
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Introdução
Cerca de 60% das reservas mundiais de óleo e 40% de gás estão em
reservatórios carbonáticos (Castro et al., 2013), que em sua maioria são heterogêneos e
possuem propriedades geológicas complexas que diferem amplamente dos reservatórios
siliciclásticos. Dentre os processos geológicos atuantes em depósitos carbonáticos a
carstificação é um forte agente modificador do reservatório.
Segundo Ford e Williams, 1989 o carste é um termo utilizado para descrever
terrenos distintos cuja geomorfologia e hidrologia são resultados da combinação entre a
alta solubilidade das rochas e a porosidade secundária bem desenvolvida. Nesse sentido,
a carstificação pode gerar uma classe de reservatórios definidos como paleocársticos.
Os sistemas palocársticos são importantes reservatórios carbonáticos e podem
formar campos de óleo significantes. Tais sistemas se desenvolvem próximos a
discordâncias, quando a plataforma carbonática experiencia exposição subárea sob
condições húmidas durante um período geológico significante. Este processo pode ser
associado ao aumento da permo-porosidade como resultado da dissolução carbonática
ou pelo decréscimo por precipitação (Tiant et al. 2016).
A caracterização de sistemas paleocársticos é um grande desafio graças a suas
escalas, geometrias e complexidades espaciais. Assim sendo, a sísmica tridimensional é
uma ferramenta essencial, permitindo o estudo de reservatórios a grandes
profundidades. As discordâncias cársticas podem ser mapeadas uma vez que,
costumam constituir fortes refletores sísmicos e o alto contraste de impedância acústica
entre as feições cársticas e a rocha hospedeira cria anomalias de amplitude conhecidas
como bright spots. Entretanto, a extração e interpretação de dados sísmicos não é trivial
e necessita de técnicas de processamento e de atributos sísmicos que realcem
informações e facilitem o entendimento do sistema.
Portanto, este trabalho se propõe a caracterizar por meio da sísmica 3D o sistema
paleocárstico correspondente ao topo da Fm. Macaé localizada na Bacia de Campos,
litoral Sudeste do Brasil. Para tal é apresentado um artigo principal que busca o
entendimento de como a carstificação modificou a Fm. Macaé e quais elementos foram
criados em superfície e subsuperfície.
Em complemento encontram-se em anexo dois artigos escritos em segunda
autoria que visam o detalhamento de dois processos metodológicos que se mostram
essenciais para o processo interpretativo. O primeiro trata da classificação multiatributo
não supervisionada por meio do Self-Organizing Map (SOM) buscando a delimitação
automática de feições cársticas no horizonte e o segundo desenvolve a técnica
diferencial de gradiente vertical QR que se mostrou essencial para extração de
geobodies relacionados a sistemas de cavernas.
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Referências Bibliográficas
Castro, L. et al, Medidas de Propriedades Petrofísicas e Identificação Mineralógica de Afloramentos
Carbonáticos. XIII Congresso Internacional da Sociedade Brasileira de Geofísica, 2013. Rio de Janeiro,
Brasil.
Ford, D.C.; Willians, P.W.. Karst Geomorphology and Hidrology. Unwin Hyman, Boston, Mass., 601 pp.
1989.
Tian, F.; Jin, Q.; Lu, X.; Lei, Y.; Zhang, L.; Zheng, S.; Zhang, H.; Rong, Y.; Liu, N. Multi-layered ordovician
paleokarst reservoir detection and spatial delineation: A case study in the Tahe Oilfield, Tarin Basin,
Western China. Marine and Petroleum Geology v. 69, p. 53 – 73, 2016.
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Artigo 1: Three- Dimensional Seismic Geomorphology of the Macaé Formation
Paleokarst, Campos Basin, Brazil
BASSO, Mateus1; KURODA Michelle
1; AFONSO, Luis Claudio Sugi
1; VIDAL,
Alexandre Campane1
1Centro de Estudos do Petróleo (CEPETRO), Universidade Estadual de Campinas -
Unicamp, Campus Universitário Zeferino Vaz – Barão Geraldo, CEP 13083-970,
Campinas, SP, BR
Endereços eletrônicos: [email protected], [email protected],
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ABSTRACT
The three-dimensional seismic data of the Campos Basin, Southern Brazil, allowed the
detailed characterization of a paleokarst horizon that corresponds to the top of the
Macaé Fm. (Albian-Cenomanian). Macaé Fm. carbonates underwent intense
karstification process associated with subaerial exposition during a hiatus of 10 to 15
million of years, which led to the development of karst features, such as valleys,
canyons, ravines, sinkholes and caves systems. With the growing interest in
understanding paleokarst reservoir architecture, driven by the occurrence of this type of
formation in several productive oil fields, this study aims to characterize the exokarst
and endokarst features and understand how karstification affects and compartmentalizes
the carbonate reservoirs. The analysis was divided into two main parts: (1) surface
geomorphology, including the studies concerning the drainage system and relief
features present on the horizon; and (2) endokarst features including cave systems and
collapsed cave systems. Two geomorphological domains were identified, highlands –
characterized by abrupt relief with well-developed erosive features, and lowlands –
characterized by smoother topography. Subjacent collapse sinkholes define the
relationship between caves collapse and surface geomorphology with circular, closed
depressions. Lastly, the endokarst study by means of the identification of amplitude
anomalies indicates heterogeneous cave systems with different preservation levels.
Key Words: Paleokast structure, 3-D seismic geomorphology, Campos Basin.
INTRODUCTION
The identification and evaluation of subsurface paleokarsts is a scientific frontier
in carbonate reservoir characterization (Feazel, 2010; Sayago et al., 2012). Paleokarst
are complex unconformities which can reflect from brief periods of karstification with
shallow dissolution elements, to long-term subaerial exposition with mature landscapes,
topographic variations of hundreds of meters and large cave systems (Juhász et al.
1995).
The understanding concerning this system is of great importance to the oil
industry, because paleokarsts are globally relevant carbonate reservoirs, able to create
important oil fields (Tian et al., 2016). Among them are included the Upper Devonian
Grosmont Formation of Northeastern Alberta, Canada (Dembicki and Machel, 1996;
Bown, 2011); the Ordovician fields in Tarim Basin, China (Yu et al., 2016; Zhao et al.,
2014; Zeng et al., 2011a, b; Tian et al., 2016) and the Lower and Upper Paleozoic
carbonates in Western Texas, USA (Kerans, 1988).
In addition to the inherent complexity of surface and subsurface karstification,
there are processes promoted by burial at great depths, producing complex reservoir
architectures and high spatial heterogeneity (Sayago et al. 2012). In this sense, three-
dimensional seismic survey is an important tool for paleoenvironmental and
geomorphological subsurface studies (Rafaelsen, 2006), making possible the acquisition
of continuous horizons and the identification of relief elements, as well as the
interpretation of certain features and several structures, such as caves and collapsed
cave systems.
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In other to assist the seismic interpretation process, many advances have been
made in the development of seismic attributes and other data processing methodologies.
Zhao et al. (2014) and Tian et al. (2015) conducted works integrating the use of well
logs, cores and high-quality seismic data sets combined with the application of different
attributes to perform the characterization of karst reservoirs in the Tarin basin, China;
Sayago et al. (2012) applied 18 different attributes seeking for the multi-attribute
seismic classification of a paleokarst located in the Barents Sea. In turn, Maoshan et al.
(2011) developed the directional amplitude gradient diference technique, in order to
detect carbonate-karst reservoirs.
In this sense, this paper presents a study concerning three-dimensional seismic
data obtained from the Campos Basin, Southern of Brazil, focusing on the Macaé Fm.,
whose top corresponds to an unconformity associated with extensive subaerial
exposition and karstification periods. Based on previous studies about paleokarst
seismic interpretation and current karstification models, this study aims to identify and
describe surface and sub-surface karstic features, as well as understanding the processes
that created them. To this end, various attributes and data processing techniques were
applied to facilitate and increase the precision of the interpretation process.
MATERIAL AND METHOD
The three-dimensional seismic volume used in this study comprises a
rectangular area of approximately 1,000 km², 63 km long (SW-NE) and 16 km wide
(NW-SE). It has a bin size of 12.5 x 18.5 m, with a sampling interval of 4 ms and length
record of 5 s. The seismic traces are characterized by 1,250 samples, in a frequency
spectrum between 0 and 125 Hz with a 35 Hz dominant frequency.
The theoretical seismic resolution, taken as ¼ of wavelength, is approximately
15 m, allowing the identification of a wide variety of macro karst features both in
seismic section and horizon. In addition, using a velocity model obtained by seismic-
well tie it was possible to perform morphometric analyses in depth of the identified
features. The time-depth conversion was done automatically by the sotware OpendTect.
In this sense, the paleokarst study was divided into two main areas to be
discussed: (1) surface geomorphology mainly covering the study of erosional features
incised on the horizon; (2) subsurface features represented by collapsed and non-
collapsed cave systems. The karst features interpretation was conducted based on
current geomorphological and geological models, as well as seismic evidences
identified and described by previously published studies.
The use of seismic attributes and other processing techniques proved essential
for identification and description of karst features (table 1). On the horizon study, the
features identification was facilitated by attributes such as, similarity, spectral
decomposition, most positive and negative curvature, envelop weighted frequency,
amplitude second derivative and isopach maps. The attributes were combined and then
classified by the Self-Organizing Map (SOM), enabling the extraction of features
corresponding to different classes (see attachment A).
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In turn, the key for endokarst study in seismic section was the identification of
bright spots. The amplitude anomalies were highlighted by attributes like root-mean-
square amplitude (RMSA), signal envelop, energy and other kinds of amplitude filters.
Once identified the brightspots were compared and classified based on Xu et al. (2016)
work.
In order to detect karst geobodies, the QR factorization gradient technique was
also applied. The assisted method is an adaptation of the gradient difference (Maoshan
et al., 2011), computed by QR decomposition, which is mathematically more stable than
the least-norm solution (Golub and Reinsh, 1970). However, besides emphasizing karst
features, the technique requires caution, once the gradient difference can highlight other
strong reflections that can be related to structural and stratigraphic characteristics, as
faults and internal horizons. Among the advantages of the method, it allows karst
features extraction in 3D, suppressing other reflections (see attachment B).
Table 1: The main seismic attributes and processing techniques, their description and application on karst interpretation.
Seismic Attribute/ Processing
Description Application
Similarity Indicates how much two or more
trace segments look alike Drainage patterns,
Sinkholes indentification
Spectral Decomposition (FFT)
Decomposes a trace segment into frequency components
Geomorphology domains, Drainage patterns
Sinkholes identification
Second derivative of the
amplitude
Provides a measure of the
sharpness of amplitude peak
Sinkholes identification, Drainage patterns, SOM
classfication input
Most positive and most negative curvature
Measures the deformation of a surface at a point.
Relief patterns, SOM classification input
Envelope weighted frequency
It is the instantaneous frequency weighted by the envelope over a
given time window
Sinkholes identification, Drainage patterns,
SOM classificaiton input, Bright sposts highlight
Isopach Map Provide difference of thickness
between two horizons Sinkholes identificaiton, SOM classfication input
RMSA
Calculates the sum of the roots of the amplitudes divided by the
number of samples in the window.
Bright spots highlight
Energy Sum of amplitudes squared in a
time-gate Bright spots highlight
Amplitude Filter Discards values within a range of
amplitude (+17.500 e -17.500) Bright spots highlight
SOM Classificaiton Unsupervised multi-attribute
classification through the Self-Organizing Map (SOM)
Allows the 3D extraction of surface
geomorphological features
22
QR factorization gradient technique
Adaptation of the gradient difference of Maoshan et al.
(2011)
Allows the 3D extraction of bright spots anomalies,
suppressing other reflections
GEOLOGIC SETTINGS
The Campos Basin is a typical continental passive margin basin located in the
southeast Brazilian Coast, extending from northern Rio de Janeiro to southern Espírito
Santo, and occupying an area of approximately 100.000 km² (Figure 1). Currently, it is
the most prolific oil producer basin of Western South Atlantic, responsible for nearly
80% of the Brazilian oil production (Cardoso and Hamza, 2014).
Originally interconnected to the Santos Basin, the Campos Basin has its tectono-
stratigraphic evolution linked to the Gondwana breakup and rifting mechanism with
subsequent formation of the South Atlantic Ocean (Guardado et al., 1989; Dias et al.,
1990; Riccomini et al., 2012).
Figure 1: Location of the Campos Basin in the southeast Brazilian continental margin. Areas in pink and orange indicate, respectively, basin onshore and offshore segments; areas in green correspond to main oil
fields (modified from Cardoso and Hamza, 2014).
The Campos Basin evolution initiated about 130 million years ago during
Cretaceous period, and it is currently divided into six megasequences (Ponte and Asmus
1976; Guardado et al., 1989; Dias et al., 1990; Horschuts and Scuta, 1992; Cainelli and
Mohriak, 1998; Mohriak et al., 2007): (1) continental pre-rift megasequence; (2)
continental rift megasequence; (3) transitional megasequence, related to the early drift-
phase; (4) shallow carbonatic platform megasequence, related to the late drift-phase; (5)
transgressive marine megasequence; and (6) regressive marine megasequence (Figure
2).
During the shallow carbonatic platform megasequence, occurred deposits of
carbonates of Albian-Cenomanian age from the Macaé Fm. (considered by some
authors as Group). The Macaé Formation represents the definitive settlement of the
Campos Basin marine environment, and it is characterized by the association of
23
calcarenite, calcirudite and calcilutite, deposited in a moderate to high energy
environment (Franz, 1987).
The Macaé Fm. was directly affected by the movement of the evaporite deposits
from the transitional megasequence, which structural configuration is directly related to
salt tectonics, resulting in salt pillows and roll-over type structures, controlling
faciologic distribution of shallow waters carbonates (Guardado et al., 1989; Spadini,
1992).
In the target region of this study, the top of the Macaé Fm. is characterized by an
unconformity with Carapebus Fm., relative to a hiatus of 10 to 15 million years, which
was possibly created due to a tectonic uplift (Raunholm et al., 2014). The subaerial
exposure of the carbonate deposits promoted an extensive karstification process,
possibly multiphasic, developing erosive features and karst structures, such as canyons,
valleys, sinkholes and caves.
Figure 2: The Campos Basin stratigraphy and tectono-stratigraphic evolution. The Macaé Formation from the shallow carbonate megasequence is highlighted in red. (Modified from Mohriak et al., 2008).
THEORETICAL FOUNDAMENTATION – EPIGENIC KARST AND
PALEOKARST
The literature introduces several definitions for karst, emphasizing morphology,
descriptive and genetic parameters. One of the most recurrent definition was formulated
by Ford and Williams (1989) as a term used to describe distinctive terrains whose
24
landforms and hydrology result from a combination of high rock solubility and well-
developed secondary porosity.
Thus, the relief primarily created by chemical corrosion process results in unique
geomorphological features, divided into three major domains defined by Bogli (1980)
as exokarst, epikarst and endokarst (Figure 3). The exokarst comprises the surface
reliefs with positive and negative forms; meanwhile, epikarst includes a subcutaneous
zone severely altered by the soil and rock contact and the endokarst encompasses the
subterranean formations.
Figure 3: Block diagram of an epigenic karst terrain, including the main features observed in the exokarstic, epikarstic and endokarstic domains.
Karstic terrains have a singular and, predominantly, well developed drainage
system, with exokarstic features, such as large valleys, canyons, ravine and gullies.
Sinkholes, associated with dissolution, subsidence and collapse processes, are generally
observed in variable amount and spatial distribution. Similarly, tower karsts are related
to more mature terrains, characterized by cone shaped, highly steep or vertical walls.
In the subsurface, the water flow rates and aggressiveness determine the rates of
generation of cave systems, genetically linked to natural discontinuities in the rock,
such as fractures, faults and beddings planes (Lowe, 2000). Thus, the endokarstic
domain is characterized by caves, channels, conduits, passages and chambers, which
can be completely or partially occupied by cave sediments or breccia as result of walls
and ceiling collapse, processes inherent to the development of caves in carbonate rocks
(White and White, 1969).
Once buried, the karstic terrain can be classified as paleokarst, defined by
Wright (1982) as “karstic features formed in the past, and related to a hydrological
system or antique surface”. Paleokarsts can be associated with discontinuities or high
amplitude sea level variations, with long exposition periods and complex base level
changes, resulting in several development phases. However, most paleokarsts are less
developed, yet able to evolve secondary porosity, associated with low scale sea level
variations (Wright and Smart, 1994).
25
The burial process impacts the karstic terrain mainly through paleocaves systems
collapse. The overlying strata overweight generates vertical stress, collapsing the empty
spaces (Wright, 1982; McDonnel et al., 2007; Zeng et al., 2011b). According to Loucks
(1999), the relationship between depth and collapse is highly variable, although, most
empty spaces tend to disappear approximately 2,000 meters in depth, even though, they
can also be observed at 3,000 meters depth.
As a result of the paleocaves collapse, much larger damaged zones than the
original empty spaces are created by faulting and fracturing. Usually, the massive rock
mass movement in the subsurface are compensated by suprastratal faulting. Circular,
closed depression structures are created, limited by steep and concentric faults
(McDonnell et al. 2007). According to Loucks (2007), suprastatal deformation effect
can reach more than 700 m above karstic region.
In three-dimension seismic surveying, the study of paleocave systems is guided
by seismic amplitude anomalies or bright spots mapping, more specifically, bright spots
classified as string of beads response (SBR), characterized by limited lateral extension
and the intercalation of minimum and maximum amplitude points. These features,
previously studied by Yu et al. (2016), Zeng et al. (2011a, b), Xu et al (2016) and Tian
et al. (2016), are originated from the combination of the high acoustic impedance
contrast between cave and host rock, and the finite caves scale.
RESULTS AND DISCUSSION
Surface Geomorphology and Drainage Patterns
The overall vision of the study area is shown in the figure 4, including the main
interpreted karstic features of the time horizon that corresponds to the top of the Macaé
Formation. The surface has main dip oriented to SE towards the basin center, and it is
characterized by an irregular paleorelief with abrupt altimetric changes reaching over
250 m, and maximum altimetric amplitude greater than 1 Km towards the main dip.
The horizon was subdivided into two distinct geomorphological zones: the
highlands and the lowlands. The highlands have greater altimetry and comprehend an
erosive domain with fluviokarstic features, such as well-developed valleys and canyons,
which tend to suddenly disappear toward the lowlands. The lowlands have less rugged
paleorelief and absence of fluviokarstic features, excepting a canyon in the northeastern
region. Both regions present closed circular depressions, concentrated mainly in the
northeastern region, and most are associated with sinkholes.
Four large scale valleys were interpreted as incised in the highlands area,
oriented according to NW/SE direction (Figure 4B). The valleys follow the surface
hydraulic gradient, receiving in cases B and C possible tributaries and extending about 7
Km until its erosive features disappear into the lowlands domain. A canyon measuring
at least one order of magnitude above the valleys is found in the extreme northeastern
portion. This feature is not limited to the highlands, spreading through the horizon, also
towards NW/SE.
26
Figure 4: (A) Relief map of the paleokarst corresponding to the top of the Macaé Fm, indicating main identified karstic features. Dotted line of wider spacing indicates the limit between highlands and lowlands
zones. Dotted line of shorter spacing limits a region of high noise levels and lower confidence to interpretation. (B) Schematic map delimiting the valleys in blue, a canyon in green, ravines in Orange and
sinkholes in pink.
The canyon differs from the valleys mainly by having greater depth/width ratio
(Table 2) and featuring steep sided walls, thus indicating a preferably vertical
development at the expense of the horizontal development of the valleys. The symmetry
of the canyon edges is also a diagnostic factor of this type of feature. It is important to
note too that the valleys and the canyon tend to reduce depth/width ratio towards
downstream, indicating proximity to the base level.
In the center-southwestern and northeastern regions of the area smaller erosive
features are also found, presenting low surface continuity, and values of depth and
width ten times smaller than those of the valleys. These features can be associated with
intermittent water flows with lower erosive capacity, characterizing ravines, or small
channels, whose continuity was erased by erosion.
Table 2: Morphometric data of fluviokarstic features
Fluviokarstic Feature
Mean Width(m)
Mean Depth (m)
D/W Extension
(Km) Direction
Valley A 1119 61 0,53 5,2 N135
Valley B 561 32 0,6 5,5 N145
Valley C 742 31 0,49 7,1 N155
Valley D 466 21 0,46 7,5 N125
Canyon 1218 107 0,95 14,2 N155
The seismic sections analysis of the fluviokarstic features indicates a direct
relationship between valleys and canyon with complex structural systems. Every
27
described feature is somehow affected by steep faults that most of the time disappears
when the paleokarstic horizon is reached. This fact supports that the valleys and the
canyon development probably followed a previous structural pattern, influencing
regions of flow convergence and enhanced erosion.
The structural interpretation of valley A and the canyon is shown in figure 5.
Both features are associated with a large number of normal and reverse faults, so that in
the valley A most faults are limited to the Macaé Fm., whereas faults that affect the
canyon disseminate to greater depths and produce greater vertical displacement.
In addition, the detailed evaluation of the paleoforms of valleys A and B reveals
incised channels in the thalweg central zone (purple arrow, figure 5A). These features
dimensions are ten times smaller than those of the valleys, with mean depth and width
of 10 and 100 m respectively, proportionally similar to the channel identified by Bown
(2011) in an analogous situation. However, a higher uncertainty is related to channel
features, as its continuity and scales are limited.
Figure 5: SW – NE seismic sections indicating the relationship between valley A (A), the canyon (B), and complex structural systems. On the left, non-interpreted images and on the right the interpretation of main faults associated with the fluviokarstic features. The pink arrow indicates an apparent paleochannel in the
valley A
Besides the erosive features related to the drainage system, the diagnostic
surface features of the karstification process are the sinkholes or dolines. Approximately
40 closed depressions, with geometry varying from circular to sub-circular, were found
unequally distributed throughout the northeastern region of the study area, on highlands
and lowlands domains (Figure 6A).
The identification of these features is difficult due to their limited scale. Thus, it
is necessary to use different attributes on the target horizon. The attributes similarity,
amplitude second derivative, envelope weighted frequency, spectral decomposition and
isopach maps showed good results. Figure 6 B, C and D illustrate how some of these
attributes highlight different structures.
28
Figure 6: (A) A relief map of the NE region of the study area, indicating the circular depression occurrence (black circles), dotted line designates the limit between lowlands and highlands. (B) Image resultant from spectral decomposition and posterior color composition to frequencies of 20, 40 and 65 Hz. (C) Result of thr attribute similarity used in the paleokarstic horizon. (D) Isopach map due to thickness variation in the
Macaé Fm. The red arrows indicate examples of circular closed depressions, whose occurrence is variably better demarcated by the different images.
In addition, it was possible to combine the attributes most positive and most
negative curvature, envelop weighted frequency, amplitude second derivative, isopach
map and classify them by the method of neural networks multilayered SOM (Self-
Organizing Map). This allows the extraction of the geometry of different karst features
that correspond to one of the obtained classes (Figure 7). It was found that class 2
corresponds to most of the features observed in surface such as the canyon, ravines and
sinkholes.
29
Figure 7: The 3D result of an unsupervised multi-attribute classification by means of the Self-Organizing Map (SOM) combining the attributes most positive and most negative curvature, envelop weighted
frequency, amplitude second derivative and isopach map. The red arrows point to various sinkholes.
The seismically mapped sinkholes have diameter varying between 70 and 600 m
and depth of 5 to 60 m, which is proportionally similar to the data obtained by Zeng et
al. (2011a) for the Tarin Basin, China. The features with diameter more than 200 m
present linear tendency of depth increasing with diameter growth; this pattern is not
repeated by smaller features, in which small diameter and great depth structures can be
observed (Figure 8).
Figure 8: Depth (m) vs width (m) of circular features mainly associated with sinkholes. There is an increasing depth tendency according to the diameters of the depressions; however, this behavior is less
clear, when it comes to small depressions.
In the seismic section, sinkholes are associated with bright spots positioned
directly beneath the closed circular depressions or up to depths of 70 m from the
horizon. These amplitude anomalies are, possibly, produced by paleocaves collapse,
resulting in intrastratal e suprastratal deformation. According to Jennings (1985)
classfication, these features can be classified as a subjacent collapse sinkhole.
McDonnel et al. (2007) described two structural zones connected to paleocaves
collapse, an inner zone mostly composed of reverse faults and characterizing a
compressional environment, and an outer zone connected to normal faults resultant from
an extensional setting. Identification of these zones is difficult due to Macaé Fm. being
structurally disturbed by halokinesis events. Nevertheless, it is possible to observe that
some features are mainly delimited by inverse faults, indicating occurrence of a
contractional inner zone.
30
In addition, the intrastratal movement results in suprastratal faulting, which
expands up to approximately 200 meters above the horizon. The variability of the
suprastratal influence zone height can indicate that the sinkholes developed in different
periods during the burial process, perhaps as a response to different overweight loads.
Figure 9 exemplifies the occurrence of these structures, in interpreted and non-
interpreted sections, through sinkholes A and B (Figure 6A). Both features are similar in
relation to the structural control of intrastratal deformation, so that bright spots are
associated with the occurrence of inverse faults. However, both sinkholes differ by the
collapse depth regarding the horizon, and, specially, by the extension of the supraetratal
deformation, significantly larger in sinkhole A.
Figure 9: Seismic interpretation of two sinkholes (A and B), possibly associated to paleocaves collapse. On the left, images exhibit non-interpreted features in seismic section. On the right, images are structurally interpreted, indicating suprastratal (SD) and intrastratal (ID) deformation zones. Green line corresponds to
the top of the Macaé Fm. top.
Endokarstic Features
Caves Systems
The endokarst study was guided by the identification of bright spots string of
beads response (SBR), related to the high acoustic impedance contrast between caves
and host rock, whether they are filled by caves sediments or represent empty spaces.
According to Tian et al. (2016), caves larger than 15 m can be identified through
conventional seismic data, so that vertical resolution can be improved up to 6 m using
appropriate processing techniques and adequate seismic attributes groups.
Figure 10 exhibits the attributes and techniques that better highlighted bright
spots on the studied seismic volume. Attributes sensitive to extreme amplitude
variations were utilized, such as root-mean-square amplitude (RMSA), applied for cave
identification by Yu et al. (2016) (Figure 10B); signal envelop (E), indicated by
31
Subrahmanyam and Rao (2008) (Figure 10C); and energy attribute based on the
reflectivity potential. In addition, an amplitude filter was used to discard values between
+17.500 e -17.500 (Figure 10D), and, at lastly, a new method based on QR factorization
gradient technique (Figure 10E).
RMSA, signal envelop, and energy attributes are equally effective to highlight
bright spots, emphasizing features in which the amplitude contrast was not very
prominent. However, these attributes also highlight features that the high amplitude
contrast was not associated with the endokarst, such as horizons within the Macaé Fm.
Similarly, amplitude filter emphasizes other features of maximum and minimum
amplitude. Thus, the method based on the directional amplitude gradient difference
showed to be the most effective to minimize non-karstic features.
Figure 10: Comparative chart of different attributes and techniques used to identify SBRs. (A) Indicates possible SBRs in seismic section, green line indicates the top of the Macaé Fm. (B), (C), (D) correspond to
RMSA, signal envelop and energy, respectively. (E) Results from the amplitude filter obtained in conventional seismic data, and (F) corresponds to the QR factorization gradient technique.
By means of the application of different techniques and attributes, it was
possible to notice a large number of bright spots occurring within the Macaé Fm. These
features occur at variable depths and are found next to the paleokarst horizon, as well as
at depths up to 180 m. The bright spots are composed of two to six intercalated focus of
maximum and minimum amplitude (with values in module three to six times higher
than the surroundings), occurring in most cases as three focus. Their vertical extension
varies from approximately 33 to 80 m in depth.
32
These features are in a different geological context from the bright spots
associated to sinkholes, showing no evidence of intraestratal and supraestratal
deformations and, therefore, no direct connection with the horizon. This supports that
these anomalies result from of non-collapsed, open caves, which may well exist at
depths bellow 3,000 m.
The identified bright spots present great heterogeneity of shapes and sizes,
which can reflect different cave properties. However, the relationship between bright
spots shapes and sizes to caves geometry is not linear, thus, the study carried out by Xu
et al. (2016) serves as an important guide. The authors conducted a physical experiment
searching for the relationship between caves properties, such as diameter, width, height,
geometrical arrangement and filling, and the different types of generated SBRs.
The comparison between the observed features and the results obtained by Xu et
al. (2016) was conducted, but it is necessary to bear in mind the limitations of
representativeness inherent to any experiment. Figure 11 presents responses obtained by
the author to different cave diameters (A), and to different geometries/distributions (B)
and possible analogous features observed in the target area.
The observed SBRs exhibit from weak responses composed of only one
maximum and one minimum focus, similar to result obtained by Xu et al. (2016)
regarding caves with diameter of 40 m, to stronger and greater vertical extension
responses compatible with experimental results for caves with diameters up to 100 m.
However, most SRBs are among responses obtained for diameters between 60 and 80
m. The segregation effect of bright spots found by the authors to features with diameters
greater than 100 m, was not identified within the study area, defining an upper limit to
the occurrence of caves.
Concerning shapes variability, it is possible to locate features with configuration
compatible with each one of the six classes identified by Xu et al (2016). This factor
indicates the high geometrical diversity that the endokarstic system possesses. However,
most of the SRBs found are of the short type, followed by the long type, possibly
indicating that the cave systems have preferably vertical development.
33
Figure 11: Comparison between the bright spots found in the study area and the ones produced as a result of the physical experiment conducted by Xu et al. (2016). In (A) SBRs different variations related to the
cave diameters and in (B) the different responses associated with changes in form and distribution of the caves. (After Xu et al. 2016).
Coalesced Collapsed-Caves Systems
Loucks (2007) describes the development of coalesced collapsed-caves systems
as a result of the collapse of the caves system with high spatial density of passages. The
extended subaerial exposition of the karstic terrain can promote the amalgamation of
successive caves development events, creating an interconnected net which can extend
for kilometers. Once such systems are exposed to stress generated by the overlying
sediments overweight, they can collapse, affecting a great rock volume.
Differently from the collapse of isolated passages or small systems recorded in
the area, which horizontal coverage rarely exceeding 500 m, coalesced collapsed-caves
systems can reach 3,000 m in width. These systems were observed in northeasternmost
region, characterized by the presence of a high concentration of bright spots intercalated
with multiple faults, mostly high angular ones (Figure 12).
34
Similarly, to isolated collapses, large scale complexes promote supraestratal and
intraestratal deformation. Structural analysis of these areas indicates preferential
occurrence of reverse faults separating and limiting bright spots, and normal faults
developed above these features, affecting the horizon and underlying sediments,
according to identified by Zeng et al. (2016) regarding the Tarin Basin, China.
This structural configuration reflects the same processes of individual collapses,
but at higher scale and complexity. Inverse faults are related to nearby compressional
setting associated to the several collapse focuses, whereas normal faults are originated
within extensional settings created by overlying masses movements.
Figure 12: Example of coalesced, collapsed-caves systems in seismic section SW-NE. (A) Non-interpreted image indicating bright spots, and (B) interpreted image indicating normal (N) and reverse (R) faulting. SD
and ID correspond respectively to the supra and intrastratal deformation zones.
Spatial distribution of karstification
As a result of the spatial distribution analysis of the exokarstic and endokarstic
features it is possible to note that the northeastern region underwent an enhanced
karstification process when compared to the rest of the area. This statement is confirmed
by the preferred concentration of sinkholes and brightspots associated with cave
systems and collapsed cave systems in this region. In addition, the occurrence of the
canyon and ravines including in the of lowlands domain also indicates a better
developed karstic system.
Since the karsts systems are dependent on extrinsic and intrinsic factors (Sayago
et al. 2012), such variability in geomorphological development of the area can only be
explained by intrinsic variations, because extrinsic factors are equally active at the scale
of the study area, being homogeneously affected by climate and time of atmospheric
exposure. Thus, the northeastern region possibly differs because of lithologic and/or
structural variations that directly affect the solubility such as mineralogy, grain size,
porosity and permeability and the occurrence of discontinuities as fractures and bedding
planes.
Seeing that much of the evidence of endokarst features are concentrated in the
northeastern region, a more detailed analysis of this area is necessary. For this purpose,
35
the QR factorization gradient technique was used, enabling the extraction of geobodies
related to karst features. As a result, a three-dimensional distribution pattern of bright
spots was obtained (Figure 13)
It is important to note that the model does not reflect the complete geometry of
the karst system, but the main focus in isolated manner, characterized by caves and
collapse systems that occur within the sensitivity limits of seismic data and the applied
technique. So, is possible to realize that the amplitude anomalies are distributed
heterogeneously in the target sub volume.
The model analysis in plan superimposed by the horizon reveals at least 6
regions with a higher concentration of karst features, separated by undisturbed areas or
with the presence of isolated features (Figure 13 B). Region II stands out for presenting
at least twice the concentration of karst features than other regions. These features vary
in depth and are mostly related to the collapse of caves, thus possibly defining zone of
coalesced collapsed caves.
Figure 13: Analysis of the northeasernt region subvolume in (A) three-dimensional model of the distribution of bright spots related to karst features obtained with QR vertical gradient amplitude difference technique
and (B) plan visualization of the 3D model superimposed with the paleokarst horizon. Dotted áreas indicate regions with the highest concentration of karst features.
Finally, when analyzing the depth of the anomalies with respect to the horizon,
these are grouped into at least four distinct depth ranges (Figure 14). A first group of
features is found near the surface in up to 20 meters depth, followed by a second and
most numerous group whose occurrence ranges from 30 to 70m. These groups are
associated with the most identified sinkholes at the surface. The other features occur
between 100-140m and 160-180min depth, and are associated with deep caves with
variable degree of preservation.
According to Tian et al. (2015) caves tend to grow primarily in the run-off zone
which consists of a phreatic oscillation zone. Thus, changes in the regional base level
alternate different regions of caves development. In this way, the distribution of depths
into 4 main ranges should reflect then 4 main moments of phreatic level drawdown.
36
The most superficial caves possibly developed first, following the evolution of
the canyon. As the phreatic level falls and the canyon deepened, new development of
cave zones appeared with the reestablishment of the run-off zone. Finally, the canyon
reaches its maximum depth at approximately 200m to the horizon, and the creation of
the last group of caves near to this depth followed.
Figure 14: Depth (m) of the bright spots in relation to paleokarst horizon. Four main ranges of depth were identified, group 1 represent the oldest caves and group 5 the youngest. The purple line indicates the
maximum depth reached by the Canyon (Cmd).
CONCLUSION
This study aimed to conduct an integrated analysis concerning the paleokarst
system located in the Macaé Fm. by means of seismic interpretation. It was possible to
identify and describe features and processes concerning exokarst and endokarst domain.
The seismic horizon that corresponds to the top of the Macaé Fm. recorded the
karstification process, exhibiting a geomorphology carved out by a well-developed
hydric system and by processes related to endokarst dynamics. Two
geomorphologically distinct domains were identified, highlands corresponding to
rugged terrain with incised valleys, canyons, ravines, and lowlands characterized by a
smoother topography.
The study of fluviokarstic features indicates a specific hydric dynamics that lose
its erosive power southeastwards. This fact is indicated by the decrease in the
depth/width ratio. Valleys and canyons characterized in this study seem to have a strong
structural control, associated to a large number of faults that disappear when they reach
the horizon.
Similarly, closed, circular depressions were identified in the northeastern region,
spread throughout lowlands and highlands. These features studied in seismic section,
indicates the association with passages or small caves systems collapses. These features
are characterized by presenting supraestratal and intraestratal deformation and may be
defined as underlying collapse sinkholes, created after the burial of the karstic terrain.
37
In addition, amplitude anomalies defined as bright spots (SRB), dissociated from
the deformation context, were interpreted as non-collapsed caves. SRBs were identified
by proper attributes and techniques association, in order to characterize endokarst, as the
host of a diverse cave system, which presents great variety of diameters, shapes, and
spatial arrangements.
Coalesced collapsed-caves systems are located in the northeasternmost region.
These systems define the collapse of a great quantity of passages and affect areas up to
six times bigger than the isolated collapses.
Lastly, in order to understand the three-dimensional distribution of endokarstic
system the QR factorization gradient technique was used, which proved efficient and
enabled the identification of six regions with higher concentrations of karst features
distributed in at least four main depth ranges.
ACKNOWLEDGMENT
We would like to thank Statoil for financial support and for allowing us to
publish this study. We are grateful for the multiclient seismic data provided by PGS and
for the softwares Petrel, Opendtect and Transform. Sinochem is also acknowledged for
the permission of this publication.
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Considerações finais
A pesquisa de reservatórios carbonáticos envolve grande complexidade. Os
reservatórios carbonáticos são por natureza altamente heterogêneos e apresentam
feições geológicas abrangendo as mais diversas escalas. Neste sentido, a sísmica
tridimensional é uma ferramenta essencial para o entendimento de reservatórios,
permitindo inclusive o estudo de formações a grandes profundidades.
Este trabalho procurou por meio de dados sísmicos tridimensionais da Bacia de
Campos, sudeste do Brasil, apresentar um estudo detalhado do horizonte paleocárstico
correspondente ao topo da Fm. Macaé. Para tal são apresentados três artigos que
abrangem a caracterização geológica e gemorfológica do sistema paleocárstico, como
também as principais metodologias que foram desenvolvidas para atingir tal objetivo.
Por meio do trabalho “Geomorfologia Sísmica Tridimensional do Paleocarste da
Formação Macaé, Bacia de Campo, Brasil” foi possível a identificação de feições
remanescentes do processo de carstificação tanto em superfície quanto em
subsuperfície. Diferentes domínios geomorfológicos foram definidos e caracterizados,
permitindo o entendimento de que o processo de carstificação não agiu de forma
homogênea sobre a área de estudo, gerando sub-regiões onde as feições cárticas se
disseminam de forma mais intensa.
Contudo o estudo geomorfológico se mostrou altamente dependente da aplicação
de técnicas de processamento e atributos sísmicos e realçassem as feições alvo. O
trabalho “Uma Abordagem Rápida para a Identificação Não-Supervisionada de Feições
Cársticas Usando GPU” permitiu por meio da classificação não-supervisionada pelo
método SOM a identificação automática de feições, permitindo que tal tarefa levasse
consideravelmente menos tempo para ser realizada. De forma análoga o trabalho
“Identificação de Anomalias de Alta Amplitude pela Técnica de Gradiente por
Fatorização QR” possibilitou a extração automática de geobodies e o entendimento de
como se dá a distribuição espacial do sistema endocárstico.
Desta forma, os três artigos aqui apresentados compõem o estudo realizado no
Departamento de Engenharia do Petróleo da Faculdade de Engenharia Mecânica da
Unicamp, como parte dos requisitos para a obtenção do título de Mestre em Ciências e
Engenharia de Petróleo.
41
ANEXOS
42
Anexo A, Artigo 2: A Fast Approach for Unsupervised Karst Feature Identification
Using GPU
AFONSO, Luis Claudio Sugi1; BASSO, Mateus
1; KURODA, Michelle Chaves
1;
VIDAL, Alexandre Campane1
1Centro de Estudos do Petróleo (CEPETRO), Universidade Estadual de Campinas -
Unicamp, Campus Universitário Zeferino Vaz – Barão Geraldo, CEP 13083-970,
Campinas, SP, BR
Endereços eletrônicos: [email protected], [email protected],
43
ABSTRACT
Among the geological features, karst is the one that has received special attention in oil
and gas exploration for being a strong indicator of the potential existence of
hydrocarbon reservoirs. The integration of automatic pattern recognition methods and
GPU provides a powerful tool to help geological interpretation of seismic data. In order
to provide insightful information for interpreters, this work investigates the usage of
GPUs in addition to image segmentation by means of unsupervised classification for
identification of karst features in 3D seismic data. For this purpose, an implementation
of the robust Self-Organizing Maps for GPUs (SOM/GPU) is employed. A comparison
against a CPU-based SOM (SOM/CPU) is performed to assess the speeding-up
provided by GPU. Experiments have shown promising results for geological
interpretation using seismic data.
INTRODUCTION
At least 40% of the recoverable hydrocarbons are trapped in stratigraphic
unconformities such as the ones originated from karstification (Sayago, 2012). Among
the fields originated from karst, one can refer to the Lower Ordovician Puckett and the
Permian Yates in west Texas (Loucks, 1999), the Upper Devonian Grosmont Formation
in Alberta, Canada (Luo, 1994; Buschkuehle, 2007) and the Lower Ordovician Lunnan
field in the Tarim Basin of China (Zhao et al., 2014; Zhao et al., 2015).
The karstification process creates, in most cases, elements that are barely
continuous and with random spatial distribution in the seismic data. Also, they have
seismic responses that occur in subtle ways that can be easily misunderstood with other
geological features, seismic noise or simply not be noticed by the interpreter (Maoshan,
2011). In addition, the exploration to identify karst features is a time-consuming task
since it requires the analysis of huge volumetric seismic data. The volume of data can
have its size significantly increased if more information is added (i.e., computing
attributes) in order to help out the interpretation.
The requirements to solve this problem can be met by employing graphical
processing units (GPUs) that tackle both the problems of amount of data and computing
time by providing a low-cost device with parallel architecture that enables the
processing of high amounts of data simultaneously in a short time. Despite not having
been fully investigated (Jeong, 2006), this powerful resource has been largely employed
in a wide range of applications including simulations in geosciences research (Rubio et
al., 2014; Lacasta et al., 2015) and acceleration of calculations especially for reservoir
characterization (Liu, 2009; Komatitsch, 2010). In some applications, the GPU parallel
implementation reached high speed-up values (Tahmasebi, 2012; Cheng, 2013; Li et al.,
2014).
This work explores the usage of GPUs in the application of unsupervised karst
identification. The purpose of this study is to explore the programming challenges and
the potential benefits of embedded computing using commodity hardware components.
Due to the lack of well data from our study area and complexity of the seismic data, we
decided to apply an unsupervised classification approach using the Self-Organizing
44
Map algorithm, which has been the practice in a large number of different applications
(Chang, 2002; Ersoy, 2007; Kuroda, 2012; Mojarab, 2014).
OVERVIEW OF KARST FEATURES
Karst is described as a landscape that contains caves and extensive underground
water systems that develops on soluble rocks such as limestone, marble and gypsum
(Ford and Williams, 1989). Karst is formed from the subaerial exposure of carbonate
rocks, recognizable by features produced by dissolution, precipitation, erosion,
sedimentation and collapse (Esteban et al., 1992). It can also be the result of corrosion
caused by hydrothermal processes and differential CO2 regimes or fluids containing H2S
(Immenhauser and Rameil, 2011).
Near-surface karstification creates a terrain with distinct geomorphological and
geological elements (Figure A. 1). Well-developed drainage systems predominate in
karst terrains, having a high degree of connectivity with subsurface hydrology.
Common features found in karst terrains are deep canyons, large valleys, sinkholes,
channels, ravines, gullys and cave systems.
Figure A. 1: Block diagram of an epigenic karst terrain, including the main features observed in exokarstic,
epikarstic and endokarstic domains.
However, the most common surface features are sinkholes or dolines defined by
Waltham and Fookes (2005) as diagnostic karst elements formed by a closed circular
depression eroded around an internal drainage point into the underlying limestone.
These features mark the main relationship between surface geomorphology and the
subsurface and are usually generated by dissolution and collapse processes.
In addition, the flow rates and aggressiveness of the surface water will dictate
the construction of the underground karst, creating caves, channels, conduits, passages
and chambers. The burial compaction and diagenesis of this system will result in
paleocave system that is an important class of carbonate reservoirs (Loucks, 1999).
45
THE SELF-ORGANIZING MAP
The Self-Organizing Map (SOM) is inspired on the human brain in which each
region is responsible for a specific task (Kohonen, 1990). The main feature of SOM is
the competition of the output layer to be activated given an input sample. The
competition process results in a spatially organized “internal representation” of various
features of input signals and their abstractions, in which similar ones are located close to
each other (Haykin, 1999). The final representation is a two-dimensional topological
map composed of n×m cells (neurons) which are tuned to selectively respond to input
patterns. By doing the mapping of the input samples, SOM approximates the neurons’
weight vector to the input sample, and creates a topological map such that similar
samples will be located closer to each other in the map. This allows to visually identify
potential clusters and their number. The mapping is conducted in the same way as in a
supervised training.
The SOM learning process or pattern mapping process is divided into three
steps: competition, cooperation and adaptation. Let x be an input sample of dimension m
denoted as:
,
and a neuron j with synaptic weight vector w of size m represented as:
,
where n represents the total number of neurons.
In the competition process, neuron j is defined with the highest level of
similarity to the input sample x. This step can be summarized through Eq. A. 1, where
the similarity can be obtained by minimizing the Euclidean distance:
The result winner(x) is the index of the neuron in the map whose distance to the
input sample x is the smallest.
The cooperation process defines a topological neighborhood centered at the
winning neuron found through Eq. A. 1. The topological neighborhood reproduces the
evidence of lateral interaction among a set of neurons. It was also observed that the
strength of lateral interaction decays smoothly with lateral distance having its maximum
strength at the winning neuron. The features of this activity can be reproduced by a
Gaussian function:
in which the lateral distance can be defined through σ, and dj,i2 represents the distance
between the winning neuron i and excited neuron j. Also, the lateral interaction distance
σ decreases with time, which is given by:
46
in which σ0 is the value of σ at time 0, τ1 is a time constant, and n is a discrete time.
Thus, the topological neighborhood at time step t can be described as:
in which σ(t) is defined in (A. 3).
Finally, the adaptation process, performs the update of the neurons’ weight
vector based on Hebb’s postulate. The final weight vector update function can be
defined as:
in which wj(t+1) is the updated weight vector of neuron j at time t+1, hj,i(x) is defined in
(A. 3), and is a learning-rate parameter that decreases with time according to:
in which η0 is the initial learning-rate value and τ2 is a time constant. Kohonen (1990)
further divides the adaptive process into two phases: ordering and convergence. In the
ordering phase the topological ordering of the neurons’ weight vectors takes place. The
convergence phase is related to tuning the neural network in order to provide an
accurate representation of the input samples.
GRAPHICAL HARDWARE UNIT (GPU) AND CUDA
The Compute Unified Device Architecture (CUDA) is a platform created by
NVIDIA that enables general-purpose applications to use the power of a graphic
processing unit that provides huge increase in computing performance. Applications
using CUDA go from bioinformatics (McArt, 2013), computational chemistry
(Anthopoulos et al., 2013) to medical imaging (Shi et at. 2012), weather and climate
(Michalakes, 2008; Brown, 2015), including seismic analysis (Liu, 2009; Komatitsch,
2010).
GPUs were first designed as graphics accelerators but, in the late 1990s, their
usage for general-purpose applications had significantly increased especially by
research that took advantage of their great floating point performance. However,
developing such applications was really difficult even for those who had knowledge of
graphics programming languages such as OpenGL (2016). Later on, Ian Buck and his
research team from Stanford University developed the Brook compiler and runtime
system (Che, 2008), which upgraded GPU to a general-purpose processor in a high-
level language, making the programming task easier. Ian Buck and NVIDIA further
developed a solution that would enable to run C programs on GPU. In 2006, NVIDIA
released CUDA, in which hardware and software solutions were coupled (NVIDIA,
2010).
47
Figure A. 2 shows the memory architecture of a CUDA-enabled GPU. The terms
“host” and “device” refer to CPU and GPU, respectively. The data to be processed can
be stored in the “global memory”, which can be accessed by any GPU thread or in the
“local memory” where data access is restricted to a few GPU threads. Threads are the
units that execute kernels that are functions written for CUDA. Threads are organized in
blocks and are identified by a unique identification given by its position in the block and
the identification of its block. Blocks can assume up to 3D-dimension format and have a
group of threads given by their dimension. A block of size 3 x 3 x 3 will have 9 threads.
Figure A. 2: Memory architecture in a CUDA-enabled GPU (Extracted from Kirk and Hwu, 2010).
GPU PARALLEL IMPLEMENTATION
The GPU parallel implementation used in the experiments relies on the Somoclu
(Peter, 2015), which is implemented over Thrust (NVIDIA, 2016), that is a C++
template library for CUDA applications. Some operations using vectors and matrices
are performed using the cuBLAS (NVIDIA, 2016A), which is an implementation of
BLAS (Basic Linear Algebra Subprograms) on top of the CUDA. The program can still
make use of the Message Passing Interface (MPI) (Open-MPI, 2016), that is a
communication protocol used for parallel applications. The memory organization used
by the Somoclu follows the values presented in the Table A. 1, where SomX is the
dimension in x, SomY is the dimension in y and BLOCK_DIM is the block size:
Table A. 1: Structure dimensions used in the application.
Dimension
Grid size
Block size 32 x 1 x 1
48
# threads 32 x 1 x 1
The parallelization in the SOM algorithm is used in the tasks that compute the
best match and neuron weight vector update, defined by Eq. A. 1 and A. 4, respectively.
In the first case, it is clear that finding the distance between a sample xi and a neuron jn
is independent from finding the distance between a sample xk to the same neuron jn, for
instance. Therefore, this task is parallelized in such a way that multiple calculations can
be done simultaneously by a defined number of threads.
The neuron weight vector update in Somoclu is performed in the end of an
epoch. During an epoch, each allocated thread computes the result for Eq. A. 4, stores
the result in its local variable and awaits for the other threads to finish it. Once all
threads have finished their job, their local results are all summed up and the neuron map
is updated. In this task, it is necessary that all threads have their job finished to keep the
final result consistent.
METHODOLOGY
The experiments are conducted following the workflow depicted in Figure A. 3.
The first step computes a set of five attributes from the amplitude seismic data which
will describe each sample x as x = {x1, x2, x3, x4, x5}, where xi is an attribute. A sample s
represents a point from the seismic data defined by a unique set of inline, cross-line and
depth values. The set of attributes is comprised of:
- Most positive (Figure A. 4a) and most negative curvature (Figure A. 4b): the curvature
measures the deformation of a surface at a point. The larger the deformation, the larger
the curvature will be. The curvature value is positive if the feature is anticlinal, and
negative if it is synclinal (Chopra and Marfurt, 2007).
- Second derivative of the amplitude (Figure A. 4c): the amplitude second derivative
provides a measure of the sharpness of the amplitude peak. This attribute is an effective
discriminator for bright spots, sequence boundaries, major changes in depositional
environment, lithologic variations, etc. (Subrahmanyam and Rao, 2008).
- Envelope-weighted frequency (Figure A. 4d): it is the instantaneous frequency
weighted by the envelope over a given time window. This attribute can be used for
hydrocarbon indicator by low frequency anomaly, fracture zone indicator, bed
thickness, etc. (OpendTect, 2002).
- Isopach (Figure A. 4e): this attribute gives the variation of lateral thickness of a bed,
formation or stratigraphic interval. It highlights characteristics of a basin, such as
location of buried ridges, position of shorelines, etc. (Maltman, 2000).
49
Figure A. 3: Main workflow.
Figure A. 4: The set of five attributes shown at the Macaé top: (a) most positive and (b) most negative
curvatures, (c) amplitude second derivative, (d) envelope-weighted frequency and (e) isopach map.
Due to the amount of samples and calculations, the second step takes advantage
of the powerful processing capability of the GPU to speed-up the unsupervised learning
of the multi-attribute seismic data generated in the previous step. The unsupervised
learning will map the seismic data into a 2D topological map by means of the SOM
algorithm using both CPU and GPU implementations for performance comparison
purposes. The parameters used in both SOM implementations are listed in Table A. 2.
50
Except for the neuron map size that was chosen empirically, the remaining parameters
are the default values in the Somoclu library.
Table A. 2: Parameters used to setup the SOM algorithm.
The GPU implementation still has some additional parameters as listed in Table A.
3, which were set according to the computing environment settings. The computing
environment used in the experiments is composed of 6 nodes, where each node has the
following configuration:
- 2 Intel Xeon Processor X5570 of 2.93 GHz – 8 cores / 16 threads.
- 24 GB of RAM memory.
- 2 Nvidia Tesla M2050 graphic cards – 3 GB GDDR5 of dedicated memory, 1.55
GHz of memory speed and 148 GB/sec of memory bandwidth.
Table A. 3: Additional parameters for the parallel implementation.
As displayed in Table 3, the experiment itself makes use of only one node.
The resulting neuron map should preserve some topological distribution and
shows clusters that can be visualized through the U-matrix that depicts the distance
between a neuron and its neighbors. In unsupervised classification, the neurons have no
label assigned since the input data is unlabeled. Typically, a clustering algorithm is
applied in order to partition the neuron map into k clusters and associate a label l to each
cluster cl, where l = {1, .., k}. In our application, we applied the K-means algorithm to
create 2 clusters (karst and non-karst features).
Giving the labeled neuron map, the classification is performed by assigning the
label of the best matching neuron to the input sample. In summary, the best matching
neuron is obtained by finding the most similar neuron to the input sample (i.e.,
Euclidean distance). As in the unsupervised learning, this step is also conducted in
GPU, where the multiple GPU threads will compute simultaneously the best matching
neuron for the entire dataset.
Parameter Value
Neuron map size 20x20 Neuron map type planar
η0 0.1 ηn 0.01
Neighborhood function Gaussian Epochs 100
Initial radius 10 Final radius 1
Learning rate cooling strategy linear Radius cooling strategy linear
Parameter Value
# nodes 1 # processes per node 16
51
CASE OF STUDY: MACAÉ FORMATION
The dataset comprises the seismic data of the top of the Macaé Formation, which
corresponds to Albian carbonates. The selected study area is located in the southern area
of the Campos Basin in Brazil, which is approximately 500 km² of area, 14.6 km long
(SW-NE) and 34 km wide (NW-SE). Each bin represents a section of 12.5 x 18.75 m2 in
size, sampled of 4 ms and record length of 5 s. The seismic traces are characterized by
1,250 samples, frequency spectrum ranging from 0 to 125 Hz and 35 Hz as dominant
frequency. The working volume has a size of 2.8 GB.
The top of the study area (Figure A. 5) is mostly characterized by closed circular
depressions interpreted as sinkholes (pink arrows), a wide and sinuous canyon (red
arrow), and less developed erosive features classified as ravines (green arrows), which
comprise the features of interest to be identified in the experiment.
Figure A. 5: Top of the Macaé formation and some of the identified geological features in the amplitude
data: ravines (green arrows), a wide and sinuous canyon (red arrow) and sinkholes (pink arrows).
EXPERIMENTS AND DISCUSSION
The U-matrix resulting from the unsupervised learning is shown in Figure A. 6a.
Figures A. 6b to 6f depict the distribution of the weight values in the neuron map
respective to each attribute. As mentioned before, the application is treated as a binary
classification problem where samples will be either karst or non-karst features. Given
that, the clustering and labeling of the neuron map through the K-means algorithm
results in the partitioned map depicted in Figure A. 6g. There, neurons are labeled as
class 1 (red) or class 2 (class).
52
Figure A. 6: Maps of distribution: (a) U-matrix, (b) ampltiude second derivative, (c) most negative and (d)
most positive curvature, (e) envelope weighted frequency, (f) isopach distribution maps, and (g) labeled
neuron map.
The classification using the best matching approach gives the result shown in
Figure A. 7. There, we have that class 1 represents the non-karst features and class 2
represents the features of interest. Figure A. 8 shows in detail some of the mapped
features in the final result.
53
Figure A. 7: Classification result showing in red several geomorphologic features on the Macaé seismic horizon
Figure A. 8: Classification result in details. (a) ravines (green arrows) and sinkholes (pink arrows), and (b)
canyon (red arrow).
The delimitation of elements provided by the extraction of class 2 facilitates the
process of geological interpretation of a paleohorizon. Examining Figure A. 8a, at least
7 sinkholes (pink arrows) can be easily identified and analyzed under a morphometric
point of view, having diameters between 70 and 600 m, and depths from 5 to 60 m. In
addition, two well-developed ravines (green arrows) show rectilinear pattern and low
continuity. These features end in sinkholes, defining connection points between the
surface and subsurface hydrology. Class 2 also shows the occurrence of a canyon,
highlighting its sinuous pattern (Figure A. 8b). This feature has steep sided walls
indicating a preferably vertical development vector. Also, the high symmetry of the
canyon edges becomes evident. The canyon has dimensions ten times greater than the
ravines with average width and depth of 1,200 and 100 meters, respectively.
Under the computational point of view, the application successfully dealt with
the large volume of seismic data, being capable of working with the entire data at once
in all steps of the workflow. Regarding the computing time performance, the usage of
GPU provided a huge speedup reaching a gain of almost 39 times compared to the CPU
implementation (Table A. 4). The computing time comprises the time of mapping the
seismic data, clustering the neuron map, and classification.
54
Table A. 4: Computing time comparison
Algorithm Computing time (hours) Speed-up
SOM/CPU 90.39 1.00
SOM/GPU 2.33 38.80
The gain comes from changes made in how the best matching neuron is
computed in both training and classification phases, and in the neuron weight vector
update. In a non-parallel code, the distance from each input sample x to each neuron j in
the map is computed one by one. In the GPU implementation, the same distance can be
computed for all neurons at the same time. This is possible because multiple threads are
allocated and each is responsible for the computing of one distance.
CONCLUSION
The properties of the karst features contained in seismic data make the task of
karst identification a very difficult one. Additionally, the great amount of volumetric
data that has to be analyzed makes the interpretation very time-consuming.
Nowadays, applications need to provide useful information in the shortest time
possible. GPU comes as a low-cost option to tackle the problems of volume of data and
processing time through its parallel architecture. Allied with this powerful tool, we may
add pattern recognition methods that can retrieve insightful information in situations
such as the application presented in this paper.
This work explored the potential of GPUs in an application that usually requires
high computational resources and achieved promising results. Considering the
geological results, the application was able to successfully identify the features of
interest on the top of our study area. The computing performance has also achieved
satisfactory and important results. The application successfully processed the entire
dataset in any step, and achieved a huge speed-up against a CPU implementation.
ACKNOWLEDGMENT
We would like to thank Statoil for financial support and for allowing us to
publish this study. We are grateful for the multiclient seismic data provided by PGS.
Sinochem is also acknowledged for the permission of this publication. The authors
thank the National Center for High Performance Computing (CENAPAD/SP – Brazil)
for providing the resources used in the experiments. We also thank both OpendTect and
Petrel for the software used in this work.
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Anexo B, Artigo 3: High amplitude anomalies identification by QR factorization
gradient technique
KURODA Michelle1; BASSO, Mateus
1; CORREIA, Ulisses; AFONSO, Luís Claudio
Sugi; VIDAL, Alexandre Campane1
1Centro de Estudos do Petróleo (CEPETRO), Universidade Estadual de Campinas -
Unicamp, Campus Universitário Zeferino Vaz – Barão Geraldo, CEP 13083-970,
Campinas, SP, BR
Endereços eletrônicos: [email protected], [email protected],
59
ABSTRACT
The economic impact of seismic anomalies has arisen attention. In order to automatize
the interpretation in an assisted way, this work purposes the improvement of the usual
gradient difference technique calculated by LSF (least-squares fitting) through QR
factorization, a more robust mathematical tool to identify and highlight outliers or
anomalies. To illustrate the method, tests were applied for identification of karst
features and igneous intrusions in two areas of the Campos Basin, Brazil.
INTRODUCTION
High-amplitude anomalies in seismic data have been focus of research since the
early 1970s when they were associated with hydrocarbon traps and gas-filled sands
(Avseth et al. 2008). However, the experience shows that bright spots or high amplitude
anomalies can be false hydrocarbon indicators and be associated with many other
events: igneous intrusions and volcanic ash layers, karst features, sandstone cement
made of carbonate minerals, low porosity heterolithic sands, overpressured sands or
shales, wet sands, coal beds, and top of salt diapirs (Alves et al. 2015; Avseth et al.
2008; Cortez et al. 2016; Maoshan et al. 2011; Omosanya et al. 2016).
According to the wide range of possibilities associated with high-amplitude
anomalies and economic importance, the identification of these features and their
correct interpretation set important targets to be achieved. In this way, many methods
have been developed to highlight bright spots (Tian et al., 2016), among the most
relevant: neural networks (Sayago et al., 2012), energy gradients and spectral
decomposition (Chopra and Marfurt, 2007), magnetic resonance (Mazzili et al., 2016),
seismic velocity and waveform analysis (Xu et al, 2016), curvature analysis (Chopra
and Marfurt, 2008), and amplitude variety rate calculated by LSF (least-squares-fitting)
(Maoshan et al., 2011).
Maoshan et al. (2011) highlight that the main disadvantage of these methods is
the fact that they fail to eliminate noise. According to the authors, amplitude variety rate
has proven to lead to more accurate results.
Therefore, this paper presents a new method to identify amplitude anomalies
automatically by gradient difference analysis. The advantage of the proposed technique
is the possibility of extracting seismic bodies that cause high-amplitude anomalies
without the use of sophisticated volume-rendering and RGB blending methods.
For this purpose, the new vertical amplitude gradient difference technique
calculated by QR factorization is recommended. Applied to real seismic data from
Southern Brazil, the method can recognize amplitude anomaly patterns associated with
karst features and igneous intrusions.
As a second step of the method, the anomaly patterns identified automatically
are checked by an interpreter.
60
MATERIAL AND METHOD
Geologic Settings and Dataset
To evaluate the proposed technique, two areas of the Campos Basin, Southern
Brazil, were analyzed: one in the northeastern portion, which is characterized by karst
features and defined as polygon A, and the other in the southwestern region,
characterized by igneous intrusions and defined by polygon B (Fig. B. 1).
The Campos Basin developed on a continental platform and its tectono-
stratigraphic evolution is linked to the Gondwana breakup and rifting mechanism that
led to the opening of the South Atlantic Ocean (Guardado et al., 1989; Dias et al., 1990;
Riccomini et al., 2012). It started about 130 million years ago during the Cretaceous,
and evolved in association with the development of six megasequences (Horschuts and
Scuta, 1992; Cainelli and Mohriak, 1998; Mohriak et al., 2008).
The Macaé Formation correlates with the deposition of the shallow carbonatic
platform megasequence in the Albian-Cenomanian. The top of the Macaé Formation is
characterized by an unconformity with the Carapebus Formation, which corresponds to
a hiatus of 10 to 15 million years, possibly resulting from tectonic uplift. The subaerial
exposure of the carbonate deposits promoted extensive karstification, with the
development of erosional features and karst structures (Raunholm et al., 2014).
Magmatic events occurred after the deposition of the post-Aptian (post-salt)
sedimentary succession (Oreiro et al., 2008), by means of several pulses from the
Triassic to the Early Eocene (Thomaz Filho et al., 2008). Sills and dykes constitute the
intrusive bodies, and lava flows and volcanic mounds the extrusive bodies, identified at
several stratigraphic levels from the Albian to the Eocene (Oreiro et al., 2008). In
particular, the largest occurrence of high-amplitude intrusions in the Cabo Frio High is
characterized by the intercalation of volcaniclastic rocks and lower-impedance
sedimentary sequences (Oreiro et al., 2008).
The seismic data are characterized by blocks of 12.5 m x 18.5 m, recorded every
4 m, and vertical resolution of about 15 m, which allows the identification of karst
features and igneous intrusions.
Figure B. 1: Time slice showing the two study areas. In A, the polygon in which the high-amplitudes are predominantly associated with karst features, and in B, the polygon associated with igneous intrusions and
the sections used to illustrate the results.
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Vertical QR gradient technique
Derived from an image processing technique, the amplitude gradient difference
attribute is characterized as a structure attribute used to detect geobodies, from which
coherence, dip azimuth, curvature and texture can be calculated (Maoshan et al., 2011).
Maini and Aggarwal (2009) highlight several techniques used to detect edges, such as
Canny, Log, Robert, and Sobel. Maoshan et al. (2011) demonstrate that the directional
amplitude gradient difference technique leads to the best results, by means of the
identification of high-amplitude seismic anomalies, which can be associated with
irregular amplitude variety.
The premise used by Maoshan et al. (2011) to highlight seismic anomalies is
based on the application of the least square fitting method (LSF) traditionally used in
regression analysis. The method minimizes the sum of squared errors for every single
equation. The linear equation parameters are estimated from Eq. B. 1:
y = Ax + b (B.1)
in which A is the angular coefficient, x and y define the directions of the amplitudes
(vertical or horizontal), and b is the intercept. Finally, the amplitude-gradient is the
product of the intercept and the angular coefficient.
The LSF characteristic equation can be solved by different techniques, for
instance by the least-norm solution proposed by Maoshan et al. (2011).
The least-norm solution finds the solution for Ax = b by solving the following
normal equation:
ATAx=A
Tb, (B.2)
in which AT is the transposed matrix of A. If the matrix A is ill-conditioned, then the
method is not appropriated, because the condition number of ATA is the square of the
condition number of A. This means that it loses twice as many digits using normal
equation than other methods, and consequently becomes less accurate.
The proposed method LSF by QR factorization decomposes the matrix A, as
A = QR, (B.3)
in which Q is an orthogonal matrix, i.e., QTQ = I, and R is upper-triangular, non-
singular matrix, then RR-1
= I = R-1
R.
Applying Eq. B. 3 in Eq. B. 2 it leads:
(QR)T(QR)x=(QR)
Tb (B.4)
RTQ
TQRx = R
TQ
Tb (Q is orthogonal) (B.5)
RTRx = R
TQ
Tb (B.6)
x = (RTR)
-1R
TQ
Tb (B.7)
x = R-1
R-T
RTQ
Tb (R is nonsingular) (B.8)
x = R-1
QTb (B.9)
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Note the QR factorization transforms the linear LSF problem into a triangular
LSF (Eq. B. 9), which is faster and easier to be calculated than Eq. B. 2. Although the
calculation of Q and R matrixes can be time consuming, in practice, this method is more
accurate, numerical stable, and preferred than the calculation of the inversion matrix of
ATA of Eq. B. 2 (Golub and Reinsh, 1970).
QR factorization and LSF gradient difference techniques were tested for two
different window directions: vertical and horizontal. Their difference was also analyzed,
as suggested by Maoshan et al. (2011), and called final version. According to the
authors, the radiuses are defined by the size of the features. For karst highlighting, the
best radiuses were considered five samples in both directions, and for igneous
intrusions, four samples.
Seismic attributes
Many attributes can be used to highlight amplitude anomalies. Among them,
Alves et al. (2015) describe: average energy, envelope, variance, instantaneous phase,
and frequency.
In order to improve the emphasis of high amplitude, Maoshan et al. (2011)
suggest the application of Hilbert’s transform, from which the reflection strength is
extracted and the impact of wave peaks and troughs is also eliminated.
With caution, the seismic attributes can be combined to be used as input. As the
gradient act as a linear filter, the better the evidence of anomalies, the better the
algorithm result. For the applications shown in this paper, the better input was a
combination between energy and Hilbert, which better evidenced the desired anomalies.
APPLICATION AND RESULTS
Karst features
The identification of karst features is a great challenge in the characterization of
carbonate reservoirs, since they have high geological complexity. Features such as
sinkholes, caves, and collapsed cave systems often have subtle seismic responses that
are difficult to identify.
The high acoustic impedance contrast between the karst features and the host
rock, in addition to the small scale of these structures, creates seismic anomalies known
as bright spots. In this way, the seismic response of most of the karst features occurs as
the intercalation of 2 to 6 seismic points of maximum and minimum amplitude
vertically distributed.
To highlight karst features, LSF and QR factorization were performed using a
window of five samples and two directions, according to Maoshan et al. (2011). The
input of the technique was the Energy minus Hilbert transform. Although not visually
different, the anomalies are increased (Fig. B. 2).
63
Figure B. 2: a) Amplitude of section AA’, used to illustrate gradient results to highlight karsts. The attributes
calculated were: b) Hilbert’s Transform; c) Energy, and d) Input, the Energy minus Hilbert. The yellow circles
represent the karst feature highlighted in all figures.
The application of the LSF gradient to this seismic attribute does not reveal
advantages of the directions difference in the Macaé Formation seismic data. The results
show noise in both window directions in the final image (Fig. B. 3 d). The karst feature
is highlighted, as can be seen in more detail in Figs. B. 5 b and c, but the images contain
other information not related to seismic anomalies that the method was not able to filter.
Another important event, the Macaé top horizon, which is associated with an
amplitude anomaly, is also highlighted in western area of the section.
64
Figure B. 3: a) LSF results obtained for the Macaé Formation section. b) Horizontal LSF. c) Vertical LSF. d) Final LSF. The top of the Macaé Formation highlighted in a) is also well seen in other images. The
yellow circles represent the karst feature, highlighted in all figures, despite of the noise. After Maoshan et al. (2011).
QR factorization yields better results when it comes to karst features. Despite the
reflectivity of the Macaé top horizon, it is still strong, which is expected, once it is also
a seismic anomaly (Fig. B. 4). The karst features were better delimited and highlighted
in vertical radius. Homogenous areas, which display less noise than the LSF gradient,
are also seen (Fig. B. 5). Final QR leads to a high gradient value, which is not as well
evidenced as the result of Vertical QR, considered the best result of QR factorization
(Fig. B. 4 c).
65
Figure B. 4: (a) QR factorization results obtained for the Macaé Formation section. b) Horizontal QR. c) Vertical
QR. d) Final QR. The top of the Macaé Formation highlighted in a) is also well seen in other images, as
proposed by Maoshan et al (2011), but with less noise. The yellow circles represent the karst feature
highlighted in all figures.
As illustrated in Fig. B. 5, the contribution of the vertical window is the best. As
a final result, the QR factorization technique provided the assisted 3D identification of
karst features (Fig. B. 6) for the desired interval, after removing the Macaé top horizon.
66
Figure B. 5: Zoom of the karst features and regions without karst features. a) The original amplitude and
the associated karst feature and areas without karst features below. b) Vertical LSF. c) Final LSF. d) Vertical QR. Note the homogeneity and better karst delineation of the proposed QR factorization method in
d.
67
Figure B. 6: In blue, geobodies of karst features defined by QR factorization gradient difference technique,
after selecting the interval between the Macaé top and bottom horizons. For the correct imaging of the volume, the seismic anomaly associated with the Macaé top horizon was removed.
Igneous Intrusions
Seismic interpretation of igneous intrusions is generally applied to anomalies
defined by a strong amplitude contrast with a downward-increasing impedance, known
as hard-on-soft reflections with distinct geometric features concordant and discordant
from the surrounding rock (Alves et al., 2015; Planke et al., 2005).
Planform morphologies of intrusions are characterized by closed sub-circular to
sub-elliptical features, in which, in most of cases, saucer-shaped and transgressive sills
comprise a sub-horizontal to flat inner center forming the base, an inclined segment that
cross-cuts the stratigraphy upwards and a sub-horizontal outer rim ending at the sill tips
(Planke et al., 2005, Polteau et al., 2008). All types of intrusions have in common abrupt
terminations (Planke et al., 2005). However, the geometric shapes can vary depending
on the geological setting and the structural and stratigraphic framework that controls the
overall geometry of igneous intrusions (see Jackson et al., 2013 and Walker, 2016).
For igneous intrusion studies, the focus was given to the best gradient of both
techniques: vertical LSF and vertical QR. Using the same input used for karst
identification, but with a window of four samples, QR factorization achieved the best
68
results in highlighting the desired feature and filtering all the other reflections not
associated with amplitude anomaly (Fig. B. 7f). It is possible to see the LSF method
was not as efficient, showing a high correlation with the input seismic attribute (Fig. B.
7 d and e).
We associate the tabular high-amplitude anomalies to horizontal to sub-
horizontal igneous intrusions, known as sills, as they are comparable to seismic
anomalies with similar expressions described by some authors (Thomson and Hutton,
2004; Planke et al., 2005; Magee et al., 2015).
The highlighted intrusive body (Fig. B. 8), consisting of laterally restricted
seismic reflectors, has a sub-elliptical saucer-shaped geometry (Garlene et al., 2011)
similar to the slightly saucer-shaped sill of Planke et al. (2005). In addition, dominantly
layer-parallel shape is characterized by a thick inner sill with a convex-up morphology,
thinning towards the edges, on which short inclined sheets developed transgressing
upwards from the inner sill edge. In addition, it presents a bilateral symmetry. The
thickness of the inner sill might be associated with one of the phases of sill
emplacement described in Alves et al. (2015) and Walker et al., (2016). In turn, the
transgressing segments might be associated with the change in stress regimes and
properties of the surrounding rock, also described in Walker (2016).
69
Figure B. 7: a) Amplitude of section BB’, used to illustrate the gradient results to highlight igneous intrusions. b)
Hilbert’s transform. c) Energy. d) Input used for both methods. e) Vertical LSF. f) Vertical QR factorization. The
yellow box highlights the igneous intrusion. Note the benefit of applying the QR method, which could eliminate
most of the noise, evidencing the desired amplitude anomaly.
70
Figure B. 8: Final result of vertical QR factorization gradient applied to igneous intrusion in 3D identification. In
blue the seismic body of the highlighted igneous intrusion illustrated by Fig. B. 7 f.
CONCLUSIONS
The good Vertical QR result emphasizes the ability of the method to identify
seismic features associated with seismic anomaly features, helping the interpreter to
visualize and isolate them, even in 3D.
In this case, the final result (the combination of vertical and horizontal gradients)
was not advantageous for the identification of high-amplitude anomalies. It can be
associated with the structural inclination of the Macaé Formation, which does not allow
the repetition of the non-anomalous reflections in both directions, creating undesirable
noise.
As a common seismic attribute, the higher the geologic complexity in which the
anomalies are inserted, and the smaller the dimensions of the features to be highlighted,
the higher the intervention of the interpreter to evaluate the results given by the method.
Anyway, the new attribute can be used as a guide to interpret seismic anomalies, as
shown in this study by applying it to two different targets, karst features and igneous
intrusions of the Campos Basin.
The two major advantages of the proposed method are ability to filter and
computational velocity, once it is not necessary to apply it to two different directions
(horizontal and vertical), but only one (vertical). The better ability of the Vertical QR
factorization can be associated with the mathematical advantages of the method to the
detriment of LSF, which include primarily accuracy and stability.
Furthermore, the method has only one free parameter, the number of samples to
be set. In this paper, the best numbers were five and four, for karst features and
71
intrusions, respectively. Mathematically, a small number could invalidate the method,
and a much bigger one could limit its capacity to identify outliers.
ACKNOWLEDGEMENTS
We would like to thank Statoil for financial support and for allowing us to
publish this study. We are grateful for the multiclient seismic data provided by PGS.
Sinochem is also acknowledged for the permission of this publication. Rockdoc – Ikon,
Drilling Info – Transform, Schlumberger – Petrel, and Emerson – RMS are
acknowledged.
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