Inversion of Fracture Weaknesses Based on Linearly Approximated Traveltime

Abstract

Seismic traveltime is crucial for the inversion of anisotropy parameters. In the inversion for fractured rock, a typical transversely isotropic medium with a horizontal symmetry axis (HTI), the joint utilization of traveltime of P- and split shear waves can provide more anisotropy information than the utilization of only P-wave traveltime. The computational effort of nonlinear parameter inversion also increases with the involvement of split shear waves. Therefore, based on the series expansion of vertical slowness projection, we derive the linear approximations for the first-break traveltimes of P-, S1-, and S2-waves with respect to fracture weaknesses, which are used to accelerate and stabilize the inversion process. Linear coefficients are used to analyze the sensitivity of the traveltime to fracture weakness and thus the accuracy of the results. To make our proposed approximation more practical, we expand our linear equations to the traveltime difference between the HTI model and its isotropic background model and derive the joint inversion equation for fracture weaknesses in a vertical seismic profile (VSP) survey by jointly using P-, S1-, and S2-waves. Field data application shows that our method is feasible for estimating fracture weaknesses by using walkaround VSP data. The error caused by linear approximation can be reduced by the joint utilization of multiple wave modes.