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

Abstract

S U M M A R YWe 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 raytheoretical approximation in the vicinity of strong velocity discontinuities.

Resolution analysis by random probing

“…It follows that the computational requirements of the proposed resolution analysis are roughly equivalent to a full‐waveform inversion with only five iterations. However, between 10 and 100 iterations are typically needed in real‐data applications [e.g., Igel et al , ; Pratt , ; Dessa et al , ; Fichtner et al , ; Virieux and Operto , ; Kawai and Geller , ; Tape et al , ; Rickers et al , ; Afanasiev et al , ].…”

“…New challenges in uncertainty quantification arose with the advent of tomographic techniques based on purely numerical wavefield simulations and adjoint techniques [e.g., Igel et al , ; Pratt , ; Dessa et al , ; Fichtner et al , ; Virieux and Operto , ; Kawai and Geller , ; Tape et al , ; Rickers et al , ; Colli et al , ; Afanasiev et al , ]. Commonly referred to as full‐waveform inversion, these methods have computationally expensive forward problem solutions, large model spaces, and a nonlinear dependence between measurements and model parameters.…”

Large‐Scale Seismic Inversion Framework

“…The adjoint sources will be stored in whatever format the chosen numerical waveform solver requires. Currently, implemented misfit measures include the L 2 waveform difference typically used in exploration applications (e.g., Igel et al, 1996;Pratt et al, 1998;Afanasiev et al, 2014), the cross-correlation travel-time shift used in waveform traveltime inversion (Luo and Schuster, 1991), and the timefrequency phase misfit (Fichtner et al, , 2013.…”

“…Furthermore, methodological developments have sharpened our picture of the Earth. Depending on the nature of the data, the scientific question, and the available resources, seismic tomographers can choose from a rich variety of techniques, including ray tomography (e.g., Kissling, 1988;Spakman, 1991;Grand et al, 1997;Rawlinson and Sambridge, 2003), various finite-frequency methods (e.g., Yomogida, 1992;Dahlen et al, 2000;Friederich, 2003;Kennett, 2004, 2005), or full-waveform inversion based on numerical solutions of the wave equation (e.g., Tarantola, 1988;Chen et al, 2007;Fichtner et al, 2009;Zhu et al, 2012;Fichtner et al, 2013;Afanasiev et al, 2014).…”

Data Fast Transmission Method in Wireless Vehicle Ad-hoc Network

“…Traffic accidents are still a bottleneck restricting the development of society (Tao et al, 2015). Taking intelligent transportation measures can reduce the incidence of traffic accidents, improve road utilization and vehicle travel efficiency, and effectively guarantee people's property and life safety (Afanasiev et al, 2017).…”