Citation

R. Benkert, M. Prabhushankar, and G. AlRegib, “Effective Data Selection for
Seismic Interpretation through Disagreement,” in IEEE Transactions on
Geoscience and Remote Sensing, April 2024

Review

Date of submission: 21 July 2023
Date of 1st revision: 11 September 2023
Date of 2nd revision: 29 January 2024
Date of acceptance: 29 April 2024

Bib

@article{benkert2024effective,
title={Effective Data Selection for Seismic Interpretation through
Disagreement},
author={Benkert, Ryan and Prabhushankar, Mohit, and AlRegib},
journal={IEEE Transactions on Geoscience and Remote Sensing},
year={2024},
publisher={IEEE}}

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# Effective Data Selection for Seismic Interpretation through Disagreement

Ryan Benkert, , Mohit Prabhushankar, ,
and AlRegib, Ghassan The authors are with the School of Electrical and
Computer Engineering, College of Engineering, Georgia Institute of Technology,
Atlanta, GA 30332 USA (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

This paper presents a discussion on data selection for deep learning in the
field of seismic interpretation. In order to achieve a robust generalization
to the target volume, it is crucial to identify the specific samples are the
most informative to the training process. The selection of the training set
from a target volume is a critical factor in determining the effectiveness of
the deep learning algorithm for interpreting seismic volumes. This paper
proposes the inclusion of interpretation disagreement as a valuable and
intuitive factor in the process of selecting training sets. The development of
a novel data selection framework is inspired by established practices in
seismic interpretation. The framework we have developed utilizes
representation shifts to effectively model interpretation disagreement within
neural networks. Additionally, it incorporates the disagreement measure to
enhance attention towards geologically interesting regions throughout the data
selection workflow. By combining this approach with active learning, a well-
known machine learning paradigm for data selection, we arrive at a
comprehensive and innovative framework for training set selection in seismic
interpretation. In addition, we offer a specific implementation of our
proposed framework, which we have named ATLAS. This implementation serves as a
means for data selection. In this study, we present the results of our
comprehensive experiments, which clearly indicate that ATLAS consistently
surpasses traditional active learning frameworks in the field of seismic
interpretation. Our findings reveal that ATLAS achieves improvements of up to
12% in mean intersection-over-union.

###### Index Terms:

Active Learning, Semantic Segmentation, Seismic Interpretation.

##  I Introduction

Deep learning models have become the preferred method in seismic
interpretation, bringing about a revolutionary change by reducing the time and
effort needed for experts to annotate seismic volumes [1]. Instead of
geophysicists annotating seismic volumes for weeks [2], deep models can infer
similar information within a matter of hours. The success of machine learning
algorithms relies heavily on sufficient quantities of training data and a
well-constructed optimization process. When provided with accurate training
data, model representations effectively capture geological information and
mirror the manual interpretation process. However, when faced with scarce
training sets, model representations deteriorate, leading to unpredictable
behavior and semantically incoherent outputs [3].

Unfortunately, scarcity and label inaccuracies are commonplace in seismic
datasets, posing significant challenges for the deployment of deep learning
models. For seismic interpretation, training labels require expert annotation
and can substantially differ depending on the available information to the
interpreter. As a result, labeled training sets are frequently a small subset
of the entire seismic volume and the algorithmic performance is heavily
influenced by location and content of the individual training sections.
Therefore, selecting the appropriate training volume is critical for the
successful deployment of deep learning models.

Within the context of machine learning, a common mechanism for limited data
settings is active learning. Active learning is a machine learning paradigm
where the deep learning algorithm selects an appropriate training set that
maximizes test performance [4]. Traditionally, active learning is an iterative
process, where the model is trained on an initial set of annotated training
samples and actively selects additional samples in subsequent rounds. While
active learning has proven successful in a wide range of natural image
applications [5, 6, 7], its direct applicability to seismic data acquisition
workflows is not trivial. Specifically, active learning algorithms must assign
an importance score to entire seismic sections instead of individual pixels.
In seismic data, regions of geological interest constitute complex structures
and underrepresented classes that frequently constitute minor portions of the
seimsic section. Consequently, blindly applying active learning algorithms can
result the selection of arbitrary sections as relevant geological areas are
neglected when combined into a single section score value. In other words, we
argue that successful data selection in seismic interpretation requires
_spatial awareness_ to informative geological regions.

This paper concerns data selection for the application of seismic
interpretation. Mainly, the paper formulates a spatially aware framework to
select the most informative seismic sections for deep learning algorithms.
From a geophysical standpoint, a common definition of informative content
would entail label ambiguity. In fact, it is common practice for different
interpreters to disagree on annotations and significantly alter
interpretations when additional information becomes available. In Figure 1a,
we show a toy example of information content for manual interpretation.
Information is measured by evaluating the disagreement ($\Delta h$) between
two separate interpretations of the same section. In this paper, we argue that
incorporating interpretation disagreement within the selection of the training
volume is both intuitive and beneficial in terms of generalization
performance. For neural networks, interpretations are based on the
mathematical representations of the individual data points within a seismic
section. As a result, disagreement between neural networks is measured in
terms of difference or _shift_ between the representations. Figure 1b, gives a
high level overview of the measurement. In order to imitate the manual
interpretation process, we leverage two separate networks and measure
disagreement through the shift between the mathematical representations
(denoted as $\Delta h$). We formalize the concept mathematically in Section
IV-A and provide an implementation of representation shift measurements in
Section IV-C.

Within our selection framework, disagreement plays an instrumental role for
identifying regions of geological interest spatially within a seismic section.
Specifically, we measure the representation shift between two separate neural
networks trained on labeled training data. Subsequently, we restrict the input
image to regions of high disagreement by masking with a representation shift
measure. The masked image is then fed to the active learning algorithm. Our
algorithm represents a strong contrast to conventional active learning where
the input image is fed to the algorithm directly. We provide a formalization
of our framework in Section IV-B. In Section IV-C, we provide an instance of
our framework, ATLAS, which significantly outperforms conventional active
learning pipelines with a variety of popular acquisition algorithms. We
perform detailed analysis and experiments in Section V, and report
improvements up to 10% in mean-intersection-over-union on a variety of popular
active learning algorithms.

In summary, the contributions of this paper are as follows:

  1. 1.

We identify representation shifts as an attractive tool for data selection in
seismic interpretation.

  2. 2.

We develop ATLAS, a plug-in algorithm for targeted data selection in seismic
interpretation.

  3. 3.

We perform empirical evaluation of ATLAS on two seismic surveys and provide
both quantitave and qualitative evidence for performance improvements up to
10% in mean-intersection-over-union on a variety of popular active learning
algorithms.

Figure 1: High-level overview of our measure of information content in seismic
interpretation. a) information content for manual interpretation. Two
different interpreters annotate the same seismic data section. Information
content is measured by the disagreement between both interpretations $\Delta
h$. b) our measure of information content with deep neural networks.
Information content is measured by the disagreement or shift between
representations of the same seismic section $\Delta h$.

##  II Related Work

###  II-A Sampling Efficiency in Seismic Interpretation

The present literature to data selection for machine learning in seismic
interpretation is relatively narrow in its coverage. Initially, deep learning
models for seismic data were predominantly developed under fully supervised
settings [8, 9]. However, the high cost associated with annotating large
volumes of seismic data presents a challenge in building large-scale models.
Consequently, researchers have explored alternative approaches, such as semi-
supervised, self-supervised, or weakly supervised methods, to alleviate the
annotation burden during model training [10, 11, 12, 13, 14, 15, 16, 17, 18].
While these approaches succeed in reducing the number of required training
sections, they are not interactive sampling strategies and therefore cannot be
considered as active learning acquisition functions.

In addition to methodological advancements, researchers have explored
different modalities and applications within seismic interpretation, each with
their own distinct data requirements. For example, fault detection has been
addressed in various studies [19, 20, 21, 22, 23, 24], while the delineation
of salt bodies has been investigated as well [25, 26, 27]. Classification of
facies, has seen contributions from multiple researchers [28, 29, 30, 12, 31].
Another area of interest involves predicting rock lithology from well logs,
where researchers have explored semi-supervised approaches [14, 32, 33, 34].
In each case, annotation requirements are unique and result in a different
annotational burden. Our work is tangential, and applicable to arbitrary
settings where annotations are limited and costly.

In all the previously discussed related work, the training set was considered
fixed without active acquisition of new training sections. Recently, a few
research directions have explored data selection pipelines, representing the
initial steps toward active learning algorithms in seismic interpretation [35,
36, 37, 38]. However, each of these approaches follows a conventional active
learning workflow where informativeness is evaluated over the entire seismic
section. The utilization of this approach for seismic data is considered
unfavorable due to the underrepresentation of geophysically significant areas,
such as faults and salt domes. These areas only contribute minimally to the
informativeness score. Our work enhances these approaches by limiting the
active learning algorithm to areas of geophysical significance, reducing the
focus on commonly occurring or well-represented structures or classes. It is
important to note that our method has the capability to be utilized with any
active learning acquisition function, which ultimately leads to a beneficial
workflow for seismic interpretation.

###  II-B Active Learning

Within the context of machine learning itself, data selection methods are well
established with extensive research in active learning active learning [39,
40, 41]. Within this context, our work strongly relates to the practical study
of different data selection functions. In our research, we draw on the
principles and methodologies of active learning, specifically focusing on the
study of various methods to acquire unlabeled data. These methods play a
crucial role in determining the importance ranking of unlabeled data points
based on their information content. We will review several prominent active
learning algorithms and differentiate them based on their respective
definitions of information content.

The first significant research direction involves defining information content
with generalization difficulty [42, 5, 43, 44]. For instance, several
approaches define informativeness with softmax probabilities [42, 43] where
information content is related to the output logits of the network. Closely
related, [44, 45] consider information in the for of decision boundary
proximity. Other directions [46] interpret generalization difficulty as model
uncertainty and establish acquisition functions with Monte-Carlo Dropout. The
second direction, defines information content based on data representation
within the dataset. Here, a popular family of algorithms construct the core-
set of the unlabeled data pool [47, 48]. Further, [49] reformulate active
learning as an adversarial training problem and [50, 51] consider prior
representative information within the data. The third category considers
combinations of generalization difficulty and data representation. In several
cases [6, 52, 53], algorithms establish a ranking based on difficulty and
sample based on representational components. [54] extend the difficulty based
algorithm [7] to diversifying batch acquisitions. Finally, [55, 56] propose
”bandit-style” algorithms that interactively alternate between difficulty-
based, and representational algorithms each active learning round. In this
paper, we benchmark our method on difficulty based approaches due to their
particular interest in seismic interpretation. In particular, seismic machine
learning workflows are frequently directed towards complex structures and
underrepresented classes (e.g. faults and salt domes); components that are
unrepresentative of the entire volume and especially targeted by difficulty-
based approaches.

Finally, several active learning algorithms exist that target semantic
segmentation explicitly [57, 58, 59]. Our work is complementary to these works
along two dimensions: first, existing approaches represent separate
acquisition functions instead of a plug-in framework applicable _on top_ of
any active learning algorithm. Hence, our approach is modular and can be
utilized in combination with current acquisition functions, as well as novel
approaches operating on seismic data. Second, current segmentation approaches
in active learning are not designed on seismic data which comes with
fundamentally different challenges. For instance, [57] label individual super-
pixels in lieu of the entire input image. While effective for several natural
image applications, the approach is not applicable to settings where data
points are labeled in their entirety; a common case in seismic data workflows.

###  II-C Deep Feature Extraction for Seismic Interpretation

Our work further relates to deep feature extraction applied to seismic
interpretation with a focus on informative representation learning. For
seismic interpretation, feature extraction is frequently studied within the
context of carefully constructed attributes. Attributes represent quantitative
measures (attributes) of interesting geological characteristics that can be
used to infer information about the subsurface [60]. The choice of these
attributes depends on the interpretation objective. For instance, several
attributes are based on geometric properties [61], [62], [63] while others are
derived from the human visual system [27, 64, 65]. More recently, the field
has been extended to utilizing deep models as powerful feature extractors [66,
16, 23]. Notably, [67] propose combining both spectral and spatial features
within the feature extractor for hyperspectral image classification.

Within the context of deep learning, our work relates to learning informative
representations. Here examples include contrastive feature learning [68, 69]
or gradient based representations [3, 53, 70]. In addition, recent
architectural advancements [71] gave rise to a set of powerful feature
extractors in the form of foundation models. Here, a wide range of foundation
models have been explored including multimodal feature learners such as CLIP
[72], MM1 [73] or LLaVa [74]; or application specific learners such as segment
anything [75], dept-anything [76], and DINOv2 [77]. The trend has since
expanded to remote sensing in the form of SpectralGPT [78]. While these works
are extract represent powerful feature extractors, they operate on the
representation directly which is undesirable when the representation is
inaccurate. Our work complements these approaches by extracting information or
features from representation shifts rendering a robust alternative for seismic
interpretation.

##  III Background

In this section, we introduce definitions and notations for both active
learning and semantic segmentation within the context of seismic
interpretation.

###  III-A Notation and Problem Setup

In this paper, we view seismic interpretation as a semantic segmentation task.
We model a conditional distribution $p^{*}(\mathbf{y}|\mathbf{x})$ with a deep
model $p_{w}(\mathbf{y}|\mathbf{x})=h_{w}(\mathbf{x})$ where
$\mathbf{x}\in\mathcal{X}\subset\mathbb{R}^{HxW}$ represents the an
in-/crossline from the target volume $\mathcal{X}$. Further,
$\mathbf{y}\in\\{1,..,K\\}^{HxW}$ represents the interpretation label with $K$
subsurface categories and $p_{w}$ the conditional distribution of the neural
network with weight parameters $w$. In practice, the weight parameters are
optimized from training data $\mathcal{D}=\\{y_{i},x_{i}\\}_{i=1}^{N}$
collected from a subset of the full input space
$\mathcal{X}_{ID}\subset\mathcal{X}$. Consequently, the target distribution
$p^{*}$ consists of an in-distribution component (ID)
$p^{*}(y|\mathbf{x},\mathbf{x}\in\mathcal{X}_{ID})$, as well as an out-of-
distribution (OOD) $p^{*}(y|\mathbf{x},\mathbf{x}\notin\mathcal{X}_{ID})$
component which is not supported by the training data [79]:

$\begin{split}p^{*}(y|\mathbf{x})=&p^{*}(y|\mathbf{x},\mathbf{x}\in\mathcal{X}_{ID})*p^{*}(\mathbf{x}\in\mathcal{X}_{ID})+\\\
&p^{*}(y|\mathbf{x},\mathbf{x}\notin\mathcal{X}_{ID})*p^{*}(\mathbf{x}\notin\mathcal{X}_{ID}).\end{split}$
(1)

During training, the model learns the in-distribution component
$p^{*}(\mathbf{y}|\mathbf{x},\mathbf{x}\in\mathcal{X}_{ID})$ but does not have
access to $p^{*}(\mathbf{y}|\mathbf{x},\mathbf{x}\notin\mathcal{X}_{ID})$. As
a result, predictions on out-of-distribution volumes
$\mathbf{x}\notin\mathcal{X}_{ID}$ are arbitrarily incoherent and may
significantly differ from the underlying geology.

###  III-B Active Learning

In active learning [4], the objective involves maximizing neural network
performance under minimal data annotations. We consider a dataset
$\mathcal{D}$ where the subset $\mathcal{D}_{train}$ represents the current
set of annotated sections and $\mathcal{D}_{pool}$ the unlabeled target
subset. Using the above notation, the input domain reduces to the union of
both $\mathcal{D}_{train}$ and $\mathcal{D}_{pool}$ \- i.e.
$\mathcal{D}_{train}\cup\mathcal{D}_{pool}=\mathcal{X}_{ID}$ where
$\mathcal{D}_{train}\cap\mathcal{D}_{pool}=\emptyset$. In batch active
learning, the algorithm selects the most informative batch of $b$ sections
$\mathbf{X^{*}}=\\{\mathbf{x^{*}_{1}},...,\mathbf{x^{*}_{b}}\\}$ that, when
annotated, result in the highest interpretation performance of the network.
Formally, we define the selection of $\mathbf{X^{*}}$ as

$X^{*}=\operatorname*{argmax}_{\mathbf{x_{1}},...,\mathbf{x_{b}}\in
D_{pool}}a(\mathbf{x_{1}},...,\mathbf{x_{b}}|h_{w}).$ (2)

Here, $a$ represents the acquisition function mapping sections individually
(or collectively) to a single value of informativeness defined differently
across active learning algorithms.

##  IV Methodology

###  IV-A Representation Shifts

Within Equation 2 we observe the direct dependency to the model representation
$h_{w}(\mathbf{x})$. While effective within the general context of computer
vision, the characteristic is undesirable for seismic active learning
applications:

First, seismic interpretation settings struggle under limited annotated data.
Due to the high time and monetary cost, sparse training sets with a handful of
annotated sections are common settings in seismic interpretation. Within the
context of active learning, the characteristic results in significantly less
samples within the initial training pool as well as a reduced acquisition
batch size. As a result, model representations $h_{w}(\mathbf{x})$ can overfit
to the training domain $\mathcal{D}_{train}$ and collapse knowledge of the
domain distribution $p^{*}(\mathbf{x}\in\mathcal{X}_{ID})$ or the unlabeled
target subset $p^{*}(\mathbf{x}\in\mathcal{D}_{train})$ respectively; A
phenomenon referred to as feature collapse [80]. For machine learning
paradigms such as active learning, knowledge of the domain distribution
contributes to less randomization within the selection algorithm. We show a
toy example of feature collapse in Figure 2. On the left, we show
representations of a model trained with significant training data. Here, the
active learning algorithm accurately selects informative samples (e.g. data
points close to the decision boundary). In contrast, when limited data is
available the representations can collapse features and results in selection
randomization as different points are difficult to distinguish from each
other.

A second major challenge in seismic data is label ambiguity. Specifically,
annotations in seismic interpretations can differ depending on the annotator
or due to information availability. Consequently, high data noise causes the
network to associate structures and features to incorrect facies, rendering
the representation inaccurate for active learning.

Figure 2: Toy example of an a acquisition batch selection with an accurate
representation (left) and a representation suffering under feature collapse.
The collapsed representation results in a significant randomization within the
selection algorithm.

In light of the severe disadvantages, a more prudent strategy involves
deriving relevant distributional characteristics from the representation
indirectly through representation shifts. Within this context, we consider two
separate models $h_{w_{1}}$ and $h_{w_{2}}$ derived from an optimization
process over $D_{train}$. We define a representation shift $\Delta
h(\mathbf{x})$ as a suitable distance metric $\mathbf{d}$ between
$h_{w_{1}}(\mathbf{x})$ and $h_{w_{2}}(\mathbf{x})$:

$\begin{split}\Delta
h(\mathbf{x})=\mathbf{d}(h_{w_{1}}(\mathbf{x}),h_{w_{2}}(\mathbf{x})).\end{split}$
(3)

From a machine learning perspective, representation shifts are more robust to
feature collapse as they are measured from the model dynamics indirectly
instead of originating from a possibly inaccurate data representation
$h_{w}(\mathbf{x})$. To illustrate the robustness process, we show a toy
example of representation shifts in Figure 3. While both models
$h_{w_{1}}(\mathbf{x})$ and $h_{w_{2}}(\mathbf{x})$ are trained on limited
data and suffer under feature collapse, we can differentiate data points even
though the majority of samples are collapsed to similar positions within the
model manifold.

Figure 3: Toy example of a representation shift under feature collapse applied
to a binary classification problem. Left: the model representation of
$h_{w_{1}}(\mathbf{x})$. Right: the model representation of
$h_{w_{1}}(\mathbf{x})$.

Apart from mathematical advantages, representation shifts have an intuitive
interpretation within the context of geophysics. Specifically, we can view
$h_{w_{1}}(\mathbf{x})$ and $h_{w_{2}}(\mathbf{x})$ as two separate
interpretations of the same section and $\mathbf{d}$ as a measure of
disagreement between the two. Thus, our approach intuitively models a
practical interpretation workflow for geophysical applications.

###  IV-B Spatially Aware Active Learning

In the previous section, representation shifts were introduced to capture
disagreement information in seismic interpretation. Within the following
section, representation shifts are applied to active learning to extract
regions of geophysical interest from an unlabeled seismic section. Using our
previous notation, we reduce the randomization occurring due to feature
collapse by focusing our selection on interesting structures or textures
within the seismic section. More formally, given a seismic section
$\mathbf{x}$, we want to filter relevant geological areas $\phi(\mathbf{x})$
that contain distributional information within the model manifold
$h_{w}(\mathbf{x})$. Applied to Equation 2, the selection of the next set of
sections $X^{*}$ amounts to

$X^{*}=\operatorname*{argmax}_{\phi(\mathbf{x_{1}},h_{w}),...,\phi(\mathbf{x_{b}},h_{w})\in
D_{pool}}a(\phi(\mathbf{x_{1}},h_{w}),...,\phi(\mathbf{x_{b}},h_{w})|h_{w}),$
(4)

where $\phi:\mathbb{R}^{HxW}\rightarrow\mathbb{R}^{HxW}$ is broadly defined as

$\phi(\mathbf{x},h_{w})=\mathbf{x}*m(\mathbf{x},h_{w}).$ (5)

Here, $m:\mathbb{R}^{HxW}\rightarrow\\{0,1\\}^{HxW}$ represents a binary
function that maintains seismic traces containing relevant information and
removes redundancies. We refer to paradigms based on Equation 4 as _Spatially
Aware Active Learning_. In Figure 4b, we provide an overview of the spatially
aware active learning workflow with the embedded disagreement filter $\phi$.
Instead of directly feeding the representation of the entire sectoin into the
active learning algorithm, the disagreement filter reduces the active learning
input to regions of geophysical interest.

###  IV-C Active Transfer Learning for Attention Sensitivity

Within this subsection, we propose a concrete implementation of the filter
$\phi$ with representation shifts. We illustrate the workflow in Figure 4a.
For every unlabeled section, we extract the model predictions from the
current, and previous active learning round ($n$ and $n-1$ respectively) and
perform a prediction comparison. We filter regions where the interpretations
disagree and allow the acquisition function to process sections based on the
conflicting regions exclusively. We consider our algorithm an added attention
mechanism to regions of geophisical interest and call our plug-in method
_Active Transfer Learning for Attention Sensitivity_ or ATLAS in short. Within
the following paragraphs, we formalize the concept with an explicit expression
for $\phi$.

Within the context of Equation 3, deriving the prediction difference is
equivalent to monitoring representation shifts with respect to individual
traces or pixels. Applied to the entire section, $\Delta
h(\mathbf{x})\in\\{0,1\\}^{HxW}$ reduces to a binary heatmap with each pixel
$k$ indicating a prediction switch or conflict in between the predictions of
both active learning rounds. More formally, we define an individual trace
$k\in\\{0,...,H*W-1\\}$ of $\Delta h$ as

$\Delta
h(\mathbf{x})_{k}=int(\tilde{y}^{n}_{k}(\mathbf{x})\neq\tilde{y}^{n-1}_{k}(\mathbf{x}))=s_{k}(\mathbf{x}).$
(6)

Here,
$\tilde{y}^{n}_{k}(\mathbf{x})=\operatorname*{argmax}_{c\in\\{1,...,K\\}}h_{w_{n}}^{c}(\mathbf{x})$
represents the predicted class when using the fully trained model from the
$n$-th active learning round $h_{w_{n}}$. Consequently, we define $\phi$ as a
multiplication with the binary heatmap $\Delta h(\mathbf{x})_{k}$:

$\phi(\mathbf{x},h_{w})=\mathbf{x}*\Delta h(\mathbf{x}).$ (7)

We emphasize that Expression 3 represents a generalized version of the
explicit implementation in ATLAS. Specifically, $h_{w_{1}}$ and $h_{w_{2}}$
translates to $h_{w_{n}}$ and $h_{w_{n-1}}$ respectively and the distance
metric $\mathbf{d}$ is represented by the binary prediction switch image
$\mathbf{s}$. While beyond the scope of this paper, we note that different
implementations of $\Delta h$ and $\phi$ are possible and left for future
research.

Figure 4: a) high-level workflow of our plug-in active learning framework,
ATLAS. For each unlabeled section, we extract the predictions from both the
current round as well as the previous round and derive the prediction
difference. Subsequently, we filter regions where the predictions conflict,
and process the disagreeing regions by the active learning algorithm
exclusively. b) spatially-aware active learning workflow. The active learning
framework is modified by introducing a disagreement filter that restricts the
input of the active learning algorithm to regions of geological interest.

##  V Experiments

Within this section, we address the following questions: 1) how does ATLAS
perform in combination with several active learning acquisition functions? 2)
are improvements consistent across several test volumes?; and 3) which regions
does ATLAS generally target?

###  V-A Experimental Setup

Figure 5: Training and test split of both seismic datasets. a) The F3 dataset
located in the Netherlands. We use the split of [31] with one contiguous
training, as well as two test volumes. b) The Parihaka volume from New
Zealand. We split the volume into one contiguous training and test volume.

For our active learning experiments, we select two random sections within the
training volume as our initial $D_{train}$ and select two additional sections
each active learning round for annotation. We select a small acquisition batch
size of two as it represents a realistic magnitude for the application of
seismic interpretation. For our active learning benchmark, we analyze the
performance of ATLAS by comparing different acquisition functions with and
without applying ATLAS. Specifically, we compare ATLAS to ranking
informativeness based on the entire section $\mathbf{x}$ instead of the
spatially targeted subsection $\phi(\mathbf{x})$. In all experiments, our
architecture is based on the deeplab-v3 architecture first proposed by [81].
If not otherwise specified, we implement the backbone with a resnet-18 [82]
feature extractor, and optimize using the adam variant of stochastic gradient
descent with a learning rate of $5e^{-5}$. During each active learning round,
we train the model until it achieves an at least an mean-intersection-over-
union (mIoU) performance of $0.9$ and log performance on the test volume in
overall mIoU, as well as class accuracy. All experiments are conducted over
five separate random seeds.

In this paper, experiments are provided on two different seismic data volumes.
The first is the F3 benchmark located in the Netherlands [31], with
annotations corresponding to six different facies categories. To facilitate
conditions of the original paper, we use the same experimental setup as the
original paper: we use the pre-processed volume provided by the original
implementation, and split the volume according to the initial benchmark. The
partition contains one contiguous training set, and two test volumes (Figure
5a). The second volume is the publicly available Parihaka dataset located in
New Zealand. The seismic data is provided by New Zealand Petroleum and
Minerals, while the associated labels are provided from Chevron U.S.A. Inc.,
and are licensed under CC BY-SA 4.0. Similar to F3, the labels include
annotations for six different facies. Before training, the seismic dataset is
clipped within the range of $[-1500,1500]$, and sub-sampled in depth direction
by factor three. Further, we remove the first 200 and deepest 42 depth slices
as they contain the same classes throughout the volume and are not informative
to the training process. As annotations for the original test volume are not
publicly available, we split the original training volume as shown in Figure
5b. We choose this partition due to class representation and to facilitate
structural variability between training and test volume, making the dataset
more challenging. We make our code publicly available at PLACEHOLDER.

TABLE I: Average accuracy, and standard deviation on the F3 dataset.
Algorithms | mIoU | Upper N.S. | Mid. N.S. | Lower N.S. | Chalk. | Scruff | Zechstein
---|---|---|---|---|---|---|---
Entropy |  0.591 ± 0.014 |  0.975 ± 0.001 |  0.846 ± 0.012 |  0.950 ± 0.003 |  0.636 ± 0.009 |  0.373 ± 0.042 |  0.461 ± 0.010
ATLAS Entropy |  0.620 ± 0.009 |  0.976 ± 0.001 |  0.872 ± 0.007 |  0.957 ± 0.001 |  0.651 ± 0.014 |  0.495 ± 0.028 |  0.417 ± 0.071
Margin |  0.574 ± 0.017 |  0.977 ± 0.002 |  0.840 ± 0.012 |  0.951 ± 0.003 |  0.643 ± 0.012 |  0.305 ± 0.079 |  0.424 ± 0.055
ATLAS Margin |  0.612 ± 0.005 |  0.976 ± 0.001 |  0.858 ± 0.013 |  0.952 ± 0.002 |  0.652 ± 0.016 |  0.440 ± 0.019 |  0.500 ± 0.025
Least Conf. |  0.575 ± 0.022 |  0.970 ± 0.005 |  0.808 ± 0.025 |  0.944 ± 0.010 |  0.637 ± 0.022 |  0.388 ± 0.041 |  0.430 ± 0.046
ATLAS Least Conf. |  0.619 ± 0.006 |  0.974 ± 0.003 |  0.869 ± 0.006 |  0.956 ± 0.002 |  0.653 ± 0.013 |  0.480 ± 0.026 |  0.459 ± 0.046

###  V-B Numerical Experiments

In active learning, the sampling performance can vary across different rounds.
For this purpose, we summarize the overall performance of an active learning
algorithm by using the average accuracy metric [5, 52]. Specifically, we
integrate over the accuracy curve and normalize by the number of acquired
sections. Specifically, given a total number of rounds $R$, as well as the
evaluation metric $metric(r)$ for every round $r$, the average accuracy
$P_{acc}$ is defined as

$P_{acc}=\frac{1}{R}\int_{r}metric(r)\,dr.$ (8)

For our numerical analysis, we benchmark three popular active learning
acquisition functions in combination with ATLAS: entropy sampling [42], margin
sampling [43], and least confidence sampling [42]. We choose these strategies
as they represent popular difficulty based active learning approaches that are
of particular interest to seismic interpretation as areas of geological
interest are frequently concentrated in regions if high learning difficulty
[83]. In Table I and Table II, we report our results on average accuracy in
mIoU, as well as class-wise accuracy across the F3 block, and Parihaka dataset
respectively. We show the average accuracy for each metric in mean and
standard deviation.

In all settings, ATLAS results in either an improvement or a statistically
insignificant difference to the baseline. The observation reflects in the
overall mIoU performance across all classes. For each acquisition function,
ATLAS shows a significant improvement of up to approximately 4% on the F3
block, and 12% on the Parihaka volume. The improvements are agnostic to class
frequency in the volume: for F3, class accuracy is increased both within
common classes such as the middle and lower north sea group, as well as
underrepresented such as scruff; the rarest class within both training and
test sets. We reason that regions with high representation shifts are
particular common around class boundaries, regardless of class frequency.
Therefore, ATLAS targets structurally interesting regions in both well
represented, as well as less represented classes. For the Parihaka volume,
ATLAS boosts performance in nearly every class by a significant margin; even
more so as on the F3 dataset. We attribute the strong performance to the
structure of the facies. Within the F3 block, rare classes are concentrated in
salt domes or are densely located in deeper regions with less surface
boundaries between other classes. In contrast, the Parihaka volume contains
underrepresented facies (e.g. slope valley) that are thin layers between well
represented classes. As ATLAS emphasizes class boundaries it is more effective
in selecting geologically different regions on the Parihaka dataset due to the
large surface boundaries of underrepresented classes. We perform a detailed
analysis of the learning curves in Section V-C.

###  V-C Learning Curves

Within this subsection, we analyze the explicit learning curves of the
individual active learning algorithms in combination with ATLAS. In Figure 6,
we show the total mIoU on the inlines of both the first and second test volume
of the F3 block, where the second represents the more difficult of the two.
Figure 8, shows the mIoU on the Parihaka test volume inlines and crosslines.
The rows present test set one and two, or in-/crossline respectively, while
the columns show the individual algorithms entropy, margin, and least
confidence with and without ATLAS. The shaded region represents the 95%
confidence interval with respect to the five random seeds.

Our plots support our numerical analysis. In all experiments, ATLAS matches or
improves the baseline performance in all three algorithms in nearly every
round. Within the F3 volume, ATLAS is particularly effective on the simpler
test set in early rounds, and on the difficult test 2 volume in later rounds.
For instance, deploying ATLAS on the margin algorithm results in a significant
improvement on test set one in rounds four to eleven, while ATLAS strongly
outperforms on test two in round 8 and onwards. We reason that switches occur
frequently in simple structures within early active learning rounds as complex
structures are more challenging with small training sets. As a result, common
structures result in significant shifts and are queried by ATLAS rendering a
strong performance on the less difficult test one volume. In contrast, rare
structures or classes are not sufficiently represented enough in early rounds
and the model consistently misclassifies difficult samples [83]. Therefore,
difficult structures are queried in later rounds when the model representation
is mature with more representation shifts. On the Parihaka dataset, the
baseline algorithm and ATLAS follow different trends. ATLAS increases the
mIoU, while the baseline strategy stagnates or even reduces the performance.
We attribute the behavior to the structure of the facies in the Parihaka
dataset. ATLAS is effective on volumes where geophysically interesting regions
share large class boundaries. For facies that exhibit a thin layer structure
as is present in Parihaka, representation shifts concentrate around thin
underrepresented classes giving the regions more weight in the selection
process. In contrast, the baseline algorithm evaluates the acquisition
function on the entire section, biasing the selection process to well-
represented regions. Note that both strategies eventually converge to the same
performance when the entire training volume is queried. In Section V-D, we
provide an additional analysis of ATLAS by considering the network
predictions.

Figure 6: Learning curves of entropy, margin, and least confidence sampling in
combination with ATLAS on the F3 dataset. We show the overall mIoU performance
on test set one in the first row, and test set two in the second.

In addition to overall mIoU, we report the class accuracy learning curves of
chalk, scruff, and zechstein classes from the F3 block in Figure 7. For
simplicity, we report chalk using least confidence, scruff with entropy, and
zechstein with margin sampling even though the trend is largely consistent
accross the volume. In Figure 7, we show test two inlines exclusively as it
represents the more difficult challenge with complex structures. Similar to
our previous observations, our results are consistent with both the learning
curves on overall mIoU, as well as our numerical experiments in Table I. ATLAS
either matches or improves the baseline algorithm even in underrepresented
settings.

Figure 7: Class accuracy learning curves of entropy, least confidence, and
margin sampling in combination with ATLAS. We show the class accuracy of the
underrepresented classes chalk, scruff and zechstein. TABLE II: Average
accuracy, and standard deviation on the Parihaka dataset.
Algorithms | mIoU | Basement | Mudstone A | Mass Tr. Dep. | Mudstone B | Slope Valley | Canyon Sys.
---|---|---|---|---|---|---|---
Entropy |  0.364 ± 0.013 |  0.932 ± 0.011 |  0.752 ± 0.017 |  0.335 ± 0.071 |  0.620 ± 0.011 |  0.133 ± 0.007 |  0.256 ± 0.123
ATLAS Entropy |  0.481 ± 0.003 |  0.967 ± 0.003 |  0.797 ± 0.002 |  0.644 ± 0.023 |  0.738 ± 0.014 |  0.266 ± 0.022 |  0.387 ± 0.011
Margin |  0.400 ± 0.014 |  0.919 ± 0.029 |  0.777 ± 0.009 |  0.305 ± 0.081 |  0.720 ± 0.008 |  0.112 ± 0.080 |  0.370 ± 0.098
ATLAS Margin |  0.518 ± 0.028 |  0.969 ± 0.002 |  0.808 ± 0.008 |  0.687 ± 0.053 |  0.775 ± 0.013 |  0.374 ± 0.064 |  0.422 ± 0.049
Least Conf. |  0.381 ± 0.022 |  0.895 ± 0.029 |  0.762 ± 0.004 |  0.290 ± 0.042 |  0.689 ± 0.033 |  0.134 ± 0.032 |  0.292 ± 0.050
ATLAS Least Conf. |  0.478 ± 0.006 |  0.969 ± 0.003 |  0.796 ± 0.005 |  0.653 ± 0.021 |  0.735 ± 0.007 |  0.269 ± 0.016 |  0.360 ± 0.010
Figure 8: Learning curves of entropy, margin, and least confidence sampling in
combination with ATLAS on the Parihaka dataset. We show the overall mIoU
performance on test set inlines in the first row, and test set crosslines in
the second.

###  V-D Predictions

In addition to numerical metrics, we directly compare the network predictions
of ATLAS with the baseline algorithm. In Figure 9, we show the network
predictions of least confidence sampling, as well as least confidence in
combination with ATLAS. To facilitate accurate comparison, the manual
interpretation is plotted in the third column. From a machine learning
perspective, manual interpretation represents the target that the model aims
to approximate with maximum precision. All predictions depicted in Figure 9
are derived from round seven for the Parihaka dataset, and round 14 for the F3
block. Overall, we note an improved segmentation performance within the output
predictions. The baseline algorithm exhibits significantly more semantically
incorrect predictions and fails in complicated structures. In contrast, adding
ATLAS reduces mispredictions and results in less sporadic outputs. For the F3
block, the baseline algorithm on inline zero in test set one predicts a large
scruff (orange class) and zechstein (red class) region in the top right corner
even though both classes exclusively appear in deeper regions at the bottom of
the section (Figure 9b violet circle). In combination with ATLAS, the
misprediciton nearly disappears (Figure 9a violet circle). Further we note
that the horizon predictions in well represented classes such as the upper,
middle, and lower north sea groups are spatially consistent and less sporadic.
This is particularly visible in Figure 9a-b, over the left large scruff mound
(green circle). The baseline algorithm predicts the upper north sea group
(dark blue) directly next to chalk and above the scruff mound; a incorrect
prediction as the middle north sea group occurs in between the upper and lower
north sea group exclusively. The mispredictions are resolved when utilizing
ATLAS. The analysis of the crossline from test volume two (Figure 9d-e)
reveals that networks trained with ATLAS exhibit superior performance in
accurately representing intricate structures. The salt dome structure located
on the bottom left (violet circle) is depicted with greater accuracy when
trained using ATLAS, as opposed to the baseline approach. On the Parihaka
dataset, we note the clear difference in facies structure compared to the F3
block. Rare classes such as slope valley are located in shallower regions and
represent layers instead of dense mounds (Marked by the white arrow in Figure
9j, and l). As a result the class boundary areas are larger than F3 resulting
in stronger representation shifts in geologically interesting regions. In the
predictions the effect manifests in significantly improved performance. In
Figure 9g, h, j, and k the structure of the canyon system (red; marked by
violet circle) and basement (dark blue; marked by green circle) is thoroughly
visible and less sporadic with ATLAS. Further, underrepresented classes such
as slope valley (orange; Figure 9j, and k white arrow) are significantly
better preserved with ATLAS indicating a more effective sampling framework.

Figure 9: Network predictions in comparison to manual interpretation for the
F3 block and Parihaka dataset. The first two rows show predictions in round 14
from the F3 dataset, the bottom two rows are predictions from round seven on
the Parihaka dataset. We compare least confidence sampling to least confidence
in combination with ATLAS. The first column contains least confidence in
combination with ATLAS, the second contains the least confidence baseline, and
the third the manual interpretation by an expert.

###  V-E Representation Shifts

Within this subsection, we visualize the regions ATLAS selects. For this
purpose, we monitor the prediction switches for the unlabeled pool and
accumulate the shifts of each pixel across the entire active learning
experiment. In Figure 10, the heatmaps represent the accumulation of
prediction switches over 21 active learning rounds with least confidence
sampling. All heatmaps originate from the F3 block. We show both sections with
interesting structures and underrepresented classes, as well as simpler
sections that are easier for the network to learn. Within the Figure, large
amounts of representation shifts are color-coded as red while blue indicates
the opposite. We note, that prediction switches largely occur either in class
boundaries or difficult structures and underrepresented classes. For instance,
in Figure 10a, and c, the salt dome his highlighted, sub-regions with complex
structures: in Figure 10a, the boundary in between zechstein and the middle
north sea group is brightly highlighted (white arrow with red contours). A
similar observation can be made for Figure 10c, where the salt dome is
highlighted (white arrow with green contours). ATLAS focuses on these areas,
while the baseline algorithms average over the entire section. The highlighted
regions further support our performance analysis and provide a conceptual
explanation to the strong performance of ATLAS.

Figure 10: Number of representation shifts measured in prediction switches per
pixel. Red regions represent large amounts of prediction switches, while blue
regions represent the opposite. The first two rows show the unlabeled volume
$D_{pool}$ in inline zero and 310 respectively, while row three and four show
crossline 180 and 550. The first column shows the representation shift
heatmpas in round 20 as produced by least confidence sampling with ATLAS, the
second depicts the manual interpretation label. We further highlight regions
of high representation shift density with a white arrow. ATLAS focuses on
these regions within the selection, while conventional active learning
averages over the entire section.

##  VI Summary and Discussion

###  VI-A Summary

In this paper, we propose incorporating interpretation disagreement in data
selection pipelines for deep models in seismic interpretation. First, the
paper establishes a definition of information content for manual
interpretation workflows in the form of disagreement among interpreters. The
definition is grounded in a machine learning context by considering the shift
between mathematical representations as disagreement among deep models.
Combined with active learning, the paper develops a novel framework to select
the most informative sections of an unlabeled seismic volume to maximize the
generalization performance. Finally, a concrete implementation of the
framework is proposed called ATLAS. In conclusion, ATLAS has led to
enhancements in the data selection process for seismic interpretation. We
conducted comprehensive experiments to evaluate the performance of ATLAS and
our findings indicate a noteworthy enhancement of up to 10% when compared to
the baseline active learning strategy.

###  VI-B Discussion and Future Research

A key observation we made in this paper is that utilizing representation
shifts rather than direct network outputs can benefit the generalizability of
neural networks in seismic interpretation. We investigated one concrete form
of representation shift, namely disagreement to identify relevant regions
within a seismic section. While we benchmark our method within the context of
data selection, we emphasize that our method can be generalized to a wide
range of applications within seismic interpretation. For instance,
disagreement may provide an effective measure of uncertainty or of performance
degradation. Further, we note that our investigation only focused on one form
of representation shifts, namely disagreement with prediction switches. While
our initial results are encouraging, we note that our implementation reduces
representation shifts to a binary prediction switch which results in a
significant information loss. In this context, we see another important
research direction in investigating other forms of representation shifts that
are non-binary and could provide a richer understanding of the deep neural
network.

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##  VII Acknowledgements

This work is supported by the Industry Supported ML4Seismic Consortium at
Georgia Tech.

##  VIII Biography Section

|  Ryan Benkert received his Ph.D. degree in electrical engineering from the
Georgia Institute of Technology (Georgia Tech), Atlanta, Georgia, 30332, USA,
in 2024. He is currently a deep learning software engineer at NVIDIA in Santa
Clara, CA. His research interests are at the intersection of active learning,
uncertainty estimation, and performance consistency in neural network
learning. Prior to Georgia Tech, he received his B.Sc and M.Sc from the RWTH
Aachen University in Germany. He is the recipient of the Otto-Junker award for
his achievements during his graduate studies at the RWTH Aachen in Germany.
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|  Mohit Prabhushankar received his Ph.D. degree in electrical engineering
from the Georgia Institute of Technology (Georgia Tech), Atlanta, Georgia,
30332, USA, in 2021. He is currently a Postdoctoral Research Fellow in the
School of Electrical and Computer Engineering at the Georgia Institute of
Technology in the Omni Lab for Intelligent Visual Engineering and Science
(OLIVES). He is working in the fields of image processing, machine learning,
active learning, healthcare, and robust and explainable AI. He is the
recipient of the Best Paper award at ICIP 2019 and Top Viewed Special Session
Paper Award at ICIP 2020. He is the recipient of the ECE Outstanding Graduate
Teaching Award, the CSIP Research award, and of the Roger P Webb ECE Graduate
Research Assistant Excellence award, all in 2022. He has delivered short
courses and tutorials at IEEE IV’23, ICIP’23, BigData’23, WACV’24 and AAAI’24.
---|---
|  Ghassan AlRegib is currently the John and Marilu McCarty Chair Professor in
the School of Electrical and Computer Engineering at the Georgia Institute of
Technology. In the Omni Lab for Intelligent Visual Engineering and Science
(OLIVES), he and his group work on robust and interpretable machine learning
algorithms, uncertainty and trust, and human in the loop algorithms. The group
has demonstrated their work on a wide range of applications such as Autonomous
Systems, Medical Imaging, and Subsurface Imaging. The group is interested in
advancing the fundamentals as well as the deployment of such systems in real-
world scenarios. He has been issued several U.S. patents and invention
disclosures. He is a Fellow of the IEEE. Prof. AlRegib is active in the IEEE.
He served on the editorial board of several transactions and served as the TPC
Chair for ICIP 2020, ICIP 2024, and GlobalSIP 2014. He was area editor for the
IEEE Signal Processing Magazine. In 2008, he received the ECE Outstanding
Junior Faculty Member Award. In 2017, he received the 2017 Denning Faculty
Award for Global Engagement. He received the 2024 ECE Distinguished Faculty
Achievement Award at Georgia Tech. He and his students received the Best Paper
Award in ICIP 2019 and the 2023 EURASIP Best Paper Award for Image
communication Journal.
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