Cross-borehole tomography with correlation delay times

Abstract

We evaluated a comprehensive numerical experiment of finite-frequency tomography with ray-based (“banana-doughnut”) kernels that tested all aspects of this method, starting from the generation of seismograms in a 3D model, the window selection, and the crosscorrelation with seismograms predicted for a background model, to the final regularized inversion. In particular, we tested if the quasilinearity of crosscorrelation delays allowed us to forego multiple (linearized) iterations in the case of strong reverberations characterizing multiple scattering and the gain in resolution that can be obtained by observing body-wave dispersion. Contrary to onset times, traveltimes observed by crosscorrelation allowed us to exploit energy arriving later in the time window centered in the P-wave or any other indentifiable ray arrival, either scattered from, or diffracted around, lateral heterogeneities. We tested using seismograms calculated by the spectral element method in a cross-borehole experiment conducted in a 3D checkerboard cube. The use of multiple frequency bands allowed us to estimate body-wave dispersion caused by diffraction effects. The large velocity contrast (10%) and the regularity of the checkerboard pattern caused severe reverberations that arrived late in the crosscorrelation windows. Nevertheless, the model resulting from the inversion with a data fit with reduced [Formula: see text] resulted in an excellent correspondence with the input model and allowed for a complete validation of the linearizations that lay at the basis of the theory. The use of multiple frequencies led to a significant increase in resolution. Moreover, we evaluated a case in which the sign of the anomalies in the checkerboard was systematically reversed in the ray-theoretical solution, a clear demonstration of the reality of the “doughnut-hole” effect. The experiment validated finite-frequency theory and disqualified ray-theoretical inversions of crosscorrelation delay times.