Joint inversion of Rayleigh wave fundamental and higher order mode phase velocity dispersion curves using multi-objective grey wolf optimization

Abstract

Rayleigh wave dispersion curves can be inverted to retrieve subsurface seismic velocity profiles. The inverse problem is ill-posed, nonlinear and poorly conditioned, necessitating the application of global optimization methods. We present the application of the multi-objective grey wolf optimization algorithm to perform joint inversion of the phase velocity dispersion curves corresponding to the fundamental and higher order modes of Rayleigh waves to obtain shear (S-) and primary (P-) wave velocity profiles. Multi-objective grey wolf optimization is an extension of the grey wolf optimization algorithm for application to multi-objective optimization and can be adapted to solve joint inversion problems. We compare the joint inversion results obtained from the multi-objective grey wolf optimizer with those obtained from Markov chain Monte Carlo and fundamental mode inversion using the grey wolf optimizer on synthetic examples. The errors associated with phase velocity measurements are simulated by adding frequency-dependent noise, with a higher level of noise added to the phase velocities corresponding to lower frequencies as compared to the higher frequencies. In the multimode joint inversion problem, the multi-objective grey wolf optimizer gives a suite of solutions corresponding to each model parameter. The suite of S-wave and P-wave velocity profiles estimated from the multi-objective grey wolf optimizer matches closely with the true model for the synthetic case studies even in the presence of noise. However, the suite of solutions has a greater spread for the last few layers, qualitatively indicating a higher degree of uncertainty in the predicted model parameter. The uncertainty in the solution for the deeper layers is a consequence of the uncertainty in the phase velocity at lower frequencies. We demonstrate the efficacy of the algorithm on recorded data from a shallow seismic survey conducted at the Indian Institute of Technology Bombay. The results from the multi-objective grey wolf optimizer are in close agreement with those from Markov chain Monte Carlo, and the depth of investigation is found to be greater in comparison to results from refraction traveltime inversion.