Lawrence Berkeley National Laboratory

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 /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 /year decrease in water volume for the entire Central Valley, estimated from GRACE satellite gravity data. Plain Language Summary A new approach allows for the inversion of quasi‐static deformation data for parameters describing the source, such as aquifer/reservoir volume changes or fracture aperture changes. The technique utilizes the solution of the adjoint problem to find the model parameter gradients necessary for an iterative update of an initial model. Each update of the source model requires the equivalent of three forward simulations, one to determine the residuals, one to solve the adjoint problem, and one to determine the step length. The technique is applied to Interferometric Synthetic Aperture Radar line‐of‐sight displacement data from California's Central Valley in order to estimate aquifer volume loss in the Tulare Basin. Key Points An adjoint‐based gradient calculation provides the basis for an efficient inversion approach of quasi‐static deformation data A comparison with a conventional sensitivity‐based inversion technique demonstrates the accuracy of the adjoint‐based gradient An application to InSAR range change data from the Tulare Basin in California's Central Valley demonstrates the utility of the approach