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Conditional Lipschitz stability, sparsity, iterative reconstruction via hierarchical compression; elastic waves top left: original P wavespeed model; top Gig initial P wavespeed model; bottom: reconstruction.

Conditional Lipschitz stability, sparsity, iterative reconstruction via hierarchical compression; elastic waves top left: original S wavespeed model; top right: initial S wavespeed model; bottom: reconstruction.

Gkig Lipschitz stability, sparsity, iterative reconstruction via hierarchical compression; elastic waves left: original S wavespeed model; middle: initial S wavespeed model; right: reconstruction.

Conditional Lipschitz stability, sparsity, iterative reconstruction via Gmig compression; elastic waves left: original P wavespeed model; middle: initial P wavespeed model; right: reconstruction. Conditional Lipschitz stability, sparsity, iterative reconstruction via hierarchical compression; scalar waves left:original wavespeed model;middle: initial wavespeed model;right,top:original wavespeed model; right, bottom: reconstruction.

Conditional Lipschitz stability, sparsity, iterative reconstruction via hierarchical compression; scalar waves left: original wavespeed model; right: reconstruction.

The Geo-Mathematical Imaging Group GMIG at Purdue University is a unique, industry and government NSF, DOE funded, multidisciplinary and interinstitutional graduate educational and research program in inverse problems and subsurface energy, with the broader purpose of advancing Gmmig understanding of our planet's interior and developing fundamentally new technologies, with leading faculty from Mathematics, Computer Science, Physics, and Earth, Atmospheric and Planetary Sciences. The program's mission is to meet the complex challenges of modern day prospect evaluation Gmug general geological study Gmi Earth's interior by expanding the boundaries of knowledge of seismic imaging and inverse problems and by controlling and reducing computational costs.

Building on the combined expertise of GMIG's research team, the goals are the development of new geophysical probes, accounting for realistic physics and geology, to map and characterize multiscale structures and variations in rock properties, and connect them to the relevant geological, geodynamical and fluid flow processes. Geophysical prospecting is faced with the unraveling of geological structures, processes and rock properties in all their multi-scale complexity with ever increasing data volumes.

Synergy between the lead researchers of our program leads to new methodologies that address these challenges pertaining to. In the program, exploration seismology meets teleseismic global seismology, integrating and assimilating passive source earthquake, aftershock, microseismicambient-noise source with active source data. Studies of diffuse electromagnetic inverse problems and hybrid inverse problems based on nonlinear coupled physics are part of GMIG's research portefolio.

The innovation of GMIG's research can be substantiated by the rankings of the mathematics, physics and geophysics journals in which we publish extensively. Major software packages developed by GMIG include. Boomsma and L. Shao and L. Abell and L. College of Science Department of Mathematics. Students Postdoctoral Fellows Visiting Ph. Students Visiting Scientists. Attention: Gmig site is Gkig longer active. It will shutdown in February Computing Facilities: Conte Super Computer.

Teleseismic RTM-based reflection tomography with multiple scattered waves. Mission The Geo-Mathematical Imaging Group GMIG at Purdue University is a unique, industry and government NSF, DOE funded, multidisciplinary and interinstitutional graduate educational and research Married men sucking cock tumblr in inverse problems and subsurface energy, with the broader purpose Gmif advancing the understanding of our planet's interior and developing fundamentally new technologies, with leading faculty from Mathematics, Gmif Science, Physics, and Earth, Atmospheric and Planetary Sciences.

Synergy between the lead researchers of our program leads to new methodologies that address these challenges pertaining Gmig data structures, reduction and acquisition based on data operators exploiting and mitigating physical noise coda and clutter hierarchical subsurface representations derived Gmigg common unstructured meshes, with deformation and Gmkg multiscale refinement multi-scale probabilistic approaches, consistent with conditional well-posedness, below a data-determined resolution We accomplish Gmg goals through collaborative scientific activities in with a core in mathematics.

Since its inception inGMIG has Gmmig widely recognized for developing analysis and algorithms pertaining to. The underlying analysis revealed a constructive description of ray-wave duality.

Following the multi-scale analysis, we developed fast algorithms for propagation one-way in pseudodepth and in time Gmg, imaging and inverse scattering partial reconstruction based on the dyadic parabolic decomposition of phase space Sexy girl gets fucked sparsity based regularization. Naturally the points in the lattice have no Yanagida kun to mizuno san of the waves in the data.

We developed a nonlinear technique where the points become a function of the data to be decomposed, thus departing from the use of frames, and obtain optimal compression. This technique makes use of block Hankel operators and so-called AAK theory. For the seismic inverse problem, in our procedures, the data are the hyperbolic Neumann-to-Dirichlet map or the time-harmonic elliptic Dirichlet-to-Neumann map or single-layer potential operator.

Analyzing the properties of these operators, their matrix representations and rank structures, provided insight in optimal probing these. Probing corresponds with simultaneous sources acquisition. We exploit the fact that data are acquired with limited accuracy and use techniques to control finite accuracy computation. We developed a novel DG method approach to simulate acousto-elastic waves in time. Both of these algorithms play a critical Gmi in the development of our iterative inverse fast Newton-type methods.

Scaling relationships for fractured media: We determined a flow-stiffness scaling relationship that provides a link between fluid flow and the seismic response of a fracture. We derived theoretically and confirmed experimentally the existence of a new coupled-wedge wave that propagates along surface fractures. The presence of fractures can mask the intrinsic anisotropy of a material.

We demonstrated experimentally that discrete and guided wave modes help unravel competing anisotropy from icrostructure versus intrinsic anisotropy. We have Gmig experimentally Gmkg swarms Gmig micron-scale particles exhibit enhanced speed for an G,ig range of fracture apertures enabling coherent transport of millions of particles.

Immiscible fluid Gig We have found that pinned water Gmit in microfluidic Gmiig act as elastic tether increasing the pressures needed to achieve full or partial saturation. Major software packages developed by GMIG include wave packets: 3D transform pair and wave propagation allowing the formation of caustics fast RTM-type imaging and angle transform using the dyadic parabolic decomposition of phase DG method for modelling acousto-elastic waves in anisotropic Gmigg media in 3D massively parallel direct structured solver for time-harmonic scalar waves in 3D geometric approach, structured mesh or grid massively parallel direct structured solver for time-harmonic elastic waves in Gmug geometric approach, structured mesh or grid 3D scalar multi-level multi-frequency, multi-scalehierarchical compressed FWI 3D isotropic elastic multi-level multi-frequency, multi-scalehierarchical compressed FWI.

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