Target-oriented linear least squares and nonlinear, trust-region Newton inversions of plane waves using AVA and PVA data for elastic model parameters

Abstract

Variations in elastic properties directly impact observed seismic amplitude and phase, as a function of incident angle (amplitude variation with angle [AVA] and with phase [PVA]). Conventional simultaneous prestack inversion uses precritical PP reflections, or joint PP and PS reflections, data to invert for elastic properties via linearized least-squares (LS) methods. Incorporating measured phase information as additional constraints for joint PP-PS and joint AVA-PVA inversions helps to stabilize the convergence path and improves the accuracy of the inverted parameters. Combining these dual joint constraints in a nonlinear trust-region reflective Newton (TRN) solver produces a robust inversion with improved convergence rates. Partial derivatives for the Jacobian and Hessian matrices are computed numerically. Two weighting functions, one for PP/PS and one for AVA/PVA data, are developed for minimizing the global objective function during inversion. Numerical results for data from a salt interface reflection in the SMAART JV Pluto model reveals a marked improvement in convergence when using the weighted nonlinear TRN method compared with a traditional linearized LS method, for clean and noisy data.