Raw Nav-merge Seismic Data to Subsurface Properties with MLP based Multi-Modal Information Unscrambler
Authors: Aditya Desai
Zhaozhuo Xu
Menal Gupta
Anu Chandran
Antoine Vial-Aussavy
Anshumali Shrivastava
Venue: NeurIPS 2021 Poster (2021)
Keywords: seismic inversion
sustainability
seismic data ingestion

Abstract: Traditional seismic inversion (SI) maps the hundreds of terabytes of raw-field data to subsurface properties in gigabytes.  This inversion process is expensive, requiring over a year of human and computational effort. Recently, data-driven approaches equipped with Deep learning (DL) are envisioned to improve SI efficiency.  However, these improvements are restricted to data with highly reduced scale and complexity. To extend these approaches to real-scale seismic data, researchers need to process raw nav-merge seismic data into an image and perform convolution. We argue that this convolution-based way of SI is not only computationally expensive but also conceptually problematic. Seismic data is not naturally an image and need not be processed as images. In this work, we go beyond convolution and propose a novel SI method. We solve the scalability of SI by proposing a new auxiliary learning paradigm for SI (Aux-SI). This paradigm breaks the SI into local inversion tasks, which predicts each small chunk of subsurface properties using surrounding seismic data. Aux-SI combines these local predictions to obtain the entire subsurface model. However, even this local inversion is still challenging due to: (1) high-dimensional, spatially irregular multi-modal seismic data, (2) there is no concrete spatial mapping (or alignment) between subsurface properties and raw data. To handle these challenges, we propose an all-MLP architecture,  Multi-Modal Information Unscrambler (MMI-Unscrambler), that unscrambles seismic information by ingesting all available multi-modal data. The experiment shows that MMI-Unscrambler outperforms both SOTA U-Net and Transformer models on simulation data. We also scale MMI-Unscrambler to raw-field nav-merge data on Gulf-of-Mexico to obtain a geologically sound velocity model with an SSIM score of 0.8. To the best of our knowledge, this is the first successful demonstration of the DL approach on SI for real, large-scale, and complicated raw field data. 

Raw Nav-merge Seismic Data to Subsurface Properties with MLP-based Multi-Modal Information Unscrambler
Aditya Desai' Rice University apd109rice.edt edu
Zhaozhuo Xu" Rice University zx220rice.. edu
Menal Gupta
Shell Exploration & Production Company Menal. Cuaall.upta@heell.com com
Anu Chandran
Antoine Vial-Aussavy
Shell India Markets Private Limited com
Shell Exploration & Production a. viial v.iaa-AAsssayyshhlllccom
Anu.
Anshumali Shrivastava Rice University and ThirdAl Corp. dishumal@@ricm edu
Abstract
Traditional seismic inversion (SI) maps the hundreds of terabytes of raw-field data subsurface properties in gigabytes. This inversion process is expensive, requiring over year of human and computational effort, Recently, data-driven ap- proaches equipped with Deep learning (DL) are envisioned to improve SI efficiency, However, these improvements are restricted to data with highly reduced scale and complexity. To extend these approaches to real-scale seismic data, researchers need to process raw nav-merge seismic data into an image and perform convolution. We argue that this convolution-basee way of SI is not only computationally expensive but also conceptually problematic. Seismic data is not naturally an image and need not be processed as images. this work, we go beyond convolution and propose novel SI method. We solve the scalability of SI by proposing new auxiliary learning paradigm for SI (Aux-SI), This paradigm breaks the SI into local inversion tasks, which predicts cach small chunk of subsurface properties using surrounding scismic data. Aux-SI combines these local predictions to obtain the entire subsurface model. However, even this local inversion is still challenging duc to: (1) high-dimensional, spatially irregular modall scismic data, (2) there is conerete spatial mapping (or alignment) between subsurface properties and raw data. To handle these challenges, we propose an all-MLP architecture, Multi- Modal Information Unscrambler
that unscrambles seismic information by ingesting all available multi-modal data. The experiment shows that UMsl-unsrambllr outperforms both SOTA U-Net and Transformer models simulation data. We also scale MMI-Unscrambler to raw-field nav-merge data on Gulf-of-Mexico obtain geologically sound velocity model with SSIM score of 0.8. To the best of our knowledge, this is the first successful demonstration of the DL approach on SI for real, large-scale. and complicated raw field data.
"indicttes equal contribution
35th Conference on Neural Information Processing Systems (NeurIPS 2021).

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Acquastion Menthe)
Traditional Work Flow
1000 V911
Data Driven Work Flow
Raw Data
Shot Proceesing (6 munths)
Model Buildng (3 Morthhs)
Migration Welcity model refinement (6 Months)
Inversion: Getting subsurface Modal (6 Morihhs
Reflectiity Buildnn (A (ooon)))
Subsuriace Model
Oebrra
Deadda
Setemic
(b) Traaiiiaditi workflow involved in seismic processing of raw data to get a subsurface model. It requires approximately over an year time to generate a subsurface image. Data-driven workflows try to bypass this ledious process by direclly predicting subsurface model from raw data, Right: Reflection Seismology for collecting seismic data: Mechanical Perturbation (sound wave) created at source, propagates through layers of earth and reflects subsurface boundaries. The receivers record amplitude time-series information.
(a)
Figure 1:
Introduction
Seismic reflection data records the amplitude of reflected waves from the subsurface of the earth. Geophysicists perform Seismic Inversion (SI) on this data to generate the earth's 's subsurface properties. However, seismic data is known be notoriously difficult to analyse. The sheer scale of the seismic data is extremely large. For example, survey over region (100Km 100Km) inside gulf of mexico generates hundreds of terabytes of data. Moreover, the data highly complex. There is no concrete spatial mapping between subsurface properties and observed data. Furthermore, cach recording captures superimposed information of the entire subsurface. These characteristics make information unscrambling hard task in SI. Traditional approaches are loyyscs--rrvenn which require extensive amount of human expertise and time. Recently, there is an increasing interest in using deep learning (DL) to solve SI efficiently. However, current DL research in SI restricts to synthetic data and is difficult to scale to real SI settings. In this work, we solve the scalability of SI by proposing a new auxiliary learning paradigm for SI (Aux-SI). In this paradigm, we break the SI into local inversion tasks, which predicts each small chunk of subsurface properties using surrounding seismic data, Aux-SI combines these local predictions to obtain the entire subsurface model. However, even this local inversion is challenging. Firstly, the geometry of data acquisition is highly irregular. This, along with the fact that data is high dimensional (dimension > 5) puts natural choices like CNN at a disadvantage. Secondly, the seismic data is multi- as it contains different types of information like amplitude recordings timeessries), locations of sources and receivers (geo-locations), instrument sensitivity measurements, the actual signature of disturbance, time of recordings, etc. To handle these challenges. we propose neural network via only Multi-Layer Perceptron(MLIP)) dented as "Multi-Modal Information Unscrambler (Moeller"MMMLLLMM (MMI-Unscrambler)) MMI-Unscrambler can efficiently ingest varying types of data and robust to spatial irregularities. Moreover, it an all-MLP network. We show in our experiments MMI-Unscrambler can invert real and large scale raw-field nav-merge data to produce geologically sound velocity images with high SSIM scores.
Expensive seismic processing workflows: Traditional state-of-the-an methods of processing seis- mic data consume significant resources and time [1]. Figure la shows broader steps in traditional workflow commonly used in the "Big Oil" industry. It is well known [2] that each of the sequential steps in traditional workflows takes several months. This time inefficiency is primarily due to their dependence on human expertise to process and examine vast amounts of raw data. With the increas- ingly comprehensive and complex seismic data generated by advanced sensing technology, traditional workflows prove to be more expensive than ever. Hence, there is an urgent need to devise techniques to complement the existing process with automated technology to speed up the overall process.
Promise of deep Learning (DL): The data-driven approaches [3, 4, 5, 6] are progressively sought alternative to improve seismic workflows' efficiency. Data-driven deep learning (DL) approaches aim to learn non-linear mapping from the raw seismic data to the final subsurface image evading most of the time-consuming sequential steps traditional workflows. With the f'ast inference of DL models, data-driven approaches can potentially reduce workflows' duration from months to minutes. Therefore, it is not surprising that research for DL-based workflows in seismic processing are getting the attention and investment they deserve [7, 8, 9, 10, 11, 12, 13, 14, 15. 16].

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sldh 1030 6713
2L1000
Series Receivers Listening
Figure 2: Irregular Acquisition real SDL Left: A top view of a real survey. The survey area is large (around 100Km 100 Km) and the streamer (in marine survey) moves across the area to collect data. The blue dots represent the source points in the survey. Red dots and nearby green segments refer to a pair of source and series of receivers. We focus a particular area to predict the subsurface properties. Right: Details at the acquisition over a 5Km x 5Km area. Different colors and symbols are used to identify pairs of source and receiver lines. The real acquísition is highly irregular emphasizing the oversimplification of data used in current convolution models.
Convolutions in data-driven processing and limited success of DL in real seismic processing: Treating raw seismic data as images is standard the oil industry and geophysics community, Undoubtedly, image is the most convenient and interpretable representation of complex data. The recent data-driven research inherits the image bias from traditional practices. Inspired by the success of convolutions in computer vision, it attempts process the seismic data images and apply convolution-basee networks to ingest them. [13, 7, 17, 10, 11, 12, 14). Two characteristics of data put CNN-based SI great disadvantage 1) Real seismic data is at least dimensional. Applying 5D convolutions to the extensive seismic data is computationally infeasible. 2) Real seismic data collection is highly irregular and unstructured (see Figure 2) and CNNs require structured form of data. We can potentially interpolate traces to bring them on a regular grid. However, this would be sub-optimal way use seismic data. is important note that scismic data is not an image naturally, and hence it is an interesting question whether we should even try to process it as an image. Our results show that we can use only MLP blocks with HMMI-nncrambler architecture and get better results than CNN-based U-net on simulation data. Also, we obtain good results on real seismic data where applying U-net computationally prohibitive. To the best of our knowledge, most CNN-based SI approaches are prohibitive to real seismic settings. Current research in CNN-based SI focuses on simulated data on 2D subsurface data with regular acquisition geometry (see Figure 6b). We believe the gap between simulation and practice is too wide to extend these methodologies to practical environmental applications.
Major contributions in the paper:
We propose Aux-SI approach. This redefines the seismic inversion problem terabytes of data into the auxiliary task of predicting small blocks of property models from their contextual traces.
Thus, we make the training and inference of deep learning models real data feasible.
We introduce MMI-Unscrambler architecture which (1) incorporate multiple modes information seamlessly (2) scale to higher dimensions of data with the addition of more metadata. (3) is robust to highly irregular acquisition geometry, and (4) is resistant to over-fitting.
We believe, this is the first-ever data-driven approach using deep learning that can scale real data and provide geologically sound results. In the experiments on real proprictary data from the survey on the Gulf of Mexico, we achieve SSIM similarity (0-worst, 1-best) of over 0.8 on predicting 3D velocity model cubes.
It is interesting to note that we are able improve over the state-of-the-ar U-Net for SI using MIn--unsrrmbbler architecture with only MLP blocks.
2 Background
2.1 Seismic Data and Associated Applications
Reflection Leismology[18): Reflection Seismology is used to collect information about the subsur- face so that geophysicists can construct property model. As shown in Figure 1b, source and set

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of receivers are positioned on the surface of the earth. A mechanical perturbation is created using air guns at the source. The pressure waves thus generated travel through the subsurface. Waves refract and reflect at different layer boundaries in the subsurface. The rellected pressure waves that reach the receivers are recorded to generate time-series data. Hence, each source shot and receiver pair is associated with one dimensional time series data called the trace-data (D(t)) and locations of source and receivers called as acquisition geometry (A(t)). These terms are formally defined below. Apart from these, there is additional meta-data associated with cach trace, such as the signature of disturbance created, instrument sensitivity of receivers, record times (the time when this recording was made), etc.
Definition 1 (Trace data (D(t)), Let the receiver located at a location q E R listen for time duration s seconds and record at a frequency f (times per second), a trace received by the receiver a sequence {u(Ss, 2)) 2)) where ((1i.) E R is the acoustic pressure sensed at q at the ith recording.
Definition 2 (Acquisition geometry of a trace (A(t))). The location of source and receiver associ- ated with a particular trace-data, together constitute the acquisition geometry of the trace. Formally A(t) (Asre, Frev). where q R is a 3-dimensional location in space.
In a typical survey, a source is located on the streamer, and long cables with equidistant receivers attached to the streamer. The streamer moves over the area of interest and collects large set of traces for different (source, receiver) pairs. The set of all (source, receiver) locations associated with the collected traces are collectively referred to the acquisition geometry (A). Also, the set of all traces collectively is referred to as raw data, IR
Seismic Inversion(SI): The final aim of seismic processing is to obtain a subsurface property model. This problem is referred to as the seismic inversion problem stated formally below. This property model can then identify the rock and fluid types in the subsurface.
Problem 1 (SD. Given a region of interest S C Rd and R (raw data). Seismic Inversion(SI) is defined as the problem of getting the property model P where P :5 - R is mapping from each point in the subsurface to the value of the property of interest.
The property here can be any set of clastic properties, intermediate velocity or reflectivity index, etc. We use the term property in the most general manner. The subsurface region of interest, S, in Problem I can be 2D or 3D space. Accordingly, the inversion problems are categorized as 2D or 3D problems. 2D problems generally appear in synthetically generated datasets.
2.2 Relevant Prior Work
Traditional approaches [19]: Traditionally, SDI for seismic workflows comprises series of sequen- tial steps involving computcr-assistee human analysis. Generally, these steps are physics-driven. An example of workflow with approximate timelines is shown in Figure 1a. Raw shot processing cleans up the data by removing unintended noises that appear in the data. It includes sequential steps like de-noising, de-signature, de- de-multiple etc [19, 20, 21, 22]. The clean data used to generate a velocity model of the subsurface using techniques of tomography [23, 24] or full-waveform inversion [25, 26]. The velocity model is then refined iteratively by migrating the waves, and computing errors like residual move out [27]. Once refined velocity model is obtained, it is used to build a reflectivity cube of the subsurface. This cube is then inverted to obtain elastic properties of the subsurface (subsurface property model). Types of rocks and fluids in the subsurface are identified by analyzing the property model. Each of these steps require the involvement of domain experts to guide the inversion to an effective and applicable solution. These procedures extend the overall process to as lengthy year. For a detailed discussion on these steps, we refer the readers to [19].
Recent DL approaches: Though the application of Mata-driven methods to seismic processing dates back to the 1990s [28], there has been a renewed interest since the success of deep learning [29]. The data-driven methods [13, 11] aim to utilize the strength of deep learning [29] to exploit the available extensive complex seismic data fully. Most existing methods formulate Problem as an image segmentation problem and utilize convolutional neural networks (CNN) [30, 31]. In this formulation, the traces are combined as multi-channel images, and the corresponding subsurface property model is regarded as segmentation mask. Then CNN architectures such as U-Nets[10, 11, 12] or encoder- decoders [13, 14] are applied to learn a non- lonllinear mapping between image- maak pairs. As stated carlier, these approaches do not scale to real data.

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Gig.
Blcckr predicted by
MLP
MLP
MLP
Mr
Block predicied by Mo
Projecion
Blocks prodicted by Ms
Bit)
Pooling
MLP
(b)
Relevant Acquisition
recetver
E
Target Velocity Model
uy,,
trace-data
Q Flattened Propery Block
(c)
Figure 3: (a) General MMI-UnnsramblerAcchtteeee See the MMI architecture applied to velocity inversion figure 7. (b) Creating entire property model using different models at different depths with each model traversing entire horizontal surface predicting of context for particular property model block placed near surface carth
block time (c) Construction
3
Our Approach to Seismic Inversion with Deep learning
3.1 Aux-SI: Viewing Scismic Inversion Machine Translation
Applying deep learning to SI entails finding a map from several terabytes of raw-field data to several gigabytes of property- model of the subsurface. We call this problem global-inversiee It is prohibitive to train a single mapping from entire raw data to property model. We solve the global-inversion problem by proposing auxiliary learning paradigm, namely Aux-SI. In Aux-SI, break down the problem of global-inversion into multiple local-inversion tasks. The local-inversion tasks are much smaller in scale and allow efficient training of DL models. The solutions of these local inversion tasks can then be combined (stitching) to obtain a solution for the global-inversion problem. One can draw an analogy to Male-of-the-au NLP solutions for machine document translation. Instead of learning complete mapping between two documents (global- tranull-trnllaiion. DL models are learned to solve the
problem: predict the next word considering a small context around it. The reel--rannlation model is then used to predict the entire document one word at time. Aux-SI is inspired by this approach.
We first discuss the formulation of the local-inversion task. The target of this task a small 3D chunk in the complete property model. Let P(g, Wp, d) R xw, denote chunk of property model of size wp X Wp in area and d in depth at location q E R in subsurface. The input to this task is all the seismic traces that are found in a local area around P(g, Wp. d). We call this as the context the block. This is illustrated in Figure 3c. Formally, context is defined as
Definition 3 (Context C(g. w)). The context, C(g, w), at point q, parameterised by width w is defined as the set of traces whose acquisition (source and receiver locations) lies inside Area(g, w). i.e. the area w x w centered at (q.I,4-z)
Clg. w) [t]t E IR, A(t) Arealg, w))
where IR is the entire data.
DL based solutions to the local inversion problem would learn a mapping M, between context(q, wa) and property model block P(g, Wp. d). The scale of this learning problem is much lesser than the
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original problem, making it feasible to train a model efficiently. In section 3.2, we will discuss the MMI-Unscrambler architecture to solve local-inversion.
Theoretically, the information about a particular P(g, wp, d) is captured in all the traces across the entire survey, However, the impact of P(g, Wp, d) is strongest on traces near it, and the effect wanes out as we go to farther traces. Choosing the size of the context is standard eecurac--ffficienyy trade- off. Nevertheless, geophysics dictates that the effect of property model chunks at deeper locations would be captured in traces located further away from the block. Hence, in Aux-SI, we propose to learn different mappings for different depths and choose wider contexts for deeper blocks. To obtain the complete property model, we divide the complete subsurface into chunks as shown in Figure 3b. Each chunk, P(g, Wpp d) is then predicted using model M(g.2) and context C(g. w(g.2) "q.z", which denotes depth of point q. in previous notation are used to make dependence explicit. This is simple way to combine outputs of local inversion to get combined velocity. More evolved algorithms can be explored for better results.
3.2 MMM-Unscrambler: Multi-Modal Information Unscrambler
We introduce Multi-Modal Information Unscrambler (MMI-Unserambler) architecture to solve the problem of local inversion described above. MMIIUnscramble is specifically designed to efficiently ingest multi-modal data that is present in the seismic traces and successfully disentangle subsurface information from traces. An overview of MMI-Unscrambler is shown in Figure 3a. MMI-Unscrambler first obtains embeddings for traces, combines them to get embedding of the context, which is further used for prediction of property model chunk. In what follows, we describe the architectural choices of HuM-mmuscrmbbler and the rationale behind them.
3.2.1 Trace Embedding: Processing Multi-modal Information by Projection-concaeenaliee
Multi-modal nature of seismic data arises due to different types of data associated with trace. For example, a trace has (1) a time series amplitude information ((t) (2) source and receiver geo-location data A(t) (3) signature of disturbance created by air guns (time-series) (4) time of recording (time) (5) instrument sensitivity (float vector), etc. Ingestion of these data in a way that information obtained from them complement each other is important. MMI--nscramble achieves this by projection- concatenation. Let the different components of data associated with a trace t be denoted as {t]d]]]_ We first project cach of the component via a separate function blocks to get individual embeddings and then concatenate the embeddings to get a final embedding of the trace. Formally, E() [Fi [+[]),, F2(t)2), F((tii),,..)
Specifically in our case of traces, we have the following,
Et)) (Fa(( (.()
MLPss for each Fis: We propose to use MLP for all of these projections. The rationale for choosing MLPs is as follows: (1) (t),, the signature of disturbance and other time-scries data]: Recurrent Neural Networks (RNN) [32] and ID-CNNs are popular architectures process time-series data, Time-series data in SI has fixed frequency and number of recordings across different traces. Thus, RNN is not required process these types of data. CNN, on the other hand, needs enough depth to capture long-range dependencies. In S1, the long-range dependencies are equally important. We propose to use MLPs that are efficient to compute and capture long-range dependencies sequence gracefully. (2) [A(t), recording time, instrument sensitivity, etc] MLPs are natural solutions for processing these types data.
3.2.2 Context Embedding: Information Enhancement via Projection-mean Pooling
Embedding for context, C(q, w), is obtained by combining information from its traces, [4 )m However, combining this information is non-trivial for the following reason. Each trace data is a superimposition of waves reflected from all over the subsurface. Hence, each trace captures relevant information about the entire subsurface. In this respect, raw data is a collection of highly redundant and correlated traces containing overlapping pieces of information. the information of these pieces before combining them to predict property model block. We achieve the alignment via projecting the embeddings via functional block G. We then enhance the information by mean pooling over all the projected embeddings.
UMMI--nscrrmbler has to align
models. However,in real survey (Figure 2), the number of traces in a context C(q, w) change with changing location & of the context. It can be as low tens of traces in context to high thousands of traces. This data characteristic
Generally, sum-pooling is standard in NLP or embedding

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Datasets
SEGiSalt
RS-SEGSaft
GultM-10
GullM-20
Models
U-Net
Set Transformer
MMTU
U-Net Transforor
MMIU
MMIU
MMIU
L1
196.82
232.78
163.77
294.76
162.79
135.27
164.99
PSNR
14.64
14.21
16.65
14.90
16.68
32.34
26.95
SSIM
0.45
0.40
0.47
0.34
0.41
0.82
0.75
Table 1: Summary results of MM--Unscramblerand baselines on all the four datasets. We use MMIU to denote MMI--nscrannble..
prohibits from using sum-poode aum-pooling, which is common in NLP, where the number of words in context doesn't 't vary drastically. In our experiments, we observe that models trained with sum-pooling perform poorly than mean-pooling, especially when presented with extreme data with very high or low number of traces per context block. The combined embedding can be viewed as an embedding for the context C(q.w). Formally,
E(C(g, w)) -EER (
3.2.3 Downstream Tasks
Once a context representation is obtained, we can now use this to predict any property we desire, such velocity model, reflectivity model even elastic properties of the subsurface. The property model is predicted by processing the context embedding using a function H.
P(g, up: d) = HCE(C((g w)))
Again, we implement H as an MLP. Thus MMIIUnscramble is essentially composed of all-MLP components, and we learn all these functional blocks in end-to-end fashion. An overview of MMI-Unscrambler is shown in Figure 3a
3.2.4 Training Data
(C(g, w). P(g, Wp, d)) a training data sample for training a mapping M of depth corresponding to sample different points in the subsurface to generate multiple data points. Sometimes the availability of labeled real data is scarce. In such cases, we sub-sample the traces in context to generate more distinct training data points. Specifically, if (C(4, w), P(q, Wpp d)) a data point for training, then so is (c(q, w), P) for every non-empty c(q. w) in power set of C(q, w). So. if we have ten traces in context for particular training sample, we essentially have 200 = 1023 different training samples corresponding to this one input-output training sample. We also observe that generalization of the model is better when trained with augmented subsampled data. Because MMI-Unscrambler is robust to the different number of traces in the context, we can use subsampling to improve the model's inference time in S1.
q. Given a huge survey area,
3.3 Benefits of ins-umnsrrmbllr
Robustness: MMI-Unscrambler alleviates the issue of highly irregular spatial acquisition that plaques the convolution based approaches.
Unlike current DL-based SI approaches, scales casily to 5- dimensional real data. LIMI-nnscrambler, with its coojection-concatenati can ingest even higher dimensional seismic data obtained by adding varied available meta-data
Ingestion of Multi-modal data:
Resistance to overfitting: Labeled data in seismic tasks can be scarce. However, for MMI- Unscrambler, we create exponentially more distinct training samples from a small sample data. (see 3. 2.4.4.. Training model using this sampling approach prevents the model from overfitting. For example, SEGSalt data has 130 training samples, but the MMI-Unscrambler model with sampling technique does not overfit even when we run the model for over 1200 epochs. (see Figure 4)
Application and Empirical Results
We evaluate the M.MI-nssramblee against the competing methods on the velocity inversion problem on various datasets.
Datasets:
To extensively evaluate MMI-Unscrambler against competing approaches, select the following datasets.
(small, regular, 2D Velocity). SEGSalt is small-scale, 2D velocity prediction dataset with the regular acquisition (Fig.6b). SEGSalt is an ideal dataset for the CNN-based U-net model used in [11] and is publicly available with an MIT license. We choose this data set to compare
SEGSalt:
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Fradtoo of Used Figure 4: Above: Evolution of metries SSIM, L1 loss and PSNR on test SEGSalt dataset as the training progresses to 1200 epochs. As can be seen SSIM always improves and L1 loss PSNR achieve stable values. For elaboration on metrics see Experiments section. Model is trained with 0.8 fraction of traces. Below: Comparison on test performance when using different fractions of traces
Fraction of traces Used
Fractoon traces Used
against U-net at its best. Data generation: This data is generated by designing 2D velocity models and then rumning forward wave propagation using Devito [33][[4] to obtain seismic traces. The acquisition geometry is regular: distributing 29 sources and 301 receivers uniformly along the surface line, with each receiver listening to each source. Details of data generation and other details are mentioned in supplementary B.1.1
SEGSalt): (small, irregular, 2D Velocity) RS-SEGSalt is obtained from SEGSalt by tweaking sampling the acquisition to make it more realistic. The way sub-sample the traces is shown in Figure 6b. With such simple tweak towards real data, the U-Net model breaks and cannot be applied. Data generation: For each sample in SEGSalt for each epoch, we randomly sample fraction of contiguous traces. For experiments, we use fraction uniformly sampled between (0.7 + 0.25) and then choose the contiguous strips of receivers at a uniformly random location.
RS-SEGSalt Reallsticalllysamplle
GulfM-10 and GulfM-20( real, enormous, highly irregular, 3D Velocity) These are datasets we generate from large-scale scale real proprictary data obtained from Big-Oil company. This dataset's acquisition geometry is highly irregular, as shown in Figure 2. The data scale is also immense ( (100Km x 100Km) survey area). Due the 5-D trace data, large scale, and irregular geometry, this data set cannot be used with U-Net. We test set-transformer and MMI-Unscrambln task of contextual velocity block prediction. We also show big block predictions obtained by applying a sequence of contextual predictions and stitching together an image. Data generation: For the task of contextual prediction, we sample data points as described in 3.2.4. The difference between GulfM-10 and GulfM-20 is the height of the target velocity block. GulfM-10 and GulfM- 20 have velocity blocks with height 10% (1.5Km) and 20%(3Km) of the total velocity model, respectively. The block width and context width in both cases are 1Km and 5Km. The exact construction of the datasct and other details are described in supplementary B.
on the auxiliary
We use two baselines for MMI MMI--nnsrambllr. (1) U-Net: [11] is the state-of-the. art model recent literature for data-driven seismic processing. Also, it is the only model that was evaluated on publicly available SEGSalt data 2. Therefore, we choose this open-source [11] implementation as the representative for U-Net. (2) Bet-Transformer: [35] is the state-of-the-ar model that introduce multi-head attention mechanisms on set representation. It has demonstrated its superiority in point cloud classification and anomaly detection. The hyper-parameters these
Baseline models:
models can be found in supplementary B.2
MMI-Unscrambler model: The exact MMI-architceture details for the datascts described below are discussed in supplementary B.2. Bricfly, we use the same number of layers for SEGSalt and GulfM-10/Gulle datasets. The only difference is that we use a hidden layer of size 8192 in GulfM whereas 4096 in SEGSalt. Also, the input and output sizes of the network are determined by the dataset. More details on the architecture parameters mentioned in B.2
hhtpss//wiiki.egg.rggviiisss
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Width-6icm
Figure 5: Visualization of prediction on GulfM-20 Dataset. Left: Top: ground-truth velocity cube, Bottom: predicted velocities. Right: cross-section visualization of inference whole area. We want to stress that generating the above image from raw data via traditional methods takes several months because of the complex large scale data
Metries: To evaluate the models, we use the following three metrics widely used in recent work on data-driven seismic processing [11, 13, 14, 36]. Namely, & Loss (lower is better). PSNR [higher is better) and SSIM [38](r is better). I1 loss is l metric applied to (input,output) images. SSIM a structural similarity score widely used to measure the quality of images. PSNR (Peak Signal to noise ratio) is used to measure image reconstruction quality.
Results:
We provide results in various forms:
Performance on metrics (Table 1): lists the performance of all the models on all the datasets on all metrics. The variance of {,, PSNR and SSIM for MMI-Unserambler in GulfM-10 dataset 1.65, 0.92 and 0.02 respectively while in the same order are are 2.33, 1.07 and 0.01 in GulfM-20 dataset.
Metric evolution and robustness Fig. 4): top panel shows the evolution of metrics. The bottom panel shows the performance of the MMM-Unscrambler model trained on RS-SEGSalt when used for inference on different sizes of the sampled data.
Shows the visualization of different models on SEGSalt. The test data visualization is presented in the supplement. We also show the performance of the MMMl-unscrrmble model trained on SE-Sttallt data and inferred on SEGSalt. In Fig. we show visualisation on contextual block prediction task (left). Also, we run inference on larger blocks of velocity and show visualization (right). Details of visualization are presented in the appendix.
Visualization (Fig. 5, ). Fig.
Key highlights:
U-Net vs. MMI-Unscrambler SEGSalt: On SEGSalt, which is the ideal data set for CNN based U-Net, MMI-Unscrambler performs better than U-net on all the metries with significant margin (Table 1). This begs the question of whether convolutions Convolution-basse networks are known for their strong priors and disregard for long-range de- pendencies. MLPs, on the other hand, can capture all range dependencies and hence perform better. Visualizations in Figure 6a also echo similar results. At times, U-Net incorrectly predicts background velocity and shows weird salt structures. Though MMI--nnsrrmbler's output suffers from smootsenng the boundaries, it captures detailed the salt shape and the background. RS-SEGSalt vs. SEGSalt Training the model RS-SEGSalt leads to robust models due the availability of extensive, varied data created by subsampling. Note that RS-SEGSalt only differs from SEGSalt in the input. Thus, can train the model on RS-SEGSalt and test it SEGSalt. We can see from Figure 6a that MMI-Unscrambler gives better salt shapes when trained on RS- This is also reflected by better Li and PSNR for LLMI-Unsrramller
apt for seismic inversion.
MMI- Unscrambsrr vs Set- Sel-Transformer Table 1 also demonstrates the superiority of MMI- Unscrambler over set-transformer. On regular observation, MMI-Unscrambler achieves over 20% performance boost on set-transformrr. One intuition behind these results is that there is less dependency between traces. Thus, attending one trace with others would not improve the generalization of the set model.
MMII-nscrambler on GulfM. Figure (right), shows that we get geologically sound predictions of the velocity model by using MMI-Unscrambler model. The image is obtained by stitching together the individual blocks predicted by MMI-Unscrambler model. Figure (left) shows a mixture of small block predictions. SSIM on real velocity prediction is higher than that on synthetic data. Real velocities in a small block are relatively smooth, whereas synthetic data is filled with complexities to resemble the entire survey.

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Regular Acquisitin Geometry
SOUICe
Limand truth
LAMINEEGN
MMHU SKlaall
receivers
Realistic Acquisitin Geometry (2D)
Givand traih
MEIIU SEUSal
STIIL 18-SHLSa
receivers
(b) Regular AG used in synthetic datasets is to have sources and receivers uniformly distributed face and have every receiver listen every source. Realistic AG for 2D is designed to mimic Real acqui- sition. Here, randomly sampled contiguous segments of receivers are made to listen to each source. The color shows the pairings of receivers and sources.
(a) Visualization of Prediction on SEGSalt Dataset The prediction results for U-net vs MMI-Unscrambler model. MMI-Unserambler performs particularly well when trained RS- SEGSalt data. Also, MMI-UnSS DMM--unsrrambler model is robust to irregularities in the acquisition.
Figure 6
Experimental Hardware and Computation Power: All experiments were performed on Tesla V100 GPUs. Training large models for gulf-of-Mexice datasets require around 10 hours of training.
5 Negative Societal Impact
This paper proposes an efficient scismic data processing approach. Seismic data processing is fundamental problem in geophysics. also has tremendous applications in earthquake estima- tion [39]. ocean temperature proflling [40], and groundwater monitoring [41]. We hope that our MMI-Unscrambler could be extended to solve environmental protection problems. Moreover, MMI- Unscrambler reduces the expensive computation in seismic data processing by learning end-to-end model to generate seismic velocity maps, etc. believe this reduction would also achieve lower power consumption compared to the traditional seismic processing workflow. Furthermore, our method provides an accurate estimation the subsurface velocity model, potentially preventing unnecessary exploration for the oil and gas company. We hope our effort will help reduce the negative effects of the current exploration system.
Conclusion and Future Work
To tackle the scale seismic inversion, we introduce Aux-SI and define the auxiliary task of contextual small property model block prediction to solve the problem of large-scale property model (in Gigabytes) prediction from Terabytes of data.
can efficiently train models for this auxiliary task. We alleviate the issues of multi-modal data and highly irregular geometry of acquisition by using a novel LIMI-Unscrambler architecture to align and combine available data. Our model achieves geologically sound predictions demonstration of a model on real-scale scismic data. In the future, we plan to further improve information utilization by including all metadata available. Also, we would explore better stitching algorithms to perform large-scale inference. Currently, we deploy supervised approach to SI. This requires the availability of pre-computed velocity models, which is difficult obtain. Exploring unsupervised DL-based techniques is also an interesting future direction.
real data at its original scale. We believe this is the first-ever
Acknowledgments
This work is supported by research grant from Shell, National Science Foundation 11S-1652131, BIGDATA-1838177 AFOSR-YIL YIP FA9550-11-1101122, ONR DURIP Grant, and the ONR BRC grant on Randomized Numerical Linear Algebra.
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13


Reviews:
[{"review_id": "nhhiXVHlpZA", "reviewer": "Reviewer_ahiS", "summary": "This study proposes a new method to the problem of seismic inversion, which is an ill-posed inverse problem of major importance for understanding the composition of the earth subsurface that is used in many applications. The proposed method relies on simple MLP blocks, but organized in a clever way in order to be able to use multi-modal, size-varying and sparse input data. Moreover, the separation in different spatial blocks allows the model to be efficient and parallelizable. The results are performed on different data sets, and compared with more standard time-series or spatial methods, such as Unet and Transformer-based methods. The proposed approach seems promising and robust, which is what is needed for being applied in the real world.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The paper is interesting and worth publishing. Yet, I found that the paper was not sufficiently proofread and it was difficult to follow. I hope the authors can spend time in correcting all the typos, in changing the variable names that are not clear, and adding the missing details. Specifically, please answer the following questions:\n1) when you talk about 5D data, do you mean 3D+time (so 4D), and what is the last dimension?\n2) Please give more details on your different MLP architectures: for now we don't have any information about their size, their number of layers, their activation functions, etc.\n3) what is the size of the bock and of the context that you used for the different data sets, and more importantly how did you chose it? I only saw the size in one of the experiments. \n4) how did you perform the hyperparameter tuning? what parameter were finally selected (size of blocks, learning rate, size of embeddings..)? was the same values used for all the different data sets or not?\n5) how many samples did you finally used in practice for your training, even if there was overlap between samples thanks to data augmentation?\n6) explain better how you divide your train validation and test samples. Since your data augmentation technique has a large overlap between samples, I just want to check that the separation between the sets is done correctly.\n7) please add the 3rd part of your pipeline, the 'downstream tasks', in your figure 3.a. Add also a proper legend so we can understand the figure on its own.\n8) CNN models are able to capture long range dependency... that is why there are multiple layers with max poolings, so the dependencies at different scales can be captured. Please explain better why it might not be relevant for this application.\n9) Would you say that what actually makes the difference in your method is to separate the problem in small blocks? Could you perform the same division using the other state-of-the-art methods?\n10) explain more clearly what is G (I guess it's an MLP, from the figure, but it is never said in the main text). \n11) 'q.z' formulation is not clear, I guess you meant the vertical component of the position q? Same, there is a confusion between the time 't' and the trace 't'. please use another name for the trace so we can understand the text and the figure. Last, in Figure 3b, explain what are the 3 axis of the cube. \n12) would it be possible to interpolate the traces over the surface area in order to have a grid (or otherwise a graph of sensors)? why would that lead to larger errors than your method (if it does)?\n\ntypos: please check your paper again as it is not my job to proofread papers before the authors.\n- problem deﬁnition 1can\n- a separate function blocks\n- 2 1 0 − 1 --> 2^⁽10)-1 (I guess??)\n- Generally sum-pooling in standard in NLP or embedding based models. --> no verb\n- many spaces missing\n- many points missing\n- check capital letters\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "This paper is meant to be used to find Oil for Big Oil companies. So it is subject to personal opinion whether this application is positive or negative in terms of societal impact. Yet, it was clear in the paper from the start what is the goal, it was not hidden, and I personally think that since we, authors and reviewers, are all currently relying on Oil and gaz to live our lives, being able to find it easily is a positive impact. I hope that the company that payed for this work also spends efforts in developing other energy or even better, tries to find ways to reduce energy consumption.\nYet, the authors could remind in the societal section a sentence regarding the final application of the work.", "review_text": "", "extra_scores": {"ethical_concerns": "Could be, see section above.", "needs_ethics_review": "Yes", "ethics_review_area": ["Inappropriate Potential Applications & Impact  (e.g., human rights concerns)"], "time_spent_reviewing": "2"}, "extra_text": {}}, {"review_id": "ZZ76r7Sj5PM", "reviewer": "Reviewer_bCTP", "summary": "The paper proposes Aux-SI approach that handles the large-scale seismic inversion problem via dividing it into small blocks of property models, which makes the training feasible. The authors introduce MMI-Unscrambler architecture to handle the multi-modal information for the task. The empirical study shows that the proposed approach outperforms the state-of-the-art algorithms and is scalable to handle large-scale real-world datasets.", "questions": "", "limitations": "", "rating": 7, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The main novelty of the work is to divide the large-scale seismic inversion problem into local inversion problems, each trained based on its context. The potential challenge of this division is that each block is influenced by all traces, and traces in a single block's context will also account for other blocks. The authors explain how their approach handles these challenges well and provides reasonable empirical studies.\n\nQuestions/Comments:\n1. What does the M(q.z) in line 177 mean? Does q.z mean the depth information of q?\n2. Line 118, in problem definition 1 --> defined in Problem 1\n3. Line 195, missing space\n4. Line 210, for following reason --> for the following reason\n5. Line 217. sum-pooling in standard --> sum-pooling is standard\n6. line 220, the data prohibit us --> the data prohibits us", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors addressed them.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "8_HCg8Laay7", "reviewer": "Reviewer_2jDV", "summary": "This is an interesting paper that proposes to leverage MLP for solving seismic imaging problems, which are well known to be data-intensive and heavy in computation. \nThe paper provides an easy-to-follow introduction of the problem of seismic imaging and clearly illustrates how data-driven methods can potentially reform the seismic processing workflow, showing great promise of this specific research direction. \nThe proposed method, *MMI-Unscrambler*, consists of three phases. In the first phase, every trace $t\\in C(q,w)$ is mapped to embeddings by individual MLP for each different modal information $t[i]$. A concatenation operation is subsequently used to form one single embedding for each trace. In the second phase, the set of embeddings associated with $C(q,w)$ is further mapped by another MLP (shared across different traces) to align these embeddings followed by average pooling. The rationale for this is that each trace has a dramatically different geometric shape and can not be directly aligned.\nIn the last phase, a MLP maps the aligned embedding of $C(q,w)$ to the final value $P(q,w_p,d)$.\n\nThe authors extensively validate their method on three datasets of increasing difficulty. In particular, the last dataset is real, huge, and irregular. In all datasets, MMI-Unscrambler outperforms U-Net and Set-Transformer baselines with noticeable improvements in terms of numerical values, which supports their aforementioned claims.\n", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "**Originality:** I am not a fully active researcher in seismic imaging, but as far as I know, this paper first proposes an MLP-based network for this topic. \n\n**Quality:** The experimental validation in this paper is comprehensive and convincing. The quality of this paper is high.\n\n**Clarity:** The paper did a very good job in explaining the background of seismic imaging. Figure 1 clearly shows how data-driven methods will reform the overall reconstruction pipeline, helping draw more attention to seismic imaging or waved-based inversion. However, there is some unclarity in the notations that can make the paper not easy to follow.\n\n**Significance:** The paper is significant because it extends the recent popular MLP-base learning to seismic imaging. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "There are some confusions that need the authors' clarification:\n\n1. On what resolution level is the MMI-Unscrambler trained? Is the input of MMI-Unscrumbler a point (voxel) in the $C(q,w)$ and the output a point in $P(q,w_p,d)$? or MMI-Unscrambler takes and outputs a chunk of data, like a slice?\n\n2. Figure 3.(a) is not very clear. What is the meaning of the red circle? The notation $e_i$ is not defined. Maybe $C(q,w)$ is clearer than $C$ since in the text it is always $C(q,w)$. The caption is not informative. Please consider having a self-contain caption. In fact, Figure 7 in the supplement should be used as a replacement for Figure 3(a).\n\n3. In Figure 3.(b), what do different colors mean at the same level (i.e. dark and light red)?\n\n4. Maybe the supplement should be referenced more often in the main paper since it provides necessary information for understanding the technical details.\n\n5. For reproducibility, the author should consider publishing their code. Also, a comparison of sum-pooling and average-pooling will better justify the choice of the latter.\n\n6. The scalability of the network should be discussed. For example, how many MLPs are needed to cover the gulf dataset in the experiment?", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3 hours"}, "extra_text": {}}, {"review_id": "2pPiBuuMxpE", "reviewer": "Reviewer_XYVo", "summary": "The paper tackles the scalability issue of seismic inversion in real-world subsurface and property estimation. The authors propose the Aux-SI framework, where Multi-Modal Information Unscrambler (MMI Unscrambler) is designed, which breaks the large problem into local inversion problems and then aggregates the multi-model information. Extensive experiments are conducted, on both synthetic and real massive datasets, to show the effectiveness of the proposed method.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "This paper is well organized and presented. The main strength is the successful application of machine learning on large-scale, real-world problems. As the authors mentioned, deep learning models in such subsurface property estimation has not been applicable on the real industry level. This paper breaks the limit. Thus, I believe this work could be interesting to many NeurIPS audiences.\n\nThe problem studied is interesting to me, and using DL in this problem seems quite novel and new. The empirical results are comprehensive and convincing that the proposed method can do a good job in real-world scenarios. Thus, I think this is in general a good application paper that may interest the many practitioners, and may originate more future efforts in combining machine learning with geological prospecting or oil exploration.\n\n\nQuestions:\n\nWhat is the input dimensionality to the first MLP layer? Is that possible to break the high dimensional input (eg, 5D) into lower dimensions and apply CNN like U-Net?\n\nCould you explain more on why MLP is used instead of CNN and RNN, and the pattern of the time-series data in SI?", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "NA", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "2"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This work presents a SOTA Multi-layer perceptron solution for seismic inversion. The reviewers all recognized the improved performance relative to past approaches and the design and work involved in creating a practical block-based multi-modal approach. In particular the care taken to acknowledge and address the issues stemming from cross-block correlations. The authors also seemed to have proposed very doable revisions, which would even further strengthen the paper. Therefore I am happy to recommend that this work be accepted at NeurIPS.
Decision: Accept (Poster)