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Adjoint-Based Inversion of Geodetic Data for Sources of Deformation and Strain

Abstract

An adjoint-based formulation leads to a particularly efficient approach for inverting geodetic measurements for the source of the deformation. Specifically, the quantities necessary to iteratively improve the fit to the observations can be computed with just three forward calculations, one to obtain the current residuals, another to solve the adjoint problem, and a third to compute the step length. An inversion algorithm utilizing the adjoint-based gradient is applied to a set of Interferometric Synthetic Aperture Radar (InSAR) data gathered between 2016 and 2018 over the Tulare Basin in California's Central Valley. Because the measured deformation is due to groundwater withdrawal, a penalty function is included in the inversion to avoid placing aquifer volume change in locations that are far from any documented wells. The solution of the inverse problem provides estimates of aquifer compaction that provide a match to the observed range changes while honoring the well data. The solution indicates an average aquifer volume loss of 2.17 (Formula presented.) /year over the two year period from January 2016 to January 2018, encompassing one drought year (2016) and one wet year (2017). This magnitude of lost volume is compatible with the 3.1 (Formula presented.) /year decrease in water volume for the entire Central Valley, estimated from GRACE satellite gravity data.

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