Matched Field Processing accounting for complex Earth structure: method and review

Abstract

Matched Field Processing (MFP) is a technique to locate the source of a recorded wave field. It is the generalization of beamforming, allowing for curved wavefronts. In the standard approach to MFP, simple analytical Green's functions are used as synthetic wave fields that the recorded wave fields are matched against. We introduce an advancement of MFP by utilizing Green's functions computed numerically for real Earth structure as synthetic wave fields. This allows in principle to incorporate the full complexity of elastic wave propagation, and through that provide more precise estimates of the recorded wave field's origin. This approach also further emphasizes the deep connection between MFP and the recently introduced interferometry-based source localisation strategy for the ambient seismic field. We explore this connection further by demonstrating that both approaches are based on the same idea: both are measuring the (mis-)match of correlation wave fields. To demonstrate the applicability and potential of our approach, we present two real data examples, one for an earthquake in Southern California, and one for secondary microseism activity in the Northeastern Atlantic and Mediterranean Sea. Tutorial code is provided to make MFP more approachable for the broader seismological community.

SANS: Publicly Available Daily Multi‐Scale Seismic Ambient Noise Source Maps

“…MFP algorithms of varying complexity have been developed, for example,: to locate hydrothermal acoustic sources (Cros et al., 2011); microseismic sources in exploration geophysics (Corciulo et al., 2012); glacial tremors (Umlauft et al., 2021); or applied to three‐component seismic array data for microseisms (Gal et al., 2018). The algorithm could also be adapted to be nearly identical to full‐waveform methods by including synthetic Green's functions (Bowden et al., 2021; Schippkus & Hadziioannou, 2022). Although there may be some value to more complex MFP implementations, we prefer the computationally efficient version described below, as the subsequent inversion iterations will add further complexity.…”

“…This process is repeated for all possible noise source locations and cross‐correlations, and the values of the square envelope of the cross‐correlations are added up as illustrated in Figure 2. Of course, more sophisticated methods to model either the travel times or amplitude decays and attenuation can be implemented in MFP (Bowden et al., 2021; Schippkus & Hadziioannou, 2022). Such modeling is precisely the point of subsequent iterations of the full‐waveform approach, whereas the MFP is only intended to give a computationally efficient initial model.…”