Waveform-based simulated annealing of crosshole transmission data: a semi-global method for estimating seismic anisotropy

We successfully apply the semi-global inverse method of simulated annealing to determine the best-fitting 1-D anisotropy model for use in acoustic frequency domain waveform tomography. Our forward problem is based on a numerical solution of the frequency domain acoustic wave equation, and we minimize wavefield phase residuals through random perturbations to a 1-D vertically varying anisotropy profile. Both real and synthetic examples are presented in order to demonstrate and validate the approach. For the real data example, we processed and inverted a cross-borehole data set acquired by Vale Technology Development (Canada) Ltd. in the Eastern Deeps deposit, located in Voisey's Bay, Labrador, Canada. The inversion workflow comprises the full suite of acquisition, data processing, starting model building through traveltime tomography, simulated annealing and finally waveform tomography. Waveform tomography is a high resolution method that requires an accurate starting model. A cycle-skipping issue observed in our initial starting model was hypothesized to be due to an erroneous anisotropy model from traveltime tomography. This motivated the use of simulated annealing as a semi-global method for anisotropy estimation. We initially tested the simulated annealing approach on a synthetic data set based on the Voisey's Bay environment; these tests were successful and led to the application of the simulated annealing approach to the real data set. Similar behaviour was observed in the anisotropy models obtained through traveltime tomography in both the real and synthetic data sets, where simulated annealing produced an anisotropy model which solved the cycle-skipping issue. In the real data example, simulated annealing led to a final model that compares well with the velocities independently estimated from borehole logs. By comparing the calculated ray paths and wave paths, we attributed the failure of anisotropic traveltime tomography to the breakdown of the ray-theoretical approximation in the vicinity of strong velocity discontinuities.