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.

Probabilistic neural network-based 2D travel-time tomography

“…They have also been used in conjunction with Markov random fields and other statistical and graphical models to solve geophysical inverse problems with spatially sophisticated prior information [30][31][32]. They have been used in conjunction with seismic gradiometry to perform near-real-time 3D surface wave tomography [33]. These studies demonstrate that the pdf obtained from an MDN is comparable to a Monte Carlo sampling solution but is obtained at much lower computational cost in the cases where similar inverse problems must be solved repeatedly with different data sets, and that at the moment of application MDNs provide probabilistic solutions almost instantaneously.…”

DoA Estimation via Unlimited Sensing

“…pg 43, [12]). Even if the ADCs (equipped with AGCs) are calibrated, bursts and spikes [13] can saturate the sensor array, resulting in clipped measurements. This typically happens in the case of radars and seismic systems.…”

“…where D K ∈ R N ×(N −K) is the matrix corresponding to ∆ K and D 0 = I (identity matrix). Combining (13) and 12, we obtain the link between higher order differences and the modulo samples,…”

Bayesian geophysical inversion using invertible neural networks

“…Monte Carlo methods are quite general from a theoretical point of view and can be applied to a range of inverse problems, for example, to surface wave dispersion inversion (Bodin et al 2012;Shen et al 2012;Young et al 2013;Galetti et al 2017;Zhang et al 2018, travel time tomography (Bodin & Sambridge 2009;Galetti et al 2015;Piana Agostinetti et al 2015;Fichtner et al 2018;) and full-waveform inversion (Ray et al 2016(Ray et al , 2017Gebraad et al 2020;Khoshkholgh et al 2020). However, such solutions are acquired at significant expense, typically requiring days or weeks of computer run time, and hence cannot be applied in scenarios that require rapid solutions such as real-time monitoring (Duputel et al 2009;Cao et al 2020), or when many similar inversions must be performed (Käufl et al 2016).…”

“…MDNs have been applied to surface wave dispersion inversion (Meier et al 2007a,b;Cao et al 2020), 2D travel time tomography , petrophysical inversion (Shahraeeni & Curtis 2011;Shahraeeni et al 2012), earthquake source parameter estimation (Käufl et al 2014(Käufl et al , 2015, and Earth's radial seismic structure inversion (de Wit et al 2013). However MDNs become difficult to train in high dimensionality because of numerical instability, and they suffer from mode collapse, that is, some modes of the posterior pdf are missing in the results (Hjorth & Nabney 1999;Rupprecht et al 2017;Curro & Raquet 2018;Cui et al 2019;Makansi et al 2019).…”