Incorporating known petrophysical model in the seismic full‐waveform inversion using the Gramian constraint

Abstract

A B S T R A C TIn this paper, we develop a general approach to integrating petrophysical models in three-dimensional seismic full-waveform inversion based on the Gramian constraints. In the framework of this approach, we present an example of the frequency-domain P-wave velocity inversion guided by an electrical conductivity model. In order to introduce a coupling between the two models, we minimize the corresponding Gramian functional, which is included in the Tikhonov parametric functional. We demonstrate that in the case of a single-physics inversion guided by a model of different physical type, the general expressions of the Gramian functional and its gradients become simple and easy to program. We also prove that the Gramian functional has a nonnegative quadratic form, so it can be easily incorporated in a standard gradient-based minimization scheme. The developed new approach of seismic inversion guided by the known petrophysical model has been validated by three-dimensional inversion of synthetic seismic data generated for a realistic three-dimensional model of the subsurface.

Advanced Methods of Joint Inversion of Multiphysics Data for Mineral Exploration

“…Case studies of practical applications of the Gramian constraints have been presented in several recently published papers. For example, Malovichko et al [22] demonstrated how Gramian constraints can be used for guided full-waveform inversion of seismic data using known petrophysical properties of the rocks. In the papers [23,24], the authors applied Gramian constraints in joint inversion for density and magnetization models.…”