Direct-3D Variational Bayesian Surface Wave Inversion and Its Application to Ambient Noise Tomography beneath Great Britain

TL;DR

The study introduces a direct-3D, variational Bayesian inversion method (PSVI) for ambient-noise surface-wave tomography and applies it to high-resolution 3D shear-velocity imaging beneath Great Britain. By avoiding the conventional two-step 2D+1D scheme, the method preserves lateral correlations and yields tighter data fits, capturing features like the Great Glen Fault that align with regional geology. Variational inference enables efficient handling of the high-dimensional 3D problem, and results show improved lateral continuity and more realistic uncertainty structure compared to two-step approaches. The work suggests that fully 3D direct inversion should be preferred for surface-wave tomography when feasible, due to its accuracy and richer geological insight with modest additional computational cost thanks to PSVI.

Abstract

We present a new, variational, fully nonlinear, probabilistic ambient noise tomography method, which estimates subsurface structure and quantifies the corresponding uncertainties directly in three dimensions (3D) from inter-receiver seismic surface wave dispersion data. We use the method to invert for high resolution 3D seismic velocity models of the upper crust beneath Great Britain using seismic ambient noise data recorded around the region - a task that proved too high-dimensional and hence computationally demanding for Monte Carlo sampling to converge to a stable solution. We compare the inversion results from the new method to those obtained from two standard, indirect inversion methods, in which 2D (geographical) surface wave velocity maps and 1D (depth) shear velocity profiles are estimated in two separate, consecutive steps. The results show that the direct-3D scheme preserves better lateral continuity and produces better data fit than the two-step methods, and provides information about lateral correlations that is absent from the two-step solutions. The inversion results are consistent with large-scale geology of Great Britain, and for the first time provide seismologically-imaged evidence of the Great Glen Fault and other major tectonic faults. We therefore propose that direct-3D inversion schemes should be used where possible for surface wave inversion as they provide improved results at little additional computational cost.

Figures (21)

• Figure 1: Locations of the seismometers (red triangles) used in this study. Thick blue lines in (a) represent 4 inter-receiver paths considered in Figures \ref{['fig:uk_data_fit']}. Green lines in (a) show locations of two vertical slices on which the inversion results are compared in Figure \ref{['fig:uk_vertical']}. Blue lines in (b) denote ray paths used to estimate Love wave dispersion data.
• Figure 2: (a) Upper and lower bounds of the uniform prior distribution in different layers. (b) Prior pdf incorporating additional prior information in which shear wave velocity in the first layer is the lowest. This is used in the 1D Monte Carlo inversion. (c) Modified prior pdf used in the direct-3D variational inversion.
• Figure 3: Horizontal slices of the inverted mean velocity maps using three inversion methods, at depths of 1 km, 4.5 km and 9 km.
• Figure 4: Standard deviation maps associated with the mean velocity maps in Figure \ref{['fig:uk_horizontal_mean_3methods']}. Note that the same color scale is applied to all panels to highlight the relative amplitude of standard deviation values from the 3 sets of results.
• Figure 5: (a) and (c) Average velocity, and (b) and (d) standard deviation maps for two vertical slices through the inversion results at (a) and (b) 2$^\circ$W longitude, and (c) and (d) 51$^\circ$N latitude, respectively. The locations of these slices are marked by the green lines in Figure \ref{['fig:uk_stations_rays']}a.