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Conventional full waveform inversion (FWI) using least square distance (LSD) between the observed and predicted seismograms suffers from local minima. Recently, earth mover's distance (EMD) has been introduced to FWI to compute the misfit…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging…
Soil moisture (SM) estimation from active microwave data remains challenging due to the complex interactions between radar backscatter and surface characteristics. While the water cloud model (WCM) provides a semi-physical approach for…
Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the…
Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we…
Inelastic deformation of metallic glasses occurs via slip events with avalanche dynamics similar to those of earthquakes. For the first time in these materials, measurements have been obtained with sufficiently high temporal resolution to…
Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited.…
Operational near-real-time monitoring of Earth's surface deformation using Interferometric Synthetic Aperture Radar (InSAR) requires processing algorithms that efficiently incorporate new acquisitions without reprocessing historical…
Full waveform inversion (FWI) has recently become a favorite technique for the inverse problem of finding properties in the earth from measurements of vibrations of seismic waves on the surface. Mathematically, FWI is PDE constrained…
We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
The frequency content of seismic data is changing with propagation depth due to intrinsic absorption. This implies that the higher frequencies are highly attenuated, thus leading to a loss in resolution of the seismic image. In addition,…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
The final size of an earthquake typically cannot be predicted from its ongoing seismic radiation. Expanding observations reveal distinct exceptions, such as slow earthquakes, injection-induced seismicity, and earthquake swarms, in which…
In this pedagogically motivated work, the process of migration in reflection seismics has been considered from a rigorously mathematical viewpoint. An inclined subsurface reflector with a constant dipping angle has been shown to cause a…
The 11/5/2011 Lorca, Spain earthquake (Mw5.2) and related seismicity produced extensive damage in the town of Lorca and vicinity. During these earthquakes, evidence of rotations and permanent deformations in structures were observed. To…