Near-real-time near-surface 3D seismic velocity and uncertainty models by wavefield gradiometry and neural network inversion of ambient seismic noise

Abstract

With the advent of large and dense seismic arrays, novel, cheap, and fast imaging and inversion methods are needed to exploit the information captured by stations in close proximity to each other and produce results in near real time. We have developed a sequence of fast seismic acquisition for dispersion curve extraction and inversion for 3D seismic models, based on wavefield gradiometry, wave equation inversion, and machine-learning technology. The seismic array method that we use is Helmholtz wave equation inversion using measured wavefield gradients, and the dispersion curve inversions are based on a mixture of density neural networks (NNs). For our approach, we assume that a single surface wave mode dominates the data. We derive a nonlinear relationship among the unknown true seismic wave velocities, the measured seismic wave velocities, the interstation spacing, and the noise level in the signal. First with synthetic and then with the field data, we find that this relationship can be solved for unknown true seismic wave velocities using fixed point iterations. To estimate the noise level in the data, we need to assume that the effect of noise varies weakly with the frequency and we need to be able to calibrate the retrieved average dispersion curves with an alternate method (e.g., frequency wavenumber analysis). The method is otherwise self-contained and produces phase velocity estimates with tens of minutes of noise recordings. We use NNs, specifically a mixture density network, to approximate the nonlinear mapping between dispersion curves and their underlying 1D velocity profiles. The networks turn the retrieved dispersion model into a 3D seismic velocity model in a matter of seconds. This opens the prospect of near-real-time near-surface seismic velocity estimation using dense (and potentially rolling) arrays and only ambient seismic energy.