3-D joint inversion of surface wave and receiver functions based on the Markov chain Monte Carlo

Geophysical inverse problems (seismic tomography) are often significantly underdetermined meaning that a large range of parameter values can explain the observed data well within data uncertainties. Markov chain Monte Carlo (McMC) algorithms based on Voronoi cell parameterizations have been used for quantifying uncertainty in seismic tomography for a number of years. Since surface waves constrain absolute shear velocities and receiver functions (RFs) image discontinuities beneath receiver locations, joint inversion of both data types based on McMC become a popular method to reveal the structure near Earth's surface with uncertainty estimates.

 

Joint inversion is usually performed in two steps: first invert for 2-D surface wave phase (or group) velocity maps and then invert 1-D surface wave and RFs jointly to construct a 3-D spatial velocity structure. However, in doing so, the valuable information of lateral spatial variations in velocity maps and dipping discontinuities in RFs may not be preserved and lead to biased 3-D velocity structure estimation. Hence, the lateral neighbors in the final 3-D model typically preserve little of the 2-D lateral spatial correlation information in the phase and group velocity maps.

 

A one-step 3-D direct inversion based on the reversible jump McMC and 3-D Voronoi tessellation is proposed to improve the above issues by inverting for 3-D spatial structure directly from frequency-dependent traveltime measurements and RFs. We take into account the dipping interfaces according to the Voronoi parameterisation, meaning that back azimuth and incidence angle of individual RFs must be taken into account. We present synthetic tests demonstrating the method. Individual inversion of surface wave measurements and RFs show the limitation of inverting the two data sets separately as expected: surface waves are poor at constraining discontinuities while RFs are poor at constraining absolute velocities. The joint solution gives a better estimate of subsurface properties and associated uncertainties. Compared to two-step inversion which may produce bias propagating between two steps and lose valuable lateral structure variations, the direct 3-D direct inversion not only produces more intuitively reasonable results but also provides more interpretable uncertainties.