Mono‐Model Parameter Joint Inversion by Gramian Constraints: EM Methods Examples

Abstract

Joint inversions of coincident geophysical data are usually constrained to produce more reliable subsurface models. Structural, petrophysical, model parameter correlation, empirical, and transforms are some of the published constraints. The Gramian constraint provides a broad mathematical framework for implementing the aforementioned constraints. The Gramian constraint is formed from the determinant of the inner products of the model parameters involved. Previous works have used the Gramian constraint to invert multimodal parameters of different geophysical methods. But there has not been any extension of Gramian‐constrained joint inversion to mono‐model parameter from similar geophysical methods, for example, a similar conductivity or resistivity model from time‐ and frequency‐domain airborne electromagnetic methods. I implement the Gramian‐constrained joint inversion of time‐ and frequency‐domain airborne EM (AEM) data. This implementation allows the Gramian constraint to enhance the linear correlation of the model parameter between the two methods as the number of iterations increases. Improvement of the final joint inversion results over the standalone models is noticeable for both 3% noise‐contaminated synthetic and field data experiments. The field data jointly inverted are the high moment time‐domain SkyTEM data and frequency‐domain RESOLVE helicopter EM data acquired over the salinized Bookpurnong Irrigation District in South Australia in 2006 and 2008, respectively.

N-hidden layer artificial neural network architecture computer code: geophysical application example

“…The problem of the ANN is similar to the usual nonlinear inversion optimization problem (Ogunbo and Zhang, 2014;Ogunbo et al, 2018;Ogunbo, 2019) whose objective function can be defined in Eq. (1) as:…”

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

“…; Zhu et al . ; Čuma and Zhdanov ; Zhdanov and Cai ; Lin and Zhdanov ), electromagnetic (Zhu and Zhdanov ; Jorgensen and Zhdanov ; Ogunbo ), and seismic field data (Lin and Zhdanov ).…”