Citation

R. Benkert, O.J. Aribido, and G. AlRegib, ”Example Forgetting: A Novel
Approach to Explain and Interpret Deep Neural Networks in Seismic
Interpretation,” in IEEE Transactions on Geoscience and Remote Sensing (TGRS),
May. 12 2022

Review

Date of submission: October 2021
Date of acceptance: May 2022

Bib

@ARTICLE{benkert2022_TGRS,
author={R. Benkert, O.J. Aribido, and G. AlRegib},
journal={IEEE Geoscience and Remote Sensing},
title={Example Forgetting: A Novel Approach to Explain and Interpret Deep
Neural Networks in Seismic Interpretation},
year={2022}

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# Example Forgetting: A Novel Approach to Explain and Interpret Deep Neural
Networks in
Seismic Interpretation

Ryan Benkert, , Oluwaseun Joseph Aribido, ,
and Ghassan AlRegib Manuscript received February 08, 2022.

###### Abstract

In recent years, deep neural networks have significantly impacted the seismic
interpretation process. Due to the simple implementation and low
interpretation costs, deep neural networks are an attractive component for the
common interpretation pipeline. However, neural networks are frequently met
with distrust due to their property of producing semantically incorrect
outputs when exposed to sections the model was not trained on. We address this
issue by explaining model behaviour and improving generalization properties
through example forgetting: First, we introduce a method that effectively
relates semantically malfunctioned predictions to their respectful positions
within the neural network representation manifold. More concrete, our method
tracks how models ”forget” seismic reflections during training and establishes
a connection to the decision boundary proximity of the target class. Second,
we use our analysis technique to identify frequently forgotten regions within
the training volume and augment the training set with state-of-the-art style
transfer techniques from computer vision. We show that our method improves the
segmentation performance on underrepresented classes while significantly
reducing the forgotten regions in the F3 volume in the Netherlands.

###### Index Terms:

Example Forgetting, Seismic Interpretation, Deep Learning, Semantic
Segmentation.

##  I Introduction

In the field of geophysics, interpreting processed seismic images is a
challenging task. For decades, the process required expert oversight and a
costly interpretation process. The introduction of deep learning to the field
of geophysics significantly sped up this task and enabled accurate
interpretation with limited human interference [1]. Instead of experts
annotating volumes for weeks, the interpreter trains a deep model on a
annotated training volume and subsequently infers geological information from
similar test volumes in a matter of hours. The reason for this success is tied
to the nature of the interpretation task. Traditionally, the interpreter
extracts quantitative measures (attributes) of interesting characteristics and
infers geological information based on the extracted attributes and the
seismic section [2]. The choice of these attributes depends on the
interpretation objective. For instance, several attributes are based on
geometric properties [3], [4], [5] while others are derived from the human
visual system [6, 7, 8]. At its core, deep models function in a very similar
fashion. The model extracts complex features from the seismic section and
classifies the features based on the trained loss objective. By construction,
convolutional neural networks [9] posses the capability to model complex
spatial features that human interpreters may overlook or that hand-engineered
attributes may not capture. This specific characteristic is one of the biggest
advantages of deep neural networks, but can also be a huge pitfall. On one
hand, deep models automate the attribute extraction process and model complex
seismic features easily omitted by interpreters or geometric attributes. This
relieves the interpreter from selecting the appropriate attribute and
significantly decreases the overall interpretation time. On the flip side,
deep models lack interpretability. Even though the model automates feature
extraction, it is unclear how these features are related to the semantic
interpretation of the subsurface. In other words, the interpreter is unable to
explain the behavior of the network because the features are not necessarily
based on geophysical information. In many cases, this leads to unexplainable
predictions that undermine the confidence in deep models during inference. For
instance, a trained machine learning model may predict deep subsurface
structures as near surface facies (Figure 1). The former interpretation is
significantly less likely in the traditional workflow where attributes are
based on relevant geophysical characteristics and interpretations are
performed manually by humans.

Figure 1: An example of mispredictions of a deep neural network. Left: Seismic
input section. Center: Manual seismic interpretation. Right: Automated
interpretation of a trained deep neural network. The circled sections
represent severely mispredicted regions.

In this paper, our objective is to make interpretations more explainable and
predict the behavior of deep models when utilized on different input volumes.
In the field of computer vision, several approaches to model uncertainty or
interpretability involve Bayesian inference [10, 11] or gradient-based
approaches [12, 13, 14, 15, 16]. Even though these approaches are useful
visualization techniques, they fail to provide information about the
relationship of samples with respect to the decision boundary. In seismic
interpretation, this information is especially important as it can provide
useful insights about the geophysical relationship of the extracted features.
Based on these observations, we propose using example forgetting to explain
seismic deep models. At its core, our method tracks the frequency in which
amplitude reflections are forgotten during training and highlights difficult
regions in heat maps. From an optimization standpoint, our algorithm contrasts
difficult samples with frequent decision boundary shifts from less difficult
samples consistently mapped within class manifolds. This provides the
interpreter with a powerful tool to visualize the generalization capabilities
of the model and to verify model generalization with respect to the
interrpetation of the subsurface.

In summary, our contributions in this paper are as follows: First, we present
a framework to _explain deep model behavior_ by evaluating the learning
dynamics during training. Second, we _analyze deep models_ by visualizing
challenging regions and interpret them with respect to model predictions and
the geophysical properties of the subsurface. The framework allows us
categorize prone regions and evaluate their contribution to the model
performance. Third, we _introduce a segmentation framework_ that explicitly
targets forgotten samples and significantly reduces difficult pixels. Our
empirical findings show that our method impacts the representation space
mapping and increases the distance of pixels to their respective class
decision boundary. Moreover, our framework improves segmentation performance
of underrepresented classes.

##  II Related Work

In seismic interpretation, deep learning models first surfaced in the form of
fully supervised settings [17, 18]. However, due to the high cost, fully
annotated datasets are scarce in seismic interpretation. For fully supervised
models, this frequently causes overfitting and poor prediction capabilities.
As a result, several works explored semi-supervised and weakly supervised
approaches [19, 20, 21, 22, 23, 24] as these methods are less dependent on
costly data annotations. Apart from methodological shifts, deep models have
been further diversified on different seismic applications. A few example
applications include detection of faults [25, 26, 27, 28, 29, 30], delineation
of salt bodies [31, 32, 6], classification of facies [33, 34, 35, 21, 36],
prediction rock lithology from well logs [23, 37, 38, 39] and seismic horizon
interpretation [40, 41].

Although deep learning models are effective, they are hard to explain and
mispredictions may follow a random pattern that is semantically incorrect. In
computer vision, this is a well known issue of deep models and works on model
uncertainty or explainability are ubiquitous. For instance, one branch focuses
on utilizing gradient activations to infer information about the expected
change a model witnesses when updating weight parameters [13, 14, 15, 16]. A
more traditional approach is visualizing model uncertainty through Bayesian
inference [10, 11]. Typically, this involves estimating the posterior
probability of model parameters with respect to given data samples and their
respective labels. Subsequently, model uncertainty is visualized by sampling
from the parameter distribution and computing the entropy of the resulting
prediction distribution. In seismic interpretation, most approaches concerning
model uncertainty fall into this area of research [42, 43, 44].

In contrast to existing methods, we explain model behaviour and prediction
uncertainty by investigating the learning dynamics in neural networks. In
literature, research in this area can be broadly classified in two categories:
The first category explores the learning continuity when deep models are
trained on new tasks. In research, this behaviour is often referred to as
catastrophic forgetting [45, 46]. In seismic interpretation, we frequently
encounter this phenomenon in transfer learning scenarios where models are
pretrained on one dataset and fine-tuned on another. The second category
addresses the learning behaviour within a single task and analyzes sample
forgetting within the training distribution [47]. In this paper, we generalize
this concept to a seismic segmentation problem and visualize frequently
forgotten regions in heat maps. Further, we exploit frequently forgotten
regions by transferring their class characteristics to different sections
within the seismic volume. To achieve this, we utilize state-of-the-art style
transfer algorithms from computer vision.
In this context, several style transfer approaches are based on conditional
generative adversarial networks [48]. Starting with [49], conditional
generative adversarial networks (cGANs) have been widely deployed in many
image-translation applications due to their high quality image generation
characteristics. Examples of such applications are high resolution image
synthesis [50], multi-modal image synthesis [51, 52] and semantic image
synthesis [53, 54, 55, 56, 57]. In seismic, style transfer does not have much
research traction. However, few papers address the generation of synthetic
subsurface models by applying style transfer techniques [58, 59].

Finally, we note that this work is a continuation of [60]. In addition to
[60], we present significantly improved segmentation results as well as
thorough analysis aspects of our method.

Figure 2: An example of our proposed method. Left: Heat map of the section.
Pixels close to the decision boundary are highlighted in different shades of
red whereas pixels deep within the class manifold are dark blue. Center:
Annotation of the respective section. Right: Original seismic section.

##  III Explainability in Neural Networks with Example Forgetting

At the core of our technique stands the concept of example forgetting.
Intuitively, samples that are more difficult to learn exhibit different
properties than samples that are easy to distinguish and classify. In this
section, we formalize this concept in the form of ”forgetting”.

###  III-A Forgetting Events

Deep neural networks cannot learn continually but forget samples during the
optimization process. More generally, optimizing weight parameters causes a
shift in the representation manifold that can result in misprediction (or
”forgetting”) of previously correct samples. In neural networks, a shift
occurs when a sample has been ”learnt” (classified correctly) at some point
$t$ and subsequently ”forgotten” (misclassified) at a time $t^{\prime}>t$.
Formally, we define $(x_{i},y_{i})\in I^{M\times N}$ as a (pixel, annotation)
tuple in image $I$, where $x_{i}$ and $y_{i}$ correspond to the pixel and
annotation respectively. In image segmentation, our goal is to calculate a
prediction $\tilde{y}_{i}$ such that $\tilde{y}_{i}=y_{i}$. Based on this
definition, the accuracy of a pixel in training epoch $t$ is defined as

$acc^{t}_{i}=\mathbb{1}_{\tilde{y}^{t}_{i}=y_{i}}.$ (1)

Here, $\mathbb{1}_{\tilde{y}^{t}_{i}=y_{i}}$ refers to a binary variable
indicating the correctness of the classified pixel in image $I$. With this
definition we say a pixel is forgotten at epoch $t+1$ if the accuracy at $t+1$
is strictly smaller than the accuracy at epoch $t$:

$f_{i}^{t}=int(acc^{t+1}_{i}<acc^{t}_{i})\in{1,0}$ (2)

Similar to [47], we define the binary event $f_{i}^{t}$ as a _forgetting
event_ at time $t$.

In contrast to other deep learning applications, the nature of the
segmentation tasks enables visualization of forgetting events (Figure 2).
Following our previous definition, we visualize forgetting events in a heat
map by counting the number of forgetting events $f_{i}^{t}$ that occur per
pixel during the time frame $T$. Mathematically, heat map
$L\in\mathbf{N_{0+}}^{M\times N}$ and every element in $L$ can be written as

$L_{i}=\sum_{t=0}^{T}{f_{i}^{t}}.$ (3)

Since frequently forgotten samples were shifted over the decision boundary
frequently during training, we interpret forgetting events as an approximate
metric for decision boundary proximity. This view is complementary to [47]
where frequently forgotten samples are considered support vectors within the
representation space. Qualitatively, we note that frequently forgotten regions
typically contain overlapping class features or a significant amount of
annotation ambiguity. For this reason, we mostly find forgettable regions in
underrepresented classes (e.g. salt domes) or facies boundaries where
annotations are the most ambiguous (Figure 2).

###  III-B Heat Map Computation

In our implementation, we calculate heat maps for different distribution sets.
Following the previous definitions, we would have to track forgetting events
for each model update. Practically, this would result in interpreting every
volume set after each minibatch and updating the heat maps multiple times
every epoch. Since this approach is computationally expensive, we update the
heat maps of the current minibatch only. For the training set we monitor
forgetting events of each minibatch and update with the corresponding batch
gradient. For validation and test sets we track forgetting events after each
epoch. Algorithm 1 outlines the tracking procedure. During training, we count
the number of forgetting events for each pixel $(i,j)$ in set $D$ and store
the result in a heat map for each image within the minibatch. If $D$ is the
training set, we further update with the minibatch $B$. In all other cases
(e.g. test), we do not perform model updates since this would alter the
regular training procedure. Instead, we train the model for another epoch on
the training set synchronously.

Result: Heat Maps of Set $D$.

Let $(i,j)\in M\times N\ \text{and}\ k\in D$;

initialize $previousacc_{i,j}^{k}=0$;

initialize Heat Maps $T_{i,j}[k]=0$;

while  _Training not finished_ do

for  _$\text{batch }B\in D$_ do

if  _$D$ is training set_ then

update segmentation model on $B$;

end if

for  _$\text{pixel }(b,i,j)\in|B|\times M\times N$_ do

if  _$acc_{b,i,j}^{k} <previousacc_{b,i,j}^{k}$_ then

$T_{b,i,j}[k]+=1$;

else

continue;

end if

end for

end for

end while

Algorithm 1 Heat Map Computation

##  IV Support Vector Augmentation

Building on our previous definitions, we use frequently forgotten regions
within the training set to improve robustness and generalization capabilities
of the segmentation model. Specifically, we identify frequently forgotten
regions within the train set and add example variety through region-wise style
transfer. Since we consider forgetting events as an approximate decision
boundary proximity metric, our method can be interpreted as an augmentation
technique that generates new samples around the class boundaries. Within the
manifold, this results in a boundary shift (Figure 3). Based on the popular
machine learning paradigm [61], we name our method _Support Vector
Augmentation_.

Figure 3: Intuition of our subsurface transfer method. We target the support
vectors of class 1 (blue circled disks) and generate new samples of class 1
(green) that deliberately shift the boundary (black line) away from the blue
class manifold. The other class is presented in light blue. Figure 4: The
augmentation workflow for seismic interpretation. First, forgetting event maps
are produced by the segmentation model using the original volume (a). Second,
sections with the most frequently forgotten samples of the target class are
selected as the input for our transfer model (b). Third, the transfer model
transfers the challenging characteristics of the frequently forgotten regions
to other randomly sampled sections throughout the training volume (c).
Finally, the generated data is added to the training volume and the
segmentation model is retrained from scratch (d).

Our augmentation workflow consists of a segmentation model, a transfer model
and a data selection step (Figure 4). First, our method trains the
segmentation model on the training data and produces a forgetting event heat
map for every validation image in the training volume (Figure 4a). In
principle, heat maps could be produced for the entire training set but that
would be computationally inefficient.

In the next step of our workflow, we calculate the forgetting event density
within each facies class of a heat map (Figure 4b). Specifically, we sum all
forgetting events $f_{i\in c_{k}}$ within class $c_{k}$ of a heat map and
divide by the number of pixels of class $N_{c_{k}}$ in the image:

$U_{c_{k}}=\frac{\sum_{t=0}^{T}{\sum_{i\in c_{k}}{f_{i}^{t}}}}{N_{c_{k}}}.$
(4)

This metric allows us to rank each heat map according to its density with
regards to any arbitrary class in the dataset.

Finally, we transfer the visual features of a predefined class from the
vertical sections with the highest density to randomly sampled training
sections (Figure 4c). Our proposed architecture is a slightly altered version
of [53]. In short, the model transfers facies characteristics on the batch-
normalization activations within the image generator. Our approach enables
class specific transfers without affecting the interpretation characteristics
(texture, structure etc.) of other classes within the image. In our method, we
transfer the underrepresented class facies (e.g. salt domes) due to the
learning difficulty of the samples. After generation, the transferred images
are added to our training pool and the segmentation model is trained from
scratch (Figure 4d). In the remainder of this section, we will discuss our
transfer model in more detail as this represents a crucial step in our
workflow.

Our transfer model takes three input parameters: A source image, a target
image and a class list. The subsurface source and target image are two seismic
sections specified by the user. They represent the facies source as well as
the section to be altered by our algorithm. The class list contains the facies
that our algorithm will transfer to the target image. We show several transfer
examples in Figure 5. Here, we transfer the characteristics of the orange
scruff class from the source image (Figure 5d) to the target image (Figure 5a)
and evaluate the absolute difference between adjacent transfer images using
different sources (Figure 5f). For instance, the difference image using source
2 (middle row) represents the absolute difference between the transfer images
of the first and second row. As seen in the transfer output, the
characteristics of the scruff class are clearly different from the original
target image in all example sections. Moreover, we can see that varying the
source image results in different scruff facies that are dependent on the
scruff regions of their respective source image. For instance, the scruff
facie of the transfer image resulting from source 2 is significantly smoother
than the other two examples due to the smooth scruff characteristics of
subsurface source 2. Finally, the difference plots show what regions are
affected by our transfer model when different source images are used. Since
our class list only consisted of the scruff class we observe that only this
region of the target class is altered by our model. Note, that the difference
in the first row (column f) shows the difference between source 1 and source
0, an adjacent source image not shown in our examples.

To achieve the results in Figure 5 we employ a GAN architecture [62]
consisting of an encoder, a generator as well as a discriminator (Figure 7).
The discriminator (Figure 7c) predicts whether the presented images originate
from the generator or training distribution and is used to derive the
adversarial loss. Since this is a standard step in GAN frameworks [62] our
explanations will focus on the other two architecture elements.
We encode subsurface characteristics in two steps (Figure 7a): First, we
encode the source image to remove information irrelevant to subsurface
characteristics. Second, we use a class-wise average pooling layer to produce
subsurface representations (codes). Each code is a vector and represents the
characteristics of one class in the input source. For instance, one code will
include the class scruff whereas another code will represent the zechstein
class. These codes are used to transfer the facies within the generator.
Simply using the target image as the encoder input, will result in an image
reconstruction in the generator as the generated codes contain the target
image characteristics. However, in our application we want the output to
contain the subsurface characteristics of our source image. For this reason,
we substitute the subsurface codes with our desired source subsurface codes
during inference. This gives us full control over the transfer and allows us
to produce examples as seen in Figure 5. In our example, we substitute the
subsurface code of the scruff class with the scruff subsurface code from our
source image. Note, that we leave all other subsurface codes untouched because
we want the other classes to share the same characteristics as the target
image.

Figure 5: Examples of transferred subsurfaces. Columns from left to right: a)
Target image for subsurface transfer. b) Output of our algorithm when
transferring the orange scruff class. c) Annotation of the target image. d)
Subsurface source. e) Subsurface source annotation. f) Absolute differences
between adjacent transfer images using different sources (e.g. the difference
image of subsurface source 2 represents the difference between the transfer
image of the first row and the second row). Figure 6: SEAN layer workflow. The
normalization layer takes the subsurface codes and the target image mask as
input parameters (bottom left). The layer modulates the subsurface information
as well as the structural information from the annotation onto the normalized
output of the previous layer(right).

In our generator (Figure 7b), we use semantic region-adaptive normalization
(SEAN) layers to transfer the codes to their respective class regions [53]. In
summary, SEAN modulates the subsurface codes as well as the structural
information from the annotation onto the normalized output of the previous
layer. In Figure 6 we show a simplified visualization of the modulation
process. First, the codes are broadcasted to the respective class regions
using the structural information contained in the section annotation
(characteristics mapping step). For instance, the scruff subsurface code will
be broadcasted to all structural regions containing scruff, the zechstein
codes are broadcasted to the zechstein regions and so on. The resulting
intermediate image is then used to scale and shift the output of a previous
normalization layer.

Figure 7: The subsurface transfer architecture used in this work during
training. Top: Generator with SEAN blocks and upsampling layers (b). Bottom:
Subsurface encoder (a) with the bottleneck encoder-decoder architecture
(left), region-wise average pooling layer (center) and subsurface codes
(right). Left: Discriminator (c) with both loss functions used in training
(MSE loss and adversarial loss)

We train the architecture by learning a simple image reconstruction problem.
The subsurface encoder is trained to distinguish per region subsurface codes
and the generator is forced to transfer these codes by region adaptive
normalization. In inference, the image and annotation source can be different
to produce other subsurface codes. In our model, we feed the target image as
well as our source image into the encoder sequentially and hand-pick the
desired subsurface codes.

##  V Empirical Analysis

Our experiments in the entire paper were conducted on the F3 block dataset in
the Netherlands [36]. We partition the volume into train and test set
according to the orignal benchmark paper and show the layout in Figure 8. When
showing heat maps we restrict the examples to the test sections in Figure 9.
Here, the sections one through four represent the Test 1 crosslines 234, 310,
556, and 622 respecitvely. Further, sections five and six represent the Test 2
inline sections 575, and 596. Our choice is based on the high presence of
underrepresented classes (e.g. the orange scruff class) and complex facies
structures. Even though this paper only considers these examples, we note that
our observations and conclusions are consistent throughout the entire volume.

Figure 8: Train, test, and validation partition of the F3 dataset. For our
validation set, we select every fifth inline and every fifth crossline of the
training data.

Throughout all of our experiments, we opt for a deeplab-v3 [63] architecture
with different backbone architectures. For optimization, we use the adam
variant of stochastic gradient descent with a learning rate of $1e-4$ in
combination with a polynomial learning rate decay. We structure our
experiments in two sections: First, we show the analysis benefits of
forgetting event heat maps by displaying when pixels are forgotten during
training. We distinguish different groups within forgettable pixels and relate
them to the model interpretations. Second, we benchmark the generalization and
robustness properties of our augmentation method. We analyze the impact of our
method along the metrics of segmentation performance and heat map impact. As a
comparison we use common augmentation techniques used in literature.

###  V-A Analyzing Forgotten Regions

In our experiments, we train the segmentation architecture with a resnet-18
backbone [64] for 60 epochs on the training volume. We track the forgetting
events for the validation and test set and display the heat maps for different
observation windows of the test set (Figure 10). In each row, we show
different time frames in which forgetting events were tracked: In the first
row, all forgetting events that occurred during the 60 epochs are displayed.
The second and third row show the forgetting events that occurred between the
20th and the 60th epoch as well as the 50th and 60th epoch respectively. In
the final third row, we show the predictions of our model. Overall, we can
classify forgettable regions in the following groups:

The first group consist of pixels forgotten rarely and which disappear from
the heat maps after 20 epochs. We call these samples _early-stage
forgettable_. These regions are learned at an early stage within the training
cycle and the network does not have difficulties mapping them to the
representation space. In the context of the interpretation task, these pixels
are frequently found in areas that are structurally consistent throughout the
volume and do not show a significant variety. An example of these areas can be
found in the upper north sea group (dark blue class) and the chaotic middle
north sea group (blue class) in images one, two and three. The heat maps
within the first row clearly show highlighted regions within the upper classes
that disappear after epoch 20 and that are correctly classified by the fully
trained model.

Figure 9: Interpreted examples from the test set used for heat map comparison.
The sections are chosen based on the high presence of underrepresented classes
and complex facies structures.

The second group of pixels is more difficult to characterize by our network
and consists of pixels most frequently forgotten - _ambiguous forgettable_
samples. These areas are frequently shifted between the correct manifold and
other class manifolds during the optimization process but are _not necessarily
misclassified_. We interpret these samples to have been within a close
proximity to the decision boundary for a specific time frame during the
optimization process. Examples of these regions are either the class
boundaries or difficult textures within underrepresented classes (e.g. Section
1 frequently forgotten scruff regions in row one and two). Note, these regions
are either predicted correctly or incorrectly depending on the network
initialization and are not directly visible in the network predicitons.

The final group entails the most difficult pixels for our model. This group is
consistently classified incorrectly throughout the training procedure and is
forgotten rarely at the end of training. Due to this characteristic, we call
these samples _late-stage forgettable_ samples. In terms of the representation
mapping, the network is unable to map these regions into the target manifold
throughout training and starts to learn these pixels at a late stage when the
model has already learned a large variety of textural and structural features.
In our examples, these areas are visible in the third row showing the
forgetting events at a late stage. Qualitatively, these areas contain
difficult textures or salt dome structures that are not present in the
training distribution in that form and hence present the most difficult
regions within the test set. This is further confirmed by the false
predictions in these regions.

Figure 10: Different time frames in which pixels are forgotten. The columns
show six different seismic sections from the test set containing difficult
textures or structures. Different rows show different observation windows for
forgetting events. From top to bottom: 1. Test set heat maps containing all
forgetting events throughout training (epoch 0 through epoch 60). 2. Test set
heat maps with all forgetting events occurring between epoch 20 and epoch 60.
3. Test set heat maps with all forgetting events occurring between epoch 50
and epoch 60. 4. Predictions of all sections using the fully trained model.

###  V-B Subsurface Transfer

In this section, we benchmark our support vector augmentation method in
combination with common augmentation techniques. Our qualitative heat map
results are obtained by training the segmentation model with a resnet-18
backbone for 60 epochs with and without augmentations. For our segmentation
performance comparison, we use a resnet-101 backbone and train our model for
80 epochs on five separate random seeds. Furthermore, we train all of our
architectures by randomly cropping 255 pixel patches and test with full
sections. We choose this setup to ensure a proper comparison to the original
baseline of [36]. For consistency, we choose the validation set by selecting
every fifth inline and every fifth crossline of the training volume for all
seeds (Figure 8). We note that our numerical results are summarized over every
inline and crossline of both Test 1 and Test 2. We query six images with the
highest forgetting event density of our target class. Each section is used as
a source image to generate 64 transfer images. For generation, we sample
randomly to obtain the target image and retrain the segmentation model from
scratch. We note that due to the random target image selection our technique
is sensitive to the hyperparameter choice (number of sources, targets etc.)
and that significant experimentation had to be performed to achieve the
results in Table I. However, the investigation of different query methods is
beyond the scope of this paper and we leave this topic for future research. In
this paper, we report the results when transferring the scruff class (orange).
For evaluation, we compare our subsurface transfer technique with common
augmentation methods (random horizontal flip and random rotations; [65]) from
computer vision in terms of segmentation performance (in class accuracy and
mean intersection over union) and impact on forgetting events heat maps.
We show show the numerical results in Table I. Overall, every method matches
or outperforms the baseline in terms of class accuracy. In particular, our
method significantly increases the performance of the target class (scruff) as
well as the neighboring underrepresented classes (zechstein and chalk) in the
majority of cases. We see that our method affects the accuracy of other
classes (upper, middle, and lower north sea group) only mildly and largely
remains untouched by the algorithm. For instance, adding our method on top of
random rotate increases the scruff class accuracy by 4.5% while the upper
north sea group accuracy is increased by 0.1% which we consider insignificant.
This suggests, that our method is spatially localized and affects the classes
in direct proximity of the target class scruff.

Further, we observe that our method matches the baseline accuracy when
combined with the baseline exclusively. Specifically, we observe a maximum of
0.6% difference to the baseline on the target class as well as its neighboring
classes. We reason, that the data variations of our method are not as profound
as conventional augmentation techniques and are not as effective when paired
with the baseline exclusively. While augmentations such as random rotate
result in significant structural variation, our method adds slight subsurface
variations to a single class and maintains all other components of the seismic
image. Therefore, the augmentation alone does not affect the numerical values
strongly. However, when combined with other augmentations its effect becomes
amplified and more pronounced. For instance, we see a clear improvement when
using our method in combination with random rotate.

Finally, we note that adding an augmentation can result in minor accuracy
reductions for selective classes. For instance, adding random rotate to the
baseline results in a 1.3% reduction in terms of accuracy on the upper north
sea class. While augmentations frequently result in an overall accuracy
improvement, several augmentations can have a negative effect on specific
class groups or even entire section performances. In the example of random
rotate, the upper north sea class does not share an upper boundary with
another class and is therefore ”cut off” when rotated. However, we note that
adding our method does not result in such a behavior and reductions can be
considered irrelevant. This affirms that our method introduces realistic data
variations for seismic interpretation for every class and therefore matches or
improves the baseline performance.

In addition to Table I, we further show the predictions of crossline 60 in
Test 2 for different augmentation constellations (Figure11). We highlight
areas of improvement in green. Overall, the predictions further support our
numerical analysis of Table I. In particular, we find that adding our method
in any constellation typically results in more fine-grained predictions that
are less smooth. For instance the highlighted area when using random rotate
and random flip contains significantly smoother scruff predictions than the
model trained with our method. We reason, that our method introduces style
variations into the data that provide more boundary robustness. For this
reason, the predictions are more fine-grained.

We further show the forgetting event heat maps of the different augmentations
in Figure 12. Qualitatively, our method reduces the amount of forgetting
events significantly more than traditional augmentation methods indicating a
clear representation shift. Specifically, we find that several regions with a
high forgetting event density are transferred to a low forgetting event
density or disappear entirely (bottom scruff class in Section 2, entire left
part of Section 6, or center of Section 4). These regions are shifted away
from the decision boundary and the classification accuracy is not
significantly affected by model updates. In contrast, forgettable regions do
not disappear with standard augmentation techniques. Instead, only the
severity of the forgetting event regions is reduced or the texture of the
regions is blurred. For instance, random rotation results in blurred edges
around the forgettable regions.
Finally, we identify regions that transition from lower forgetting event
densities to higher densities (e.g. Section 6 bottom left) when using our
augmentation method. Because these regions transition to more difficult
regions, and serve as an example of negative representation shifts. However,
we also note empirically that these occasions are rare and that the reduction
of forgettable regions is significantly more common than an increase.

Class Accuracy & Overall MIoU
---
Model |  MIoU |  Upper N. S. |  Middle N. S. |  Lower N. S. |  Chalk |  Scruff |  Zechstein
Baseline |  0.689 |  0.986 |  0.875 |  0.965 |  0.771 |  $\mathbf{0.591}$ |  $\mathbf{0.622}$
Baseline + Ours |  0.687 |  0.983 |  0.886 |  0.962 |  $\mathbf{0.772}$ |  0.585 |  0.619
Rand. Rotate |  0.709 |  0.973 |  0.923 |  0.972 |  0.792 |  0.600 |  0.556
Rand. Rotate + Ours |  0.724 |  0.974 |  0.930 |  0.973 |  $\mathbf{0.811}$ |  $\mathbf{0.646}$ |  $\mathbf{0.593}$
Rand. Rotate + Rand. Flip |  0.728 |  0.973 |  0.927 |  0.974 |  0.804 |  0.650 |  0.588
Rand. Rotate + Rand. Flip + Ours |  0.732 |  0.971 |  0.927 |  0.975 |  $\mathbf{0.822}$ |  $\mathbf{0.664}$ |  $\mathbf{0.641}$
TABLE I: Averaged class accuracy. Figure 11: Model predictions for crossline
60 in Test 2 when different augmentation methods are used. Top row: Seismic
data and the corresponding ground truth predictions.Rows two, three, and four:
No augmentations (Baseline), random rotate, and random rotate as well as
random horizontal flip. The first column contains the augmentation, and the
second column contains the same augmentation with our method. Areas of
improvmenta are highlighted in green circles. Figure 12: Heat maps for the
example sections two, four, and six when using different augmentation methods.
Each group represents a different augmentation method: The first row contains
the baseline model with no augmentations. The second row contains random
horizontal flip where we flip each section randomly during training. The third
row contains randomly rotated image augmentations. The final row represents
our subsurface augmentation method. In summary, our method reduces the amount
of forgetting events significantly more than traditional methods.

##  VI Conclusion

In this paper, we presented a novel framework that enhances explainability in
deep seismic models. We track the frequency in which pixels are forgotten
during training and analyze the relationship to the sample position within the
feature space. We highlight forgotten pixels spatially in heat maps and
interpret their semantic geologic meaning. Further, we consider different time
frames in which samples are forgotten and are able to tie specific prediction
properties to model behaviour. Finally, we exploit our framework to engineer
an augmentation method that explicitly targets forgotten regions and increases
the variety of difficult pixels through subsurface transfer. Our empirical
evaluations clearly show the shift in the learned feature space when compared
to traditional augmentation methods. In future, we hope that this work will
provide a powerful concept for interpreters to verify the model functionality
and explain its behaviour. Furthermore, we have shown that the well crafted
methods can target prone regions and allow explicit control over the decision
boundary. Future work could include an application exploration and forgetting
events could be applied to multiple seismic applications such as rock
lithology predictions or salt body delineation.

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