For Peer Review - University of Oklahomamcee.ou.edu/aaspi/submitted/2019/Wu_et_al_2019-New... · For Peer Review New approach of seismic surface generation via deep convolutional

For Peer Review

New approach of seismic surface generation via deep

convolutional neural network

Journal: Geophysics

Manuscript ID GEO-2018-0672

Manuscript Type: Case Histories

Keywords: neural networks, interpretation, stratigraphy

Area of Expertise: Case Histories, Interpretation Methods

GEOPHYSICS

For Peer Review

New approach of seismic surface generation via deep convolutional neural network

ABSTRACT

Seismic surface is a key input for building the geology structure and stratigraphy

models. Unfortunately, 3D seismic surface interpretation on the 1x1 grid is a time-consuming

task. Huge effort have been put on the automatically seismic surface interpretation methods.

However, it is still extremely hard to automatically obtain an accurate interpretation within the

complicate structure zone like faults and unconformtities. We propose a novel automatically

seismic surface interpretation method by applying deep convolutional neural network. We first

manually interpret the seismic surfaces on a user-defined coarse grid of the seismic survey. The

seismic traces on the user-defined coarse grid function as the training data for the following deep

learning procedure. The rest of the seismic traces in the survey are treated as testing data. We

then generate the training labels by segmenting the training data into several different parts

according to the manually interpreted seismic surfaces and assign each segmented part with

different symbols. We next train a deep convolutional neural network by using the training data

and corresponding labels. We finally obtain the seismic surfaces over the whole seismic survey

by applying the trained neural network into the testing data. Three field data examples

demonstrate that our proposed method can accurately generate seismic surfaces by only using

manually interpreted seismic surfaces on a 50×50 grid. The interpretation result from our

proposed method is superior to the interpretation result by using the traditional method of seeded

auto-tracking.

Keyword: Seismic surface interpretation, CNNs, semantic segmentation

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INTRODUCTION

Seismic surface generation is an important step for seismic interpretation and reservoir

characterization. The seismic surfaces can be treated as the stratigraphic boundaries that

represent the depositional environments and geological features. Manually interpretation is the

most familiar but time-consuming interpretation technique. In recent decades, seismic surface

interpretation has been automated to some extent by others. Zeng et al. (1998) proposed an

interpolation method, which first manually picking several reference strata slices and then build a

surface volume by interpolating the interpreted seismic surfaces. However, the interpolated

surfaces may not follow the local discontinues, like the fault and unconformities. Stark (2003)

computed the unwrapping instantaneous phase to generate a relative geological time (RGT)

volume and produce multiple surfaces simultaneously. The seismic surfaces that generated by

RGT volume can provide a quality measure along the unconformities, but it cannot follow the

fault gap. Wu and Zhong (2012) improved this method by using the graph-cut phase unwrapping,

which performs well at strong discontinues structure zone. Lomask (2006) first calculated the

local dips over the entire seismic volume and transferred them into the time shift and then apply

the least-square method to track the seismic surfaces automatically. Parks (2010) proposed a

slope-based flattening method, which use the structure tensor to estimate the dip and track

seismic surfaces automatically. Fomel (2010) use the algorithm of predictive painting to build a

3D seismic surface volume. Wu and Hale (2015) proposed an automatic surfaces tracking

method by adding control points in the complex structure zone. However, those methods still

require significant manual effort for the strong discontinues to obtain accurate seismic surface in

complicated geology structure zone.

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Deep learning is a subset of machine learning that use the concept of hierarchy to learn

the experience of the world and performed on a similar task. Convolution neural network (CNN)

(LeCun, 1998) is one of the most popular and widely used deep learning algorithms, which

achieve great success in the field of computer vision and pattern recognition. The basic theory of

CNN is learning the features of the images and classify the images by different labels. Many

algorithms based on CNN have been proposed to address the problem of images classification

(Krizhevsky, 2012, Szegedy, 2015, Simonyan, 2015), and the accuracy have beyond the human

level. However, those methods can only recognize one dominant object in one single image.

Girshick (2014) proposed the algorithm of regions with CNN features (R-CNN), which can

localize and detect multiple objects in one single image. This method uses a series of different

scale rectangle regions to segment multiple objects, but it cannot provide accurate boundaries of

the objects. A breakthrough came from fully connected neural network (FCN) (Long et al., 2014)

that enhance the capability of image segmentation from region level to pixel level. He (2015)

developed the ResNet with skip-connection, which make the training of very deep convolutional

neural network possible. Other pixel-level image semantic segmentation methods include SegNet

(Badrinarayanan, 2015), U-Net (Ronneberger, 2015), E-Net (Paszke, 2016), and Mask R-CNN

(He et al., 2017).

In recent years, deep learning has captured significant attention in the geoscience field.

However, obtain a superiority result over traditional method is still a challenge. In this paper, we

present a new method for seismic surface generation by using the deep convolutional neural

network based algorithm. To demonstrate the effectiveness and generalization capability of our

proposed workflow, we test on three different field data examples and compare with the

traditional method of seeded auto-tracking from a commercial software. This paper is organized


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as follow. We first introduce the workflow of our proposed method. We then present the testing

results on three different field data and compare with the traditional method of seeded auto-

tracking. We finally conclude several key points that need to be notice in the training process.

Overview

In geology, seismic surfaces mark the lithology change of sedimentary layers. The

lithology change in geophysics refers to a seismic reflection event follows an impedance contrast

associated with different depositional beddings. Seismic data can be treated as image and the

seismic surfaces segment the image into several different objects. Those different objects contain

different image features that related to different depositional beddings. Thus, seismic surface

interpretation turns to be an image segmentation task. Figure 1 shows the proposed workflow for

seismic surfaces generation via deep convolutional neural network. The proposed workflow

consists of three main parts that include data preparation, training and seismic surface generation.

Data preparation

To simulate the procedure of seismic surface interpretation in the real practice, we first

define a 50×50 coarse grid for manually interpretation (Figure 2). We then manually interpret the

seismic surfaces on the defined coarse grid. The time index of seismic surfaces segment the

seismic trace into several different parts and each part contains a unique waveform related to the

corresponding depositional bedding. We next assign each segmented part with different symbols

to generate the training labels. For example, we have 4 manually interpreted seismic surfaces in

total and these 4 surfaces segment the seismic traces into 5 different sequences, so we label these

five different parts from top to bottom with 0, 1, 2, 3 and 4, respectively. Researchers can use

any unique symbols to label the segmented parts. Figure 3 shows an example of training trace


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and the corresponding training label. The red dash lines in Figure 3 represent different seismic

surfaces. We finally obtain the selected seismic traces (Figure 2) and the corresponding labels

(Figure 4) and these two models are treated as training data and training label for the following

process.

Training and seismic surface generation

For the training process, we need build a deep convolutional neural network architecture.

Figure 5 shows a representative architecture of the deep convolutional neural network. It consists

of a symmetrical architecture with two main parts: encoder network and decoder network. The

role of encoder network is generating a series of feature maps according to the input training data

and pass them to the following decoder network. The encoder network is composed of a series of

repeated layers, and each layer contains convolution filter, batch-normalization regularizer,

ReLU activation operator and a max-pooling operator. The role of decoder network is

reconstructing the image according to the feature maps and feed into the element-wise

classification layer. The decoder also contains several layers that corresponding to the encoder

network, and each layer is composed of upsampling operator, convolution filter, batch-

normalization regularizer and ReLU activation operator. The layers in the encoder and decoder

networks are connected using “skip-connection”. The last step of the network is an element-wise

classification layer and the role of this layer is defining the weight of each pixel with the

corresponding label. Hence, the well-trained neural network can be used to segment other images

and assign each segmentation with the corresponding label.

After building the deep convolutional neural network architecture, we feed the training

data and training label into the proposed deep convolutional neural network for the process of

training. The training process contains three main steps that include feature extraction, data


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reconstruction and pixel-level feature classification. We first apply the convolution filter to

generate the feature map that is defined as follow:

zwbx ∗+= (1)

where * represent the convolution operation, b is a bias term to be learned, � is the input data, �

is the output feature maps, and � is the convolution filter. Then, the batch-normalization (BN)

(Loffe, 2015) algorithm is applied to normalize the output feature maps x, which can accelerate

the following iteration process. We next pass the main features � of the feature maps to next

layer by using the rectified linear unit (ReLU) activation operator. Then, we apply a pair of

operators (max-pooling and upsampling) to extract and reconstruct the main features. Next, the

cross-entropy loss function is applied to calculate the loss between the ground truth and

prediction. The loss function is given as follows:

( )ic

ic T-e

hθ

θ+

=1

1, (2)

( ) ( ) ( ) ( )( )∑ −−+−=

m

i

ii hhm

ii cycyJ θθθ 1log1log(1

, (3)

where ℎ�� is the hypothesis function of the input data for the last classification layer, and �

is the corresponding training label. Finally, the stochastic gradient descent (SGD) algorithm is

applied to minimize the loss function:

( )

1-t

-t1-tt

θ

θαθθ

∂

∂⋅−= 1J

, (4)

( )

1-t

-t1-tt

w

Jww

∂

∂⋅−= 1θ

α , (5)

( )

1

11

-t

-t-tt

b

Jbb

∂

∂⋅−=

θα , (6)


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where t is the ieration index, α is the learning rate. The algorithm will keep updating the gradient

and parameters until the training process meets the pre-defined loss or the maximum epoch time.

Once the training process is finished, the well-trained neural network is applied on the

test data. The trained network will perform segmenting and assigning different labels trace by

trace. Figure 6 shows the model of predicted label. We extract the seismic surfaces according to

the boundaries of different labels and the result is shown in Figure 7.

Field data example

To demonstrate the effectiveness and superiority of our proposed over traditional method

on seismic surface generation. We test on three different field data examples and compare with

the tradition method of seeded auto-tracking.

The first seismic survey is named F3-block and was acquired over North-Sea, Netherland.

This survey contains 651 inlines and 951 crosslines. The time increment of the F3-block seismic

survey is 4ms. We first manually interpret six seismic surfaces on a 50×50 coarse grid (Figure 8).

We then use those manually interpreted seismic surfaces to build the training data and

corresponding training labels for the following training process. We finally apply the trained

neural network into the rest of seismic traces to predict the seismic surfaces. Figure 9 shows the

predicted seismic surfaces by using our proposed method. The traditional method of seeded

auto-tracking is also applied to predict the seismic surfaces by using the same manually

interpreted seismic traces. Figure 10 shows the seismic surfaces by using the traditional method

of seeded auto-tracking. Figure 11 shows the manually interpreted seismic surfaces for the whole

seismic survey and we treat it as the ground truth. Note that there have some unreasonable well-

shaped interpretation result by using seeded auto-tracking while it not exist in the results of our


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proposed method and ground truth. We then calculate the average absolute errors of each seismic

surface between different approaches with the ground truth. The average absolute error is defined

as follow:

N

PG

d

N

i

ii∑=

−

= 1 (7)

where denotes the absolute average difference, � denotes the time index of ground truth

seismic surface on the �� trace, � denotes the time index of seismic surface result by using our

proposed method or seeded auto-tracking on the �� trace, N is the total number of the traces.

Table 1 shows the average absolute error result of the first field data example. Note that our

proposed method achieved much smaller errors than seeded auto-tracking. To further evaluate

the performance of our proposed method, we compare these three sets of seismic surfaces from

the view of front (cdp), side (inline) and above (time-slice) (Figure 12), respectively. The

interpretation results by using our proposed method, seeded auto-tracking and manually picking

are represented by red, green and yellow curve, respectively. Figure 13 shows the zoom-in

section of the orange region in Figure 12. Note that the method of seeded auto-tracking failed to

detect the edge of the unconformities that indicated by red arrow. Figures 14 and 15 show the

zoom-in sections that corresponds to the purple rectangle and blue rectangle in Figure 12,

respectively. Also note that the seismic surfaces obtained by using our proposed method have

perfect match with the ground truth, while the traditional method of seeded auto-tracking failed

to follow the seismic surfaces on the complicated zone that indicated by blue arrows.

The second seismic survey is named Penobscot and was acquired over Scotian shelf,

Canada. This survey contains 601 inlines and 482 crosslines. The time increment of the

Penobscot seismic survey is 4ms. We first manually interpret four seismic surfaces on a 50×50


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coarse grid (Figure 16). We then repeat the procedure that have applied in the first field data

example. Figures 17, 18 and 19 show the results of seismic surfaces by using our proposed

method, seeded auto tracking and manually interpretation, respectively. Note that there also have

some unreasonable well-shaped interpretation result by using seeded auto-tracking while it not

exist in the results of our proposed method and ground truth. Table 2 shows the average absolute

error result of the second field data example. Note that our proposed method achieved much

smaller errors than seeded auto-tracking. To further evaluate the performance of our proposed

method, we compare these three sets of seismic surfaces from the view of front (cdp), side (inline)

and above (time-slice) (Figure 20), respectively. Figures 21, 22 and 23 show the zoom-in

sections that corresponds to the orange rectangle, purple rectangle and blue rectangle in Figure

20, respectively. Also note that the seismic surfaces obtained by using our proposed method have

perfect match with the ground truth, while the traditional method of seeded auto-tracking failed

to follow the seismic surfaces on the complicated zone that indicated by blue arrows.

To further evaluate the limitation of our proposed method, we choose a more challenge

field data example. The third field data was acquired over China. This survey contains 151

inlines and 401 crosslines. The time increment of this survey is 2ms. This seismic survey

contains more complicated zone and narrower space between the adjacent seismic surfaces than

other two field data examples. We manually interpret three seismic surfaces on a 50×50 coarse

grid (Figure 24) and repeat the procedure that have applied in the first field data. Figures 25, 26

and 27 show the results of seismic surfaces by using our proposed method, seeded auto-tracking

and manually interpretation, respectively. Note that there also have some unreasonable well-

shaped interpretation result by using seeded auto-tracking while it not exist in the results of our

proposed method and ground truth. Table 3 shows the result of average absolute error for the


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third field data example. Note that our proposed method achieved much smaller error than

seeded auto-tracking. To further evaluate the performance of our proposed method, we compare

these three sets of seismic surfaces from the view of front (cdp), side (inline) and above (time-

slice) (Figure 28), respectively. Note that the seismic surfaces obtained by using our proposed

method have perfect match with the ground truth, while the traditional method of seeded auto-

tracking failed to follow the seismic surfaces on the complicated zone that indicated by blue

arrows.

Discussion

Properly choosing the parameters in the training process is very important to produce

accurate seismic surfaces by using deep convolutional neural network in assisting seismic

surface interpretation. There have several key factors need to be noticed in the training process.

The first key factor is the number of layers proposed to construct the neural network architecture.

Since the size of data would be reduced by half at each layer. We need to set the number of

layers according to the size of input data. Based on the three field data examples, we suggest that

the size of data in the last layer should be around two to three times larger than the label number

(number of seismic surfaces). The second key factor is the size of the convolution filter. We

obtain a better result if we choose the downward trend size for the convolution filter when

compared to that of using constant size of convolution filter. The third key factor is the size of

coarse grid for manually seismic surfaces interpretation. We have test different interpretation

gird size (100×100, 50×50, 25×25, 15×15 and 10×10) and obtained the same level results if the

grid size equals or smaller than 50×50.

Conclusion


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We proposed a novel approach for seismic surface generation based on the deep

convolutional neural network. Three field data examples illustrate that our proposed method can

produce accurate seismic surfaces even if we only have manually seismic surfaces interpretation

on the coarse seismic grid. Testing on different seismic surveys demonstrate the generalization

ability of applying deep convolutional neural network in assisting seismic surface interpretation.

Meanwhile, it also proves that our proposed method can produce the same level seismic surface

interpretation result with the manually interpretation (ground truth) on the complicated structure

zone.


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List of Figures

Figure 1. The workflow of our proposed method for seismic surface generation via deep

convolutional neural network.

Figure 2. Illustration of the selected traces on a coarse grid.

Figure 3. One example of a training trace and the corresponding label, the red dash lines

represent different seismic surfaces.

Figure 4. The label model that corresponds to the selected traces in Figure 2.

Figure 5. One representative architecture of deep convolutional neural network.

Figure 6. Illustration of the predicted labels by using the selected traces in Figure 2 and

corresponding labels in Figure 4.

Figure 7. The predicted seismic surfaces by extracting the boundaries of the predicted labels that

is shown in Figure 6.

Figure 8. The manually interpreted seismic surfaces on a coarse grid for the first field data

example.

Figure 9. The predicted seismic surfaces by using our proposed method for the first field data

example.

Figure 10. The picked seismic surfaces by using seeded auto-tracking for the first field data

example.

Figure 11. The ground truth of seismic surfaces for the first field data example.


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Figure 12. Illustration of the comparison in the first field data example within different methods

from the view of front (CDP), side (inline) and above (time-slice), respectively.

Figure 13. The zoom-in section that corresponds to the orange region in Figure 12.

Figure 14. The zoom-in section that corresponds to the blue region in Figure 12.

Figure 15. The zoom-in section that corresponds to the purple region in Figure 12.

Figure 16. The manually interpreted seismic surfaces on a coarse grid for the second field data

example.

Figure 17. The predicted seismic surfaces by using our proposed method for the second field

data example.

Figure 18. The picked seismic surfaces by using seeded auto-tracking for the second field data

example.

Figure 19. The ground truth of seismic surfaces for the second field data example.

Figure 20. Illustration of the comparison in the second field data example within different

methods from the view of front (CDP), side (inline) and above (time-slice), respectively.




Figure 24. The manually interpreted seismic surfaces on a coarse grid for the third field data

example.


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Figure 25. The predicted seismic surfaces by using our proposed method for the third field data

example.

Figure 26. The picked seismic surfaces by using seeded auto-tracking for the third field data

example.

Figure 27. The ground truth of seismic surfaces for the third field data example.

Figure 28. Illustration of the comparison in the third field data example within different methods

from the view of front (CDP), side (inline) and above (time-slice), respectively.


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List of Tables

Table 1. The comparison of average absolute error by using our proposed method and the seeded

auto-tracking for the first field data example.


auto-tracking for the second field data example.


auto-tracking for the third field data example.


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Reference

Badrinarayanan, V., A. Kendall, and R. Cipolla, 2015, SegNet: A deep convolutional encoder-

decoder architecture for image segmentation, arXiv preprint.

Fomel, S., 2010, Predictive painting of 3D seismic volumes, Geophysics, vol. 75, no. 4, pp. A25-

A30.

Girshick, R., J. Donahue, T. Darrell, and J. Malik, 2014, Rich feature hierarchies for accurate

object detection and semantic segmentation, IEEE Conference on Computer Vision

Pattern Recognition, pp. 580-587.

He, K., X. Zhang, S. Ren, and J. Sun, 2015, Deep residual learning for image recognition, IEEE

Conference on Computer Vision Pattern Recognition, pp. 770-778.

Ioffe, S, and C. Szegedy, 2015, Batch Normalization: Accelerating deep network training by

reducing internal covariate shift, arXiv preprint.

Kingma, D. P., and J. L. Ba, 2015, Adam: A method for stochastic optimization, International

Conference on Learning Representations.

Krizhevsky, A., I. Sutskever, and G. Hinton, 2012, Imagenet classification with deep

convolutional neural network, Advances in Neural Information Processing Systems, vol.

27, pp. 1090-1098.

LeCun, Y., L. Bottou, Y. Bengio, and P. Haffner, 1998, Gradient-based learning applied to

document recognition, Proceeding of IEEE, vol. 86, no. 11, pp. 2278-2324.

Lomask, J., A. Guitton, S. Fomel, J. Claerbout, and A. A. Valenciano, 2006, Flattening without

picking, Geophysics, vol. 71, no. 4, pp. P13-P20.

Long, J., E. Shelhamer, and T. Darrell, 2015, Fully convolutional networks for semantic

segmentation, IEEE Conference on Computer Vision Pattern Recognition, pp. 3431-3440.


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Parks, D., 2010, Seismic image flattening as a linear inverse problem, M.S. thesis, Colorado

School of Mines.

Stark, T. J., 2003, Unwrapping instantaneous phase to generate a relative geologic time volume,

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SEG Annual International Meeting Expanded Abstracts, pp. 1707-1710.

Simonyan, K., and A. Zisserman, 2015, Very deep convolutional networks for large-scale image

recognition, International Conference on Learning Representations.

Szegedy, C., W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Auguelov, D. Erhan, V. Vanhoucke, and A.

Rabinovich, 2015, Going deeper with convolutions, arXiv preprint.

Wu, X., and D. Hale, 2015, Horizon volumes with interpreted constraints, Geophysics, vol. 80,

no. 2, pp. IM21-IM33.

Wu, X., and G. Zhong, 2012, Generating a relative geologic time volume by 3D graph-cut phase

unwrapping method with horizon and unconformity constraints, Geophysics, vol. 77, no.

4, pp. O21-O34.

Zeng, H., M. M. Backus, K. T. Barrow, and N. Tyler, 1998, Stratal slicing; Part 1, Realistic 3D

seismic model, Geophysics, vol. 63, no. 2, pp. 502-513.


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Figure 1. The workflow of our proposed method for seismic surface generation via deep convolutional neural network.

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Figure 2. Illustration of the selected traces on a coarse grid.

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Figure 3. One example of a training trace and the corresponding label, the red dash lines represent different seismic surfaces.

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Figure 4. The label model that corresponds to the selected traces in Figure 2.

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Figure 5. One representative architecture of deep convolutional neural network.

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Figure 6. Illustration of the predicted labels by using the selected traces in Figure 2 and corresponding labels in Figure 4.

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Figure 7. The predicted seismic surfaces by extracting the boundaries of the predicted labels that is shown in Figure 6.

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Figure 8. The manually interpreted seismic surfaces on a coarse grid for the first field data example.

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Figure 9. The predicted seismic surfaces by using our proposed method for the first field data example.

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Figure 10. The picked seismic surfaces by using seeded auto-tracking for the first field data example.

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Figure 11. The ground truth of seismic surfaces for the first field data example.

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Figure 12. Illustration of the comparison in the first field data example within different methods from the view of front (CDP), side (inline) and above (time-slice), respectively.

254x190mm (300 x 300 DPI)


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254x190mm (300 x 300 DPI)


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254x190mm (300 x 300 DPI)


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254x190mm (300 x 300 DPI)


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Figure 16. The manually interpreted seismic surfaces on a coarse grid for the second field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 17. The predicted seismic surfaces using our proposed method for the second field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 18. The picked seismic surfaces by using seeded auto-tracking for the second field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 19. The ground truth of seismic surfaces for the second field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 20. Illustration of the comparison in the second field data example within different methods from the view of front (CDP), side (inline) and above (time-slice), respectively.

254x190mm (300 x 300 DPI)


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For Peer Review


254x190mm (300 x 300 DPI)


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For Peer Review


254x190mm (300 x 300 DPI)


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For Peer Review


254x190mm (300 x 300 DPI)


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For Peer Review

Figure 24. The manually interpreted seismic surfaces on a coarse grid for the third field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 25. The predicted seismic surfaces by using our proposed method for the third field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 26. The picked seismic surfaces by using seeded auto-tracking for the third field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 27. The ground truth of seismic surfaces for the third field data example.

254x190mm (300 x 300 DPI)


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For Peer Review

Figure 28. Illustration of the comparison in the third field data example within different methods from the view of front (CDP), side (inline) and above (time-slice), respectively.

254x190mm (300 x 300 DPI)


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For Peer Review

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Documents

For Peer Review - University of Oklahomamcee.ou.edu/aaspi/submitted/2019/Wu_et_al_2019-New... · For Peer Review New approach of seismic surface generation via deep convolutional