# Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate

**Authors:** Amal Alghamdi, Marc A. Hesse, Jingyi Chen, Omar Ghattas  
**arXiv:** [2002.10706](https://arxiv.org/abs/2002.10706)  
**Date:** 2020-02-25  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2002.10706v1/

## Key points

- Importance of characterizing groundwater aquifers for predicting aquifer response and managing groundwater resources
- Introduction of a high-dimensional scalable Bayesian inversion framework based on a three-dimensional quasi-static linear poroelastic model
- Focus on determining the maximum a posteriori (MAP) point of the posterior permeability distribution using InSAR surface deformation data
- Methodological advancements including adjoint-based derivatives, inexact Newton methods, and Matérn class sparse prior precision operator to address scalability challenges
- Successful application of methodology to a test case in Mesquite, Nevada with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs
- Consistent addressing of noise levels in analysis to ensure robust aquifer characterization results
- Significant improvements in characterizing lateral aquifer heterogeneity through utilizing InSAR data
- Accurate capture of complex lateral displacement trends observed through independent daily GPS measurements

## Summary

In their study titled "Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate," authors Amal Alghamdi, Marc A. Hesse, Jingyi Chen, and Omar Ghattas emphasize the importance of characterizing groundwater aquifers to predict aquifer response and effectively manage groundwater resources. The researchers introduce a high-dimensional scalable Bayesian inversion framework based on a three-dimensional quasi-static linear poroelastic model to analyze lateral permeability variations in groundwater aquifers. The study focuses on determining the maximum a posteriori (MAP) point of the posterior permeability distribution using centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). To address the scalability challenges associated with high parameter dimensions, the authors employ adjoint-based derivatives, inexact Newton methods for determining the MAP point, and a Matérn class sparse prior precision operator. These methodological advancements ensure that the MAP point can be identified at a cost independent of the parameter dimension by minimizing the number of forward/adjoint poroelasticity solves. To validate their approach, the researchers apply their methodology to a test case involving a municipal well in Mesquite, Nevada where both InSAR and GPS surface deformation data are available. Remarkably, they successfully solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. By consistently addressing noise levels in their analysis, the team ensures that the aquifer characterization results remain robust regardless of variations in pixel spacing within surface deformation data. The findings of this study highlight significant improvements in characterizing lateral aquifer heterogeneity achieved through utilizing InSAR data. Furthermore, the InSAR-based aquifer characterization accurately captures complex lateral displacement trends observed through independent daily GPS measurements. This research contributes valuable insights into enhancing our understanding of groundwater aquifers and optimizing strategies for sustainable groundwater resource management.