Seismic Inversion by Hybrid Machine Learning

Abstract

We present a hybrid machine learning (HML) inversion method, which uses the latent space (LS) features of a convolutional autoencoder (CAE) to estimate the subsurface velocity model. The LS features are the effective low‐dimensional representation of the high‐dimensional seismic data. However, no equations exist to describe the relationship between the perturbation of an LS feature and the velocity perturbation. To address this problem, we use automatic differentiation (AD) to connect the two terms. Following this step, we use the wave‐equation inversion to invert the LS features for the subsurface velocity model. The HML misfit function measures the LS feature differences between the observed and predicted seismic data in a low‐dimensional space, which is less affected by the cycle‐skipping problem compared to the waveform mismatch in a high‐dimensional space. A low dimensional LS feature mainly contains the kinematic information of seismic data, while a large dimensional LS feature can also preserve the dynamic information of seismic data. Therefore, the HML inversion can recover the subsurface velocity model in a multiscale approach by inverting the LS features with different dimensions. Based on the different ways of utilizing AD to compute the velocity gradient, we propose full‐ and semi‐automatic approaches to solve this problem. These two approaches are mathematically equivalent; the former is easier to implement, while the latter is computationally more efficient. Numerical tests show that the HML inversion method can effectively recover both the low‐ and high‐wavenumber velocity information by inverting the LS features with different dimensions.

Physics-Guided Data-Driven Seismic Inversion: Recent Progress and Future Opportunities in Full Waveform Inversion

“…Traditional methods for tackling this challenge Fig. 10: Schematic illustration of the hybrid machine learning inversion framework (Image courtesy of [57] and used with permission). are based on hand-crafted functions, which may succeed in some datasets but fail in others [3].…”

“…are based on hand-crafted functions, which may succeed in some datasets but fail in others [3]. To overcome this issue, ML approaches have been utilized to learn a data fidelity function [57], [58], [59].…”

“…Specifically, a learning-based data fidelity function that measures high-level features has been shown to be effective in mitigating the local minima issue. Following this, Chen and Saygin [57] develop a multi-scale hybrid machine learning inversion method by defining a data fidelity function that measures the latent space features of the observed and predicted data (see Fig. 10).…”

“…Zhang and Alkhalifah [59] trained a deep neural network to first estimate the distribution of facies (the overall characteristics of a rock unit that reflect its origin and differentiate the unit from others around it), which will be used as regularization to constrain the iterative procedure of the FWI. We select the work in [57] to represent this group of approaches due to its promising performance and applicability to real data. Their idea is illustrated in Fig.…”

“…A low dimensional latent space contains the kinematic information of the seismic waveforms, while largedimensional latent space features preserve the dynamic information from the waveforms. Experiments with both synthetic and real data tests have been carried out to demonstrate the performance of the proposed method [57].…”