Physical Cross-Modal Masked Autoencoding for Seismic-to-Well Representation Learning

Meher Gajula; Keyla Gonzalez; Ben Lasscock; Alejandro Valenciano

cs.LGSep 28, 2026

Physical Cross-Modal Masked Autoencoding for Seismic-to-Well Representation Learning

Authors: Meher Gajula, Keyla Gonzalez, Ben Lasscock, Alejandro Valenciano

Abstract

Learning from scientific measurements often requires aligning modalities with different spatial support and resolution. Subsurface characterization is an extreme dense-sparse problem in which 3D seismic provides volumetric but indirect measurements and well logs provide high-resolution 1D measurements at sparse borehole locations. We introduce a physically grounded cross-modal masked autoencoder (CM-MAE) for seismic-to-well representation learning. The model jointly tokenizes seismic volumes and well-log depth patches, embeds both modalities in continuous physical coordinates using four-axis rotary position embeddings, and reconstructs masked targets with a cross-modal decoder. Sparse Mixture-of-Experts layers provide modality-specific capacity while dense attention allows information exchange between modalities. Pretraining uses 23 seismic volumes covering approximately 178,000 square km across U.S. offshore and onshore basins, together with approximately 92,000 wells. Matched-mask ablations show strongly asymmetric information flow. Seismic context improves held-out well-log reconstruction by 9.73%, while well-log context improves seismic reconstruction by 0.65%. We evaluate seismic-only pseudo-log predictions against independent interpreter-drawn salt-geobody masks to determine whether they contain geologic signal. Across offshore U.S. surveys, compressional-slowness-derived salt scores reach an AUROC of 0.910. In onshore basins, predicted compressional slowness preserves formation-scale structure and partial relative organization in an unseen survey despite calibration drift. CM-MAE learns useful seismic-to-well representations under extreme modality asymmetry, although absolute pseudo-log calibration remains survey-dependent.

Figures & tables

Figure 1: CrossModal-MAE: seismic + well foundation model. Real inputs and reconstructions from the 700k checkpoint ( $\sim$ 1.06 B parameters, $\sim$ 722 M active per token). (1) Input geometry: paired 3D seismic and sparse 1D wells are embedded with modality-specific patch tokenizers. (2) Tokenization: the joint sequence is augmented with a shared physical 4-D RoPE. (3) A shared encoder with a Mixture-of-Experts FFN block feeds a sparse CrossMAE decoder that cross-attends modality-tagged masked queries. (4) Real reconstruction outputs: seismic (left) at 90% mask ratio and well channels at 75% mask ratio.

	Encoder input		Reconstruction error
Setting	Seis.	Wells	Seis. patches	Well samples
Both modalities (training)	$\checkmark$	$\checkmark$	$0.1917$	$0.00845$
Seismic only	$\checkmark$	—	$0.1930$ ( $+0.65\%$ )	$0.02449$
Wells only	—	$\checkmark$	$0.9317$	$0.00927$ ( $+9.73\%$ )

Table 1: Held-out reconstruction error under three test-time input regimes (mask rates: 90% seismic, 75% well, applied to the present modality only). Diagonal entries are matched-mask comparisons against the “Both modalities” row; off-diagonal entries are cross-modal predictions of the fully-masked modality. Seismic error is normalised MSE; well error is variance-normalised Huber; the two are not on a common scale. Evaluated on

2{,}276

paired samples drawn from

1{,}523

unique held-out wells; significance reported in the main text uses a paired test on the corresponding

569

batch-mean differences.

Intervention	GR	NPHI	RHOB	DT	RESD	Mean $r$	$\Delta$
Baseline	0.808	0.691	0.767	0.790	0.835	0.778	0.000
Top-1 routing	0.818	0.679	0.736	0.795	0.864	0.778	$+0.000$
Merge enc. exp.	0.740	0.588	0.672	0.727	0.791	0.704	$-0.074$
Uniform routing	0.763	0.589	0.552	0.731	0.768	0.681	$-0.097$
Random router	0.556	0.250	0.277	0.427	0.372	0.376	$-0.402$
Single expert	0.525	0.229	0.247	0.330	0.497	0.366	$-0.412$

Table 2: Post-hoc MoE interventions on the frozen

700

K-step checkpoint, evaluated on held-out pseudo-log inference. Mean

r

is averaged over GR, NPHI, RHOB, DT, RESD; SP is uncorrelated with seismic in the data.

Figure 2: Qualitative pseudo-log section along Plains inline 1024. The figure shows the seismic inline (left) and seismic-only predictions for GR, NPHI, RHOB, and DT (right), with measured well logs overlaid as vertical strips. This illustrates coherent lateral petrophysical structure generated purely from dense 3D structural context.

Panel of Figure 3 — Figure 3: Top (Sanderson validation) and Bottom (Pontiac unseen) : Predicted vs. actual DT. Distributions are closely aligned across intervals in Sanderson. Pontiac shows a global bias (shifted to higher values, reduced spread) but preserves relative structural shapes across the layers. Outer panels show predicted DT pseudo-log sections with picked horizons overlaid.

Split	Interval	wells	samples	KS $D$	$\mu_{\mathrm{actual}}$	$\mu_{\mathrm{pred}}$	$r$
Sanderson train	All depths	83	1,543,096	0.176	67.30	70.87	0.703
	Salado $\to$ BCSA	56	266,399	0.289	58.34	60.56	0.467
	BCSA $\to$ Wolfcamp	45	254,493	0.287	66.47	70.99	0.448
	Wolfcamp $\to$ Strawn-Int	32	296,941	0.339	78.15	82.35	0.461
	Strawn-Int $\to$ Misso	20	169,087	0.244	70.53	75.45	0.516
Sanderson val	All depths	8	111,990	0.204	68.93	71.06	0.740

Table 3: DT KS by horizon interval (Sanderson validation and Pontiac unseen).

D

is the two-sample KS statistic (lower is closer).

\mu

values are in

\mu\mathrm{s/ft}

;

r

is the paired Pearson correlation.

Cross-Modal Representation Learning

Cross-modal representation learning connects information across data types such as images, text, audio, biosignals, and sensor measurements.

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Aleksander Berezowski, Hassan Hassanzadeh, Gouri Ginde

Schulich School of Engineering Department of Electrical and Software Engineering University of Calgary Calgary, Canada · Schulich School of Engineering Department of Chemical and Petroleum Engineering University of Calgary Calgary, Canada

Masked Autoencoders Self-Supervised Time Series Representation Learning

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The application of generalist multimodal models (GMMs) to specialized scientific domains remains limited due to the scarcity of comprehensive domain-specific datasets that integrate multiple data modalities beyond text and images. In seismology, understanding earthquake phenomena requires the synthesis of timeseries waveform data, geographical imagery, and contextual metadata, a multimodal integration absent in existing seismic datasets. We present MultiSeismo, a large scale structured multimodal seismic dataset, comprising over 16K seismic events spanning 13 years (2010 to 2023) across diverse geographical regions. Each event data integrates waveform recordings from global station networks, intensity maps, population exposure visualizations, and a comprehensive textual description within a standardized JSON format. We additionally develop MISCE, a multimodal instruction set on top of raw data to enable supervised training and evaluation of GMMs on seismic reasoning tasks ranging from basic information retrieval to complex cross modal analysis. We leverage MISCE to finetune an existing multimodal model (Unified IO 2) enhanced with a specialized timeseries encoder, which yields SeisModal, the first domain specific multimodal model for comprehensive seismic analysis. Evaluation of state of the art multimodal models on MultiSeismo reveals significant challenges, particularly with time-series data processing for general purpose models, while demonstrating SeisModal's superior performance on seismic multimodal reasoning tasks. These results prove that MultiSeismo provides a rigorous benchmark for future multimodal research in seismology and validate the success of our domain specific architectural adaptations.

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Multimodal Reasoning Seismology Multimodal Instruction Tuning

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SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior

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Georgia Institute of Technology · Oxy · Huber Engineered Materials

Seismology Conditional Generative Modeling Seismic Imaging Inverse Problems

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Abstract

Cross-Modal Representation Learning

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