A lateral model parameter correlation procedure for one‐dimensional inverse modelling

Abstract

A B S T R A C TWe present a new, fast and versatile method, the lateral parameter correlation method, of invoking lateral smoothness in model sections of one-dimensional (1D) models. Modern, continuous electrical and electromagnetic methods are capable of recording very large data sets and except for a few cases, standard inversion methodology still relies on 1D models. In environments where the lateral rate of change of resistivity is small, 1D inversion can be justified but model sections of concatenated 1D models do not necessarily display the expected lateral smoothness.The lateral parameter correlation method has three steps. First, all sounding data are inverted individually. Next, a laterally smooth version of each model parameter, one at a time, is found by solving a simple constrained inversion problem. Identity is postulated between the uncorrelated and correlated parameters and the equations are solved including a model covariance matrix. As a last step, all sounding data are inverted again to produce models that better fit the data, now subject to constraints by including the correlated parameter values as a priori values. Because the method separates the inversion from the correlation it is much faster than methods where the inversion and correlation are solved simultaneously, typically with a factor of 200-500.Theoretical examples show that the method produces laterally smooth model sections where the main influence comes from the well-determined parameters in such a way that problems with equivalence and poor resolution are alleviated. A field example is presented, demonstrating the improved resolution obtained with the lateral parameter correlation method. The method is very flexible and is capable of coupling models from inversion of different data types and information from boreholes.

Fast approximate 1D modelling and inversion of transient electromagnetic data

“…The new approximate mapping that is the main focus of this paper shares some basic characteristics with the more simple forward modelling routine of Christensen () and Christensen et al . (). For completeness and due to the simpler approximate mapping playing an important role in the new and more accurate approximate mapping, a short overview of the method is presented in the following.…”

Preview Number 145

“…The minimal data processing requirements for SkyTEM mean that inversions can be performed on field-processed data, which yield results very similar to those from final office-based processing, as illustrated by Figure 4. Using the iTEM fast approximate layered-earth inversion code (Christensen, 2002;Christensen and Tølbøll, 2009), inverted SkyTEM data is now routinely delivered the morning after data acquisition. …”

“…A number of quantitative tools have been applied to SkyTEM data, including EMaxAir CDIs (Fullagar and Reid, 2001;Fullagar et al, 2008); iTEM fast approximate layered-earth inversion (FA-LEI; Christensen, 2002;Christensen and Tølbøll, 2009;) and the full nonlinear laterally constrained inversion (LCI) from Aarhus Geophysics (Auken et al, 2005Viezzoli et al, 2009).…”

Correlation of radon and geomagnetic anomalies of the territory of Ukraine

“…(1) A 30 layer fast approximate inversion (FAI) using the iTEM code developed by Christensen [60,61]; (2) A 17 layer smooth model inversion using the 1-D laterally-constrained inversion (LCI) algorithm implemented in the Aarhus Geophysics Workbench software package [62]; (3) A 4 layer inversion using the 1-D LCI, with constraints applied to the layer resistivities in addition to the lateral constraints.…”