STRATIGRAPHIC CHARACTERIZATION OF RESERVOIRS THROUGH SEGMENTATION OF DIGITAL IMAGES OF WELL CORES FROM MACHINE LEARNING
Thesis dissertation to obtain the degree of: Geoscientist
By Juan Camilo Burgos Florez
Director Ph.D. Roderick Perez Altamar
Co director Ph.D. Jillian Pearse
UNIVERSIDAD DE LOS ANDES SCIENCE FACULTY GEOSCIENCE DEPARTMENT
Bogota, Colombia November 2018
______Jillian Pearse
______Roderick Perez Altamar
______Juan Camilo Burgos Florez
TABLE OF CONTENTS DEDICATION i
ACKNOWLEDGMENTS ii
ABSTRACT iii
RESUMEN iv
1. INTRODUCTION 1
2. TECTONIC FRAMEWORK, REGIONAL GEOLOGY AND
PETROLEUM GEOLOGY 3
2.1. Tectonic framework 3
2.2. Regional geology 5
2.2.1. La Luna formation 7
2.2.2. Cumbre formation 7
2.2.3. Umir formation 8
2.2.4. Paja formation 8
2.2.5. Tablazo formation 8
2.2.6. Simiti formation 9
2.2.7. Mugrosa formation 9
2.2.8. Cimarrona formation 9
2.3. Petroleum geology 10
3. METHODOLOGY 11
3.1. Cores description 11
3.1.1. Well X 11
3.1.2. Well Y 14
3.1.3. Well Z 16
3.2. Algorithm 21
3.2.1. Convolutional network 21
3.2.1.1. Convolution 21
3.2.1.2. Pooling 23
3.2.1.3. Flatten 24
3.2.1.4. Dropout 24
3.2.2. Classifier 25
3.2.3. Optimizer 26
3.2.4. Model 27
3.2.5. Training phase 29
3.2.5.1. Feedforward training 29
3.2.5.2. Backpropagation error 30
3.2.5.3. Weight adjustment 31
4. RESULTS 33
5. DISCUSSION 42
6. CONCLUSION 44
BIBLIOGRAPHY 45
INDEX OF FIGURES
Figure 1. Localization and boundaries of the studied area. 4
Figure 2. Generalized stratigraphic column of the Middle Magdalena Valley
Basin. 6
Figure 3. Location of the worked wells, well X, well Y and well Z. 11
Figure 4. Stratigraphy of well X with a gap between 4504 feet and 4299 feet. 13
Figure 5. Stratigraphy column of the well Y with a serie of gaps between 5788-
5814 feet, 5817-5861 feet,5864-5902 feet, 5904-6028 feet, 6033-6261 feet and
6262-7078 feet. 15
Figure 6.A Stratigraphy column of the well Z. 17
Figure 6.B Stratigraphy column of the well Z. 18
Figure 7.A. The matrix A represents the information of the input picture 5x5,
the matrix B represents the characteristics, in other words the kernel 3x3. 22
Figure 7.B. Graphic process of the convolution, where both matrices are
multiplied, and it is sum the results of each box. So, they are denominated
convolved feature. 22
Figure 8. General idea of max-pooling into an algorithm. 24
Figure 9. Internal structure of a multilayer model. 28
Figure 10. Example of backpropagation model. 29
Figure 11. Process of feedforward training. 30
Figure 12. Process of backpropagation error. 32
Figure 13. Process of weights adjustment. 33
Figure 14. Graph of loss value. Training phase in the first one and validation
phase in the second one. 34
Figure 15. Graphs of loss value in each loss component of the training phase. 35
Figure 16. Graphs of loss value in each loss component of the validation phase. 36
Figure 17. 0.1 feet of image of well cores segmented. Well X 37
Figure 18. Image segmentation of well core Sandstone and conglomerate
with hydrocarbons were identified. 37
Figure 19. Correlation of image segmentation of well core with the stratigraphic
column 38
Figure 20. 0.1 feet of image of well cores segmented. Well Y 39
Figure 21. Image segmentation of well core. Sandstone was identifying. 39
Figure 22. Correlation of image segmentation of well core with the stratigraphic
column 40
Figure 23. New well core image of a new well. 40
Figure 24. 0.1 feet of image of well cores segmented. New well 41
Figure 25. Image segmentation of well core. Sandstone was identified.
Figure 26. Stratigraphic correlation from electric register like the Spontaneous
Potential (SP) 42
INDEX OF EQUATIONS
Equation 1. Classifier 25
Equation 2. Optimizer 26
Equation 3. Backpropagation errors 31
i
DEDICATION
To God
For give me the strength and the knowledge to make this work and allow me
to overcome all the adversities. Honor and glory be to him. This work is thanks to
him.
To my family
For supporting me in all the process and to be present when I needed help. To
my mom because she is my inspiration to keep going and to my dad that advised me
in all the moments that I needed it. I love you both.
To my grandmother Herminda and my aunt Elda for always watching and
taking care of me. To my sisters Maria Paula, Letizia and Juanita, you are my reason
to continue and I hope to teach you that everything in life can be achieved with the
help of God. I love you.
ii
ACKNOWLEDGMENTS
I want to acknowledge all the institutions and people that contributed to this
work. Particularly to my directors Roderick Perez and Jillian Pearse to give me all
the advices and recommendations, also, to be present during the entire work.
Furthermore, to the Servicio Geologico Colombiano for supplying all the
information required to realize this work and giving all the support in my thesis with
tips, questions, help of geologists and petroleum engineers. Likewise, to I Oil and
Gas Summit for giving me the opportunity to expose my thesis as a poster and to
have the privilege to receive suggestions and recommendations of big companies,
geologist and petroleum engineers. Moreover, to Rigoberto Blandon for being part
of the process of obtaining information and Maria Paula Castañeda for helping me
with the written part.
Additionally, to my family because they are the inspiration to make this work.
All my friends, especially to David Angulo, Sebastian Duran, Felipe Uribe, Daniel
Diaz, Mateo Rueda, Nathalia Bernal, Valentina Blandon and Mariana Sanchez that
contributed in different moments of the process and supported me through difficult
times.
I appreciate you all very much and once again thanks for everything!
iii
ABSTRACT
The purpose of the present work is to generate an algorithm that allows an
automatic segmentation of images of well cores from machine learning. The
motivation for the use of this type of analysis is to look for an application of neural
networks in the petroleum industry, as a support tool for geologists that allows to
specify the descriptions of possible structures and patterns that are not identified by
the human eye.
Whence, it was used information of three wells of the Middle Magdalena
Valley Basin to know the lithologies and stratigraphic sequence to do a core
description. Then, they were recollected 1966 images of core with a size of 0.1 feet
to training the algorithm. So, 983 images were used to feed the training phase, and
the rest to feed the validation phase with the aim to realize a supervised training. The
final results were a training loss value of 1.0709 and a validation loss value of
1.0804, which shows that the images had a good segmentation but present some
mistakes that are product of different aspects that are mention in the discussion.
Thus, this research work will be divided into three parts: the first part will be
the description of the geological context of the study area and description of the
images of the cores. The second part will be the generation of codes and creation of
algorithms for the segmentation of the images. The third part, will be to prove the
algorithm for the segmentation of cores not used in the training and validation phase.
iv
RESUMEN
El propósito del presente trabajo es generar un algoritmo que permita una
segmentación automática de imágenes de núcleos de pozo mediante machine
learning. La motivación es buscar una aplicación de redes neuronales en la industria
del petróleo como una herramienta de apoyo para los geólogos que permita
especificar las descripciones de posibles estructuras y patrones que no se identifican.
Por lo tanto, se utilizó la información de tres pozos de la Cuenca del Valle del
Magdalena Medio para conocer la secuencia estratigráfica para su descripción.
Despues, se recolectaron 1966 imágenes de núcleo con un tamaño de 0.1 pies para
entrenar el algoritmo. De ahi, se utilizaron 983 imágenes para alimentar la fase de
entrenamiento, y el resto para alimentar la fase de validación. Los resultados finales
fueron un valor de pérdida de entrenamiento de 1.0709 y un valor de pérdida de
validación de 1.0804, que muestra que las imágenes tuvieron una buena
segmentación, pero presentan algunos errors en donde se analizaran en la discusión.
Por lo tanto, este trabajo de investigación se dividirá en tres partes: la primera
será la descripción del contexto geológico del área de estudio y la descripción de las
imágenes de los núcleos. La segunda parte será la generación de códigos y la
creación de algoritmos para la segmentación de las imágenes. La tercera parte, será
probar el algoritmo para la segmentación de núcleos no utilizados en la fase de
entrenamiento y validación.
1
I. INTRODUCTION
The present research work shows the new advances in machine learning and
neural networks in the image processing. Since, the main characteristic of this
process is that “it has been used in a wide range of fields, including in medical
diagnostics, stock exchange, robot control, transportation, aviation, heavy industries,
toys and games” (Hernández,2017). This technology is based on “how humans can
learn by simply observing the world and formulating consistent explanation”
(Zhengqi, 2018). Therefore, the purpose is to implement and to apply those concepts
in the stratigraphic characterizations of reservoirs through the use of core images
and establish their correlation with the stratigraphic column. Whence, in the image
analysis it is possible to detect characteristics and patterns that for the human eye are
harder to perceive.
Currently, there are tools of open code for the implementation of neural
networks such as Tensorflow, “a software library for high-performance numerical
calculation. Its flexible architecture allows for an easy implementation of
computing” (Tensorflow, 2018), and it can be complemented by other software
library as it is Keras. These tools will be used for the generation and calibration of
the model, and the model will be trained through the segmentation of images of well
cores within a supervised classification. Furthermore, it will be correlated with their
stratigraphic column because “the field of pattern recognition is concerned with the
2 automatic discovery of regularities in data through the use of computer algorithms
and with the use of these regularities to take actions such as classifying the data into
different categories” (Bishop, 2006).
In the same way, machine learning is an application of artificial intelligence
(AI) that provides systems the ability to automatically learn and improve from
experience without being explicitly programmed. Machine learning focuses on the
development of computer programs that can access data and use it learn for
themselves, whence, there exists many applications within different industries
(Varone,2018). For example, in medicine ML “predict prognosis empower
healthcare officials to allocate resources optimally and physicians to select better
treatment options for patients” (Guy and Chan, 2017), in biology in the
“understanding of brain functioning, obtaining models of the retina.” (Martínez,
2017), also in geoscience as climate informatics, earth and space informatics, study
of tectonics plates, study of the soils, among others. (Karpatne, 2017).
Therefore, the motivation for this kind of analysis is to search an application
for the neural networks in the oil industry as support tool to the geologists, and to
allow accurate description of lithology and sedimentary structures that are not easy
to detect by human eye. In that case if the available data is enough to train the
network, and the prediction rate is high, it is expected that the model could predict
the correct segmentation of new images of cores that are not included within the
3 phase of calibration and training. Hence, the dataset will be constructed with 88
images of cores where each picture will be cut in sizes of one inch, 50% of those
will be intended to the training phase and the other 50% will be destined to the testing
phase to prove the functionally of the model.
Regarding the ideas previously mentioned, this work is going to be divided in
three parts, the first part will be the description of the regional geology of the studied
area and the description of the images of cores, the second part will be the process
of how the algorithm was created for the image segmentation. Finally, the model
will implement new images to analyze and discuss the results like advantages and
disadvantages of the process of machine learning.
2. TECTONIC FRAMEWORK, REGIONAL GEOLOGY AND
PETROLEUM GEOLOGY
2.1 TECTONIC FRAMEWORK
The Colombian Andes are a composition of three major mountains structures
known as Eastern, Central and Western Cordilleras. The images of cores were
recollected in the Middle Magdalena Valley Basin (MMVB) between the Central
and Western Cordilleras (Lozano & Zamora, 2014)(Figure 1). Their boundaries are
to the north and south by the Espíritu Santo fault system and the Girardot foldbelt,
to the northeast is limited by the Bucaramanga-Santa Marta fault system and to the
southeast by the Bituima and La Salina fault systems, and the western limit is defined
4 by the westernmost onlap of the Neogene basin fill into the Serranía de San Lucas
and the Central Cordillera basement (Barrero, Pardo, Vargas, & Martínez, 2007).
Moreover, the MMVB is divided by the Cimitarra fault in the north of
Barrancabermeja and it is possible identify two regions known as MMV north and
MMV south in fact those areas are important for the hydrocarbon industry
(Sarmiento, Puentes, & Sierra, 2015). Due, they present a “compressive tectonics
with reverse and/or low angle faulting is restricted to the eastern portion” (Mojica
and Franco, 1990) and this characteristic stimulate the creation of traps to hold oil,
water and gas.
Figure 1. Localization and boundaries of the studied area. Taken from Lozano & Zamora (2014)
The MMVB was the result of the different tectonic processes as the lifting of
Central Cordillera and Western Cordillera starting from an intra arc evolution and
intra mountain evolution respectively (Lozano & Zamora, 2014). First, “the
5 opening that begun in the Mesozoic is characterized by efforts of course with
perpendicular extensional component, which produces a deformation in the
lithosphere and thinning in the crust, giving rise to the opening to the E of the
Cordillera Central” (Lozano & Zamora, 2014). Then, in the Cretaceous the continent
collided against the oceanic crust and produced a compressional stress, this fact
helped the lifting of the Central Cordillera and the creation of the mega forearc basin
(Lozano & Zamora, 2014)
In other hand, the Western Cordillera uprising was after the medium Miocene
with the reactivation and inversion of the normal faults of old extensional basins,
furthermore the exhumation in western flank of the cordillera was product of the
contractational deformation started 25 Ma ago (Caballero, Parra, & Mora, 2010).
Whence, the MMVB represents an asynchronous tectonic depression with two
different margins, in the occident a passive border and in the western a compressive
margin with a continuous deformation. (Mojica & Franco, 1990)
2.2 REGIONAL GEOLOGY
The description of the regional geology of the MMVB will be of the
unconventional petroleum system base on the primary exploration reservoirs as
Cenozoic continental, transitional clastic reservoirs and the Cretaceous source rock
because are the new targets for unconventional exploration and production (Spickert,
2014) their lithology is showed in the figure 2.
6
Figure 2. Generalized stratigraphic column of the Middle Magdalena Valley Basin.
Taken from Agencia Nacional De Hidrocarburos (2012)
7
2.2.1 La Luna Formation
This stratigraphic unit was subdivided in three members Salada, Pujamana
and Galembo (Sarmiento, Puentes, & Sierra, 2015). The geology of Salada member
are black mudstones, black shales, black calcareous claystone, concretions with
pyrite, and black limestone layers (Torres et.al.,2015). According to Spickert (2014),
the Pujamana member is composed of claystone, mudstone, gray shale, and chert.
The geology of Galembo member are calcareous shales with limestone layers and
nodules (Torres et.al.,2015). Furthermore, “the Galembo member generally contains
minor to trace amounts of carbonate (2,4%), in contrast, the Pujamana and Salada
members are carbonate-rich (43,2% and 40,4%)” (Quintero & Ríos, 2016)
2.2.2 Cumbre Formation
The geology of this unit are “a set of dark gray sandstones with intertwined
stratification, alternating with black pyrite shales, which emerge between Arcabuco
and Moniquira” (Pulido, Ulloa, & Rodriguez, 1986). So it is possible to identify
according to Spickert (2014) the change from continental deposition to shallow
marine deposition with a grain size of “claystone and greenish siltstones, quartz
sandstones, of medium grain and a calcareous level towards the base ” (Pulido,
Ulloa, & Rodriguez, 1986)
8
2.2.3 Umir Formation
This unit are composed by shales gray to black, carbonaceous, micaceous,
with ferruginous concretions and abundant intercalations towards the roof of lithic
sandstones, gray siltstones and the presence of exploitable carbon mantles.
(Sarmiento, Puentes, & Sierra, 2015). Particularly, base to ceiling sandstones have a
compositional increase in lithic components varying from sublitharenites to
lithoarethites (Sarmiento, Puentes, & Sierra, 2015) and their formation it is in the
upper Cretaceous (Spickert, 2014)
2.2.4 Paja Formation
It is composed by shales dark gray to blue, fossiliferous, laminated with
intercalations of fine grained yellowish gray sandstones or gray fossiliferous
limestones, locally sandy. (Sarmiento, Puentes, & Sierra, 2015). Furthermore, their
deposition took place in an open sea, epicenter-like environment with restricted
influence of terrestrial material. (Sarmiento, Puentes, & Sierra, 2015) and their
formation is in the Creataceous (Caballero, Parra, & Mora, 2010)
2.2.5 Tablazo Formation
Tablazo Formation is the uppermost unit in the basal calcareous group. It is
composed mostly of biomicrites, calcareous shales, and fossiliferous sandstones
(Spickert, 2014), and quartzites and siltstones of light color with a gravel size
(Caballero, Parra, & Mora, 2010). The age is estimated between “the upper Aptian
9 and the lower Albian, by comparison with the supra and infra-lying formations.”
(Sarmiento, Puentes, & Sierra, 2015)
2.2.6 Simiti Formation
The unit consists of shales carbonaceous, gray to black, laminated and soft,
locally calcareous with concretions commonly fossiliferous impregnated with oil
that form a thickness of 410m (Sarmiento, Puentes, & Sierra, 2015). Furthermore,
“It is estimated that 70% could be fissile claystones with flat parallel lamination,
forming sets of very thick layers. In the middle part there are intercalations of
calcareous sandstones with fossiliferous concretions and micritical layers towards
the ceiling.” (Sarmiento, Puentes, & Sierra, 2015)
2.2.7 Mugrosa Formation
The unit consists varicolored mudstones where reddish and yellow colors
predominate over gray tones. In these are interspersed in a much smaller proportion
layers of very coarse grain to conglomeratic sandstones, decreasing grain and with
moderate lateral continuity. Furthermore, the characteristics correspond to fluvial
systems of alluvial plains and meander rivers. (Sarmiento, Puentes, & Sierra, 2015)
2.2.8 Cimarrona Formation
The unit was divided into 4 Members units, The Fría, Level of Sandstones and
Shales, Zaragoza Member and Primavera Member where the lithology is
conglomerates of quartz, siliceous siltstone, cherts, feldspathic sandstones with
10 coarse grained, shales with intercalations of sandstones and siltstone. Furthermore,
the total thickness of the formation is 424 meters. (Melo, 1988)
2.3 PETROLEUM GEOLOGY
A century of exploration history in the basin has lead to the discovery of about
1,900 MMBO, 2.5 TCF and a total of 41 fields (Barrero, Pardo, Vargas, & Martínez,
2007). The source of the hydrocarbons comes from the total organic carbon (TOC)
values and the most important source rock is the Cretaceous limestones and shales
of the La Luna and the Simiti-Tablazo formations and their TOC are high (1-6%)
(Barrero, Pardo, Vargas, & Martínez, 2007). Furthermore, 97 % of the reservoirs
proceed from the “continental paleogene sandstones (Paleocene-Miocene), Lisama,
Esmeraldas-La Paz, and Colorado-Mugrosa formations, with average porosities 15-
20% and average permeability 20-600 md.” (Barrero, Pardo, Vargas, & Martínez,
2007)
11
3. METHODOLOGY
3.1 CORES DESCRIPTION
The cores used to feed the algorithm are belonging to three wells called well
X, well Y and well Z. While the well X presents 52 images of cores, the Y well
registers 26 images of cores, and the Z well shows 111 images of cores. In all cases
each image corresponds to one feet of core. The locations of the wells are showed in
the figure 3. The X and Y well belong at Mugrosa Formation and Z well to
Cimarrona Formation
Figure 3. Location of the worked wells, well X, well Y and well Z. Taken from Servicio
Geologico Colombiano (2018)
12
3.1.1 Well X
The well X is divided in two type of rock, metamorphic and sedimentary rocks
(Figure 4). The first section corresponds to fresh metamorphism as basement, and it
is a gray schist with white bands, biotitic with internal variations with probable areas
of gneiss with many and thick quartz veins. On the other hand, there are areas with
muddy sedimentary appearance or phyllite. Many ptygmatic folds are found locally
with “fluids” structures, and mostly present faults with hydrocarbon. (Servicio
Geologico Colombiano, 2018)
The second section are the sedimentary rocks where the base is a sandy
conglomerate in a supported matrix with pebbles up to 2 cm of schist and milky
quartz, towards the top are the conglomeratic sandstone and the greenish gray
sandstone due to alteration with moderate and bad selection impregnated of
hydrocarbons. Compositionally it is a sublitharenite with schist among 10% and
15%. Furthermore, in a depth of 4490 feet there is presence of sandy siltstone with
a color greenish gray and a mottle reddish yellow and dark red. The fraction of sand
oscillates between 30% and 40% with grains fine, sub-angulars and bad to moderate
sphericity. In some areas there is a transition to muddy sand with pebbles up to 4 or
5 mm of milky quartz (Servicio Geologico Colombiano, 2018)
Likewise, in a depth of 4489 feet the base is a sandy conglomerate with
supported matrix, schist pebbles, milky quartz and large muddy intraclasts. In the
13 top part it exists a transition to muddy sandstone with good to moderate selection,
grains sub-rounded to sub-angulars and good to moderate sphericity.
Figure 4. Stratigraphy of well X with a gap between 4504 feet and 4299 feet. Taken from
Servicio Geologico Colombiano (2018)
14
Compositionally it is a lithic sandstone with schists between 20% to 25%, high
bioturbation and traces of muscovite (Servicio Geologico Colombiano, 2018).
The depositional environment begun with a floodplain from of a river
depositing small grain size as sandy siltstone. Then, the flow of the river returned to
be normal and it begun to transport and to deposit big sediments that resulted in
rocks in facies of bioturbated massive sandstones, conglomeratic sandstones and
conglomerate with supported matrix (Servicio Geologico Colombiano, 2018). After
that, the environment was a floodpain again and deposited small sediments generated
siltstones. However, there was a crevasse complex depositing sandstones, and just
after, occurred an event that formed a floodplain that deposited many sediments to
generate a sandy siltstone. Finally, the environment was a river with high energy,
but as time passed the energy decreased resulting in a grain decreasing sequence.
3.1.2 Well Y
The stratigraphy of the well Y (Figure 5) starts with a feldespatic sandstone
yellowish gray, sub-angular and sub-rounded with a good selection, moderately hard
and it presents traces of muscovite and biotite <1%. Then, in a depth between 6259
and 6262 feet there is feldespatics sand, light olive gray, sub-angular and sub-
rounded with a moderate selection and traces of muscovite. Furthermore, an
arcosalitic, light olive gray colored with a composition of 70% quartz, 20%
15 feldespar, 10% lithic, sub-angular with a moderate selection, presence of bioturbation and cross stratification in tundish.
Figure 5. Stratigraphy column of the well Y with a serie of gaps between 5788-5814 feet, 5817-
5861 feet,5864-5902 feet, 5904-6028 feet, 6033-6261 feet and 6262-7078 feet. Taken from
Servicio Geologico Colombiano (2018)
16
In a depth of 6030 feet there is a feldespatic sandstone with a composition of
70% quartz, 15% lithic and 15% feldspar and it is slightly calcareous, yellowish
gray, sub-angular with moderate selection. (Servicio Geologico Colombiano, 2018).
At the depth of 5903 feet, it presents a lithic feldespatic sandstone slightly calcareous
with a yellowish gray color to light olive gray, sub-angular, moderate selection and
differential cementation, the sedimentary structures are bioturbation and cross
stratification. At the top, there is feldespatic sandstone with poor to moderate
selection, a feldespatic sandstone slightly calcareous with composition of quartz
70%, feldspar 20% and lithic 10%, sub-angular and sub-rounded with good selection
and presence of muscovite. (Servicio Geologico Colombiano, 2018)
The deposition environmental of all stratigraphy column was fluvial due to
good a moderate selection of the grains, the presences of bioturbation, traces of
muscovites and biotite, yellow and gray color characteristics of river environment
and the same lithology during almost 35 feet.
3.1.3 Well Z
The well Z (Figure 6.A and 6.B) begins with clay and sandy siltstone, slightly
calcareous with a gray color and moderate bioturbation. Also, it presents thin
intercalations of very fine quartz sandstones with an intense bioturbation. It is
possible to identify trace of pyrite and glauconite (<1%), parallel lamination
predominant, locally waved ripple with ichnofacies of Cruziana. 30 feet closer to the
17 surface it is possible to find very fine quartz sandstones gray, slightly muddy and
calcareous, with relicts of parallel lamination and remains of shell. (Servicio
Geologico Colombiano, 2018).
Figure 6.A Stratigraphy column of the well Z. Taken from Servicio Geologico Colombiano
(2018)
18
Figure 6.B Stratigraphy column of the well Z. Taken from Servicio Geologico Colombiano
(2018)
19
At a depth of 6992 feet there is gray claystones and siltstones slightly
calcareous, with traces of glauconite and pyrite (<1%), intensely bioturbated but
with relicts of parallel lamination and presence of ichnofacies of Cruziana. In a depth
of 6980 there is presence of very fine sandstone and quartz siltstones some muddy
and gray calcareous, intense bioturbation, ichnofacies of Cruziana, less of 1% of
glauconite in the top of the layer and rounded quartz pebbles. After that, there is
muddy, very fine, gray siltstones and quartz sandstones, slightly calcareous intensely
bioturbated, the lower contact is bioturbated and there is presence of ichnofacies
type Cruziana and Glossifungites. Likewise, some feet up there is presence of sandy
conglomerate supported calcareous matrix with many benthic foraminifera and
sporadic planktonic, intense bioturbation, lower contact bioturbated and ichnofacies
type Glossifungites. (Servicio Geologico Colombiano, 2018)
On the other hand, in a depth of 6954 feet there is gray siltstone, dark gray
claystones and sandstone quartz very fine slightly calcareous, low bioturbation, and
in the middle part there is siderite nodules with intervals of glauconite traces.
Moreover, there is presence of oligomitic sandy conglomerates, supported
calcareous matrix and muddy sandstone of quartz with a moderate bioturbate,
parallel and ripples lamination with a ichnofacies of Cruziana. Then, at the depth of
6932 feet, there is gray siltstone with thin intercalations of light gray very fine quartz
sandstones. In the low middle, bioturbation is intense while at the top it is low.
20
Moreover, there are traces of glauconite and pyrite <1%. After that, there is a
oligomitic conglomerate, clast supported in the base and supported matrix towards
the roof, olive gray colored, massive for bioturbation, many benthonic foraminifera
and sporadic planktonic, the matrix is very fine with traces of glauconite and pyrite.
At the top in a depth of 6922 feet, there is olive gray colored foraminifera grainstone,
with sand sheets as fine as muddy, few planktonic foraminifera, very rounded
pebbles of quartz smaller than 1 cm, traces of glauconite and pyrite less than 1% and
presence of faults that are stuffed of calcite and hydrocarbons. (Servicio Geologico
Colombiano, 2018)
The environmental deposition was coastal and it begun in the shoreface where
the fine grain size was deposited due to the fact that there was presence of ichnofacie
as skolithos. Afterwards, the tide went up and deposited grain size silts, generating
wave ripples, that lasted a long time because the lithology is 27 feet thick, if it is
inferred that the gaps between the depth of 7003 and 7029 feet are the same
lithology. Then, the tide went down and it deposited fine and very fine grain size and
this loop lasted a long time due to the presence of a sequence of sandstone and
siltstone. But, at the depth of 6958 feet there is presence of sandy conglomerate
whence their deposition was in a beach zone and then the tide loop begun again
generating a sequence of sandstone and siltstone. At the top of the stratigraphy
column, it is possible to find a sequence of conglomerate and grainstone as a result
21 of the depositional environment which was in a distal beach, and then the tide went
up in turbulent conditions to generate a grainstone with calcite filled fractures.
(Servicio Geologico Colombiano, 2018)
3.2 ALGORITHM
3.2.1 Convolutional network
The main purpose of the convolutional networks is to reduce the
computational weight when the algorithm is working with arrays of any image.
However, when the arrays contain a lot of information or are too big, the process of
the algorithm and the computational performance could slow down. Consequently,
the convolutional network extracts the most significant characteristics of an image
in order to decrease the matrices of characteristics (Martínez, 2017). Moreover, “the
outputs of the convolutional units form the inputs to the subsampling layer of the
network” (Bishop, 2006)
3.2.1.1 Convolution
Convolution process is the main step within a neural network, the purpose of
this layer in the network is to extract the characteristic of an input image because
each picture is an array (Martínez, 2017). The main idea is to have two arrays or
matrices, where one contains the information of the image and the other is the kernel
or filter that contains the characteristics of interest. So, the process behind the
convolution is to move the kernel upon the image matrix with a jump of one pixel.
22
In each position, the multiplication between the two matrices is calculated and the
results are added to obtain an integer as shown in figure 7.A and 7.B (Martínez,
2017). Moreover, it is important to mention that depending of the values of the
kernel, the algorithm will follow different aspects or patterns into the picture, and
the number of filters depend on the number of characteristics of interest. Principally,
the characteristics are determinated with the value of the pixel in the case of the
figure 7.A the regions of interest are the ones with a number one.
7.A.1 7.A.2
Figure 7.A. The matrix A represents the information of the input picture 5x5, the matrix B
represents the characteristics, in other words the kernel 3x3. Taken from Martínez (2017)
Figure 7.B. Graphic process of the convolution,
where both matrices are multiplied , and it is
sum the results of each box. So, they are
denominated convolved feature. Taken from
Martínez (2017).
23
3.2.1.2 Pooling
The purpose of this layer is to reduce the dimensions of the image while
holding the important information. Some examples of pooling are max-pooling,
average-pooling, sum-pooling among others. (Martínez, 2017). Similarly to the
convolution, the pooling extracts the most important characteristic of the image
reducing its size, depending only on the relative spatial coordinates (Shelhamer,
Long, & Darrell, 2016), in other words, pooling depends on the move of a certain
window. This window checks the values of the image and depending on the type of
pooling it extracts the characteristics. As result, the pooling “converts smaller and
more manageable input representations, reduces the number of parameters and
calculations in the network. Therefore, controls overfitting, makes the network
invariant to small transformations, distortions and translations in the image of entry”
(Martínez, 2017)
In this work, the algorithm of the convolutional network is the max pooling.
First, a window or neighborhood is defined, and the elements or high values of the
matrix image are taken. Then, the window does move to a next zone to take a new
high element, this process lasts until the image array is finished (Figure 8) (Martínez,
2017)
24
3.2.1.3 Flatten
In general, the flatten layer is used at the end of the neural network because its
purpose is to compress the final information of the picture after going through a
series of convolutional and max pooling layers. For example, at the end of the
process, the final image is too small for the convolutional and max pooling layers
but it is too deep for other filters along the process. As a result, the flatten layer
reduces all the layers or information of them in a single layer.
Figure 8. General idea
of max-pooling into an
algorithm. Taken from
Martínez (2017) .
3.2.1.4 Dropout
The dropout layer usually is the last layer of the neural networks before the
final result, because its function is to configure the number of neurons that will learn.
If the algorithm used all neurons between layers, the neural network will just learn
one way to recognize patterns and its learning rate will be low. On the other hand, if
25 it randomly it uses a determined amount of neurons, the system will learn many
possibilities to detect different patterns of the image, and the probability of neural
network learning better will increase.
3.2.2 Classifier
In the machine learning there exists many classifiers that are regressions, and
each regression depends on the purpose of the neural network. In this case, the
classifier is the softmax regression or normalized exponential (Bishop, 2006). The
softmax regression belongs to the exponential family and it is an expansion of the
logistic function (Martínez, 2017). Thus, its based on the classification of objects
into two or more families or classes.
The purpose of the softmax regression is to estimate the probability � (� =
�|�) for each value �=(1, 2,…,K). As a consequence, a vector K-dimensional is
obtained when the sum of all the probabilities of each class is equal to 1
(Martínez, 2017). The expression of softmax function derivatives of the
multinomial distribution in the equation 1 (shown below).
Equation 1. Taken from Bishop (2006)
However, when used the softmax regression, it is necessary to calculate the
function of cost that indicates if the neural networks train properly. Basically, a
26 function of cost is “a measure of how wrong the model is in terms of its ability to
estimate the relationship between X and y.” (McDonald, 2017) and the main idea is
to reduce the cost function to zero. Theoretically, the learning rate is inversely
proportional to cost function whereby its expected that while the neural networks
learn to increase the learning rate, the cost function tends to cero.
3.2.3 Optimizer
The optimizer is the function that regulates the weights between layers in each
iteration. In the present work, the optimizer is the Stochastic Gradient Descent(SGD)
or also known as sequential gradient descent. This optimizer works with a little
training data and based on that, reduces the cost function. If the cost function
comprises a sum over data points E= ΣnEn , then, after presenting pattern n, the
stochastic gradient descent algorithm updates the w vector parameter using the
equation 2 (Bishop, 2006).
Equation 2. Where τ denotes the iteration number, and η is a learning rate parameter.
Taken from Bishop (2006)
Moreover, the SGD purpose is to work with little data, because it helps to
“reduce the variance in the update of the parameters and this allows a more stable
convergence, allowing the use of linear algebra for the efficient calculation of cost
and gradient” (Martínez, 2017). It is important to take into account that in SGD the
27 way in which data is presented to the algorithm will affect its performance, since, if
in neural network “if data are presented in any order, this can introduce an offset in
the gradient and lead to a poorer convergence” (Martínez, 2017). As a consequence,
the neural network will not learn properly and give wrong results.
3.2.4 Model
In general, the algorithm consists of a multilayer model that contains an input
layer and output layer. Also, there exists one or more intermediate hidden layers that
receive the name of hidden neurons (Figure 9) (Hernández, 2017). In this context,
the specific visual model is the Fully Convolutional Network (FCN) that is a deep
learning. It consists of a multilayer model that has been used to create different
networks to classify, to segment images, to detect objects and a semantic
segmentation. Besides, the general idea of the model is to take all pixels, in which
each pixel is labeled with the class of its enclosing object or region. Some examples
of this model are Vgg16, Vgg19, Resnet50, among others. The differences are the
pixel accuracy and the learning rate of the model.
The Fully Convolutional Network used in this work is Vgg16 model. Their
structure is based on six blocks, the first two blocks contain 3 layers, the third and
fourth blocks are 4 layers, then, block number five has 8 layers and finally, the sixth
block consists of 4 layers. Furthermore, between each layer it can be found a scalar
number that configures the next layers. In general, the majority of blocks are
28 composed by two essential layers, convolutional layer and maxpooling layer.
Moreover, each block can have two convolutional layers or more, with the purpose
of extracting the features of the image that will be an array with more accuracy.
Afterwards, the last block contains a flatten and dropout layers with a softmax
regression as the activation function that prepares the final image to be shown.
Figure 9. Internal structure of a multilayer model. Taken from Hernández (2017)
Likewise, within the above structure there also exists two fundamental
structures: (i) the Faster-RCNN (Faster Region based Convolutional Neural
Network) and (ii) Mask-RCNN (Mask Region Convolutional Neural Network). The
first one has two stages where it begins with the Region Proposal Network (RPN)
and it function is to provide a candidate object framing it with boxes. Then, the
following stage is the classification and framing box regression in two different
steps. Mask-RCNN presents the same structure mentioned before. The RPN and the
classification and framing box regression, but in this case the last step is executed
29 simultaneously. Furthermore, Mask has other characteristics, such as the
segmentation of each class. (He, Gkioxari, Dollár, & Girshick, 2018)
3.2.5 Training phase
The training phase is the most important step in the neural network because in
this part the network will learn all the characteristics of the data. From this
perspective, the training model is the backpropagation and its objective is that “the
errors of the units of the hidden layers are determined by backpropagation of errors
of the units of the output layer.” (Hernández, 2017). So, the structure of the
backpropagation model can be divided in three parts: the first one, is the feedforward
training; the second one, are the errors of backpropagation; the last one, is th
weights adjustment (Figure 10).
Figure 10. Example of
backpropagation model.
Taken from Shelhamer,
Long, & Darrell (2016)
3.2.5.1 Feedforward training
Feedforward training shows in the figure 11, it can approximate virtually any
function of interest to any desired degree of accuracy, providing enough hidden units
that are available (Bebis & Georgiopoulos, 1994). Thus, “its input nodes are the ones
30 with no arcs to them, and its output nodes have no arcs away from them. All other
nodes are hidden nodes.” (Montana & Davis, 1989). So, when the state of all the
input nodes are set, the values propagates into the network while the other nodes
establish their state. But, when the output node obtains a value, it has to go traverses
a series of arcs, whereby the “n” layer of such a network consists of all nodes which
are “n” arcs traversal from an input node (Montana & Davis, 1989). The last process
of this method is to compare the value of y with the value of data training. In the
case of the images, these are the values of the pixel and the purpose of them is to
propagate the signal back to the beginning of the process of backpropagation error.
Figure 11. Process of feedforward training. Taken from Hernández (2017)
3.2.5.2 Backpropagation error
The backpropagation error is a method to supervise where the machine will
learn of its errors. The general idea is to involve an iterative procedure for
minimizing the error function, with adjustments to the weights made in a sequence
of steps. For this purpose, it is possible to distinguish two stages of the process: the
31 first one is to derivate the error function with respect to the weights that must be
evaluated; the second one is to use the derivates to compute the adjustments that
need to be made to the weights (Bishop, 2006). The general formula of
backpropagation is the equation 3, as shown below.
Equation 3. Taken from Bishop (2006)
In the equation 3, δ is the error in each neuron, �kj is the information of
backpropagation, aj is the information of the input data and h’ the derivation of
activation function. In that order of ideas, this means that “the value of δ for a
particular hidden unit can be obtained by propagating the δ’s backwards from units
higher up in the network” (Bishop, 2006). Furthermore, with the equation 3 the
algorithm calculates the error in each neuron backwards and with this information,
it adjusts the weights of the neurons. (Figure 12)
3.2.5.3 Weight adjustment
The final phase of the method of backpropagation training is the weights
adjustment. In this part the algorithm uses the activation function, in other words, it
uses the optimizer that is the stochastic gradient descent, mentioned before. This
process takes place in the final part of each iteration of the algorithm, where the
variables that affect the weight of the neurons are the following: (i) the derivation of
32