Weighted cross-gradient function for joint inversion with the application to regional 3-D gravity and magnetic anomalies

Abstract

In the absence of quantitative relationships, a cross-gradient function can be used to correlate unknown physical properties in a joint inversion of geophysical data sets. It introduces a structural correlation between properties. A commonly used, inexact approach adds a weighted cross-gradient term as a penalty to the cost function being minimized during inversion. This weighting factor needs to be tuned to balance the regularization and cross-gradient terms. In this paper we propose nonlinear weighting for the cross-gradient function which addresses the very different magnitudes of the cross-gradient and regularization terms. This approach also couples the weighting factors for the regularization and correlation terms reducing the number of tuning parameters. The approach is investigated for a synthetic case. Results are also shown for the 3-D joint inversion of high-resolution magnetic and gravity anomaly data from Southern Queensland in Australia with over 30 million cells.

Sequential joint inversion of gravity and magnetic data via the cross‐gradient constraint

“…Menichetti and Guillen, 1983; Vernant et al ., 2002; Saunders et al ., 2005; Wang et al ., 2011) or of joint inversion methods (e.g. Vozoff and Jupp, 1975; Gallardo and Meju, 2007; Candansayar and Tezkan, 2008; Moorkamp et al ., 2011; Bennington et al ., 2015; Demirci et al ., 2018; Gross, 2019; Oliver‐Ocaño et al ., 2020) have attracted some interest.…”

“…(2018) developed an enhanced joint inversion of gravity and TMI data reducing computational cost as the algorithm avoids SVD. Gross (2019) presented a weighted cross‐gradient joint inversion of gravity and magnetic data with vertical polarization. He significantly improved the structural similarity between the recovered density and susceptibility values by the local weighting of the cross gradients.…”

“…He significantly improved the structural similarity between the recovered density and susceptibility values by the local weighting of the cross gradients. This led to a second‐order correlation function that is second order in the gradients of the property function, in contrast to a cross gradient which is a fourth‐order correlation function (for more details, see Gross 2019). Recently, Zhang and Wang (2020) proposed a fast structural joint inversion of gravity and magnetic data algorithm by solving an objective function composed of three terms including the data misfit, the total variation stabilizer and a cross‐gradient constraint.…”

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

“…(), Rittgers et al . (), Manukyan, Maurer and Nuber (), Gao and Zhang (), Gross (), Lan et al . (), Zhang et al .…”

Joint inversion of GPR and ER data

“…Since then different types of geophysical data have been used in this context (Gallardo & Meju, 2007;Fregoso & Gallardo, 2009;Gross, 2019). Most relevant to our study are the works of Linde et al (2006) and Doetsch et al (2010) which use borehole GPR and ER data to solve for electrical permittivity and conductivity.…”