Deep-learning tomography

Abstract

Velocity-model building is a key step in hydrocarbon exploration. The main product of velocity-model building is an initial model of the subsurface that is subsequently used in seismic imaging and interpretation workflows. Reflection or refraction tomography and full-waveform inversion (FWI) are the most commonly used techniques in velocity-model building. On one hand, tomography is a time-consuming activity that relies on successive updates of highly human-curated analysis of gathers. On the other hand, FWI is very computationally demanding with no guarantees of global convergence. We propose and implement a novel concept that bypasses these demanding steps, directly producing an accurate gridding or layered velocity model from shot gathers. Our approach relies on training deep neural networks. The resulting predictive model maps relationships between the data space and the final output (particularly the presence of high-velocity segments that might indicate salt formations). The training task takes a few hours for 2D data, but the inference step (predicting a model from previously unseen data) takes only seconds. The promising results shown here for synthetic 2D data demonstrate a new way of using seismic data and suggest fast turnaround of workflows that now make use of machine-learning approaches to identify key structures in the subsurface.

Meta-learning pseudo-differential operators with deep neural networks

“…The discrete version of Eq. (3.1) takes the form 2) with N = 2 L . The main goal of this paper is to construct a neural network to learn the map η → G η .…”

“…The For the 1D case, the domain Ω = [0, 1] is discretized by a uniform Cartesian grid with 320 points. The positive potential η(x) is generated by (1) sampling independently from N (0, 1) on a uniform grid with 40 points, (2) interpolating to the 320-point grid via a Fourier interpolation, and (3) followed by a scaling. The source term f (x) is generated by sampling independently from N (0, 1) with the same Fourier interpolation procedure.…”

“…This paper is concerned with a more ambitious task: representing the nonlinear map from η to G η M : η → G η = L −1 η , (1.2) approximate high-dimensional solutions of high-dimensional PDEs [36,52,14,46,4,6,13,25,31,39]. In a somewhat orthogonal direction, the NNs have been utilized to approximate the high-dimensional parameterto-solution of various PDEs and IEs [30,26,18,17,19,32,25,2,38,20].…”

Deep Learning Inversion of Electrical Resistivity Data

“…The successes have also inspired many approaches for geophysical problems, particularly in the field of seismic inversion. Araya-Polo et al [34] use a velocity related feature cube transferred from raw seismic data to generate velocity model by CNNs, while Wu, Lin, and Zhou [35] treat seismic inversion as image mapping and build the mapping from seismic profiles to velocity model directly. Further, Li et al [36] figure out the weak spatial correspondence and the uncertain reflectionreception relationship problems between seismic data and velocity model, and propose to generate spatially aligned features by MLPs at first.…”

BCR-Net: A neural network based on the nonstandard wavelet form

“…3) where e i is the canonical basis vector in the i-th coordinate. Both the effective coefficient tensor A 0 and the correctors η i (x) are important for studying multiscale problems in engineering applications.…”