Bayesian seismic travel-time cross-hole tomography in vertically transversely isotropic media

Abstract

We apply a transdimensional, hierarchical Markov chain Monte Carlo sampling algorithm (McMC) for 2-D cross-hole travel-time tomography in transversely isotropic media with vertical symmetry axis. The McMC approach has several advantages compared to classical inversion approaches: It is a global search, the high number of tested models allows the statistical analysis including the calculation of a reference model as well as uncertainty estimation, no initial models or regularization parameters are needed, the amount of data noise is automatically determined, and the model parametrization is data dependent and self-adjusting. For the forward solution a FD Fast Marching method utilizing second-order Godunov schemes is used. The performance of the approach is first tested on synthetic datasets to evaluate the potential and possible limitation to recover anisotropic models. We have shown that the recovery of models described by 2 anisotropic parameters (Thomsen parameters) and the vertical velocity is possible for observation scenarios with good distribution of sources and receivers. For more realistic observational geometries (i.e. cross-hole experiments), the recovery of the 3 parameters is limited, but still possible for example for the elliptical anisotropic case (ε = δ) or regarding the horizontal velocity. Finally we applied the McMC approach to a well-studied real cross-hole data set from the MALLIK 2002 research program and compared the results with previous conventional inversions.