Joint-inverse framework with PEST examples to improve subsurface modelling

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Friedel, M.J.; Moreira, L.P. 2016 Joint-inverse framework with PEST examples to improve subsurface modelling. Lower Hutt, N.Z.: GNS Science. GNS Science report 2016/46 iii, 69 p.; doi: 10.21420/G2F598

Abstract: Joint inversions facilitate the integration of different data sets for improved subsurface interpretations. We present a framework for the implicit joint inversion of data sets using available numerical models and model-independent parameter estimation (PEST) software package. Matlab scripts are used to prepare PEST files and build appropriate joint-inversion schemes. The ill-posed joint inversion is regularized using either the Tikhonov constraint for a set of common model parameters, or the cross-gradient constraint for sets of disparate model parameters. The former constraint is implemented using the prior-information functionality, whereas the later constraint is implemented by adding the PAR2PAR program and model calls using a Linux shell script. The application of prior information is considered soft because the difference equations among adjacent parameters change as a function of the nonlinear updating procedure. By contrast, the cross-gradient equations among different model parameter types are computed as observations and then minimized as part of the measurement objective function. We demonstrate efficacy of the joint-inverse framework to: (1) estimate 2D resistivity distribution from magnetotelluric (MT) soundings subject to a Tikhonov constraint, (2) estimate a 1D velocity profile from teleseismic receiver function (RF) and surface wave dispersion (SWD) data, and (3) simultaneously estimate three 1D velocity profiles and 2D resistivity distribution from teleseismic RF, SWD, and MT data subject to a cross-gradient constraint. Example scripts and PEST files are provided for the three inverse case studies. Modification of these scripts and PEST files will make it possible to perform joint solutions for characterization and assessment of ecological, energy, environmental, mineral, and water resources. (auth)