A mathematical framework for inverse wave problems in heterogeneous media

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical properties of materials. Rocks, manufactured materials, and other wave propagation environments often exhibit spatial heterogeneity in mechanical properties at a wide variety of scales, and coefficient functions representing these properties must mimic this heterogeneity. We show how to choose domains (classes of nonsmooth coefficient functions) and data definitions (traces of weak solutions) so that optimization formulations of inverse wave problems satisfy some of the prerequisites for application of Newton's method and its relatives. These results follow from the properties of a class of abstract first-order evolution systems, of which various physical wave systems appear as concrete instances. Finite speed of propagation for linear waves with bounded, measurable mechanical parameter fields is one of the by-products of this theory

An adaptive multiscale algorithm for efficient extended waveform inversion

Subsurface-offset extended full-waveform inversion (FWI) may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain FWI. However, this robust alternative approach to waveform inversion suffers from a very high computational cost resulting from its use of nonlocal wave physics: The computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at every space-time grid point. We found that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude

IWAVE Implementation of Born Simulation

The single-scattering (or Born) approximation is the most fundamental assumption shared by all seismic imaging methods, and plays a crutial role in the non-linear waveform inversion, an iterative process of linearized inversions. The Born simulator (linearized forward map) shares a computational core with the corresponding simulator (forward map), which has been well implemented in the modeling package IWAVE. This report focuses on implementing the Born simulator based on IWAVE, and reviews the main adaptations we made in IWAVE to accommodate such an implementation in C++. Our goal is to construct a C++ wrapper of IWAVE, which fits into a general framework for inversion. This report is the first of several describing an implementation of such a wrapper

Task Level Parallelization for Seismic Modeling and Inversion

Projet IDENTThis paper present experience with using PVM to parallelize \Dseismic inversion code developed in the Rice Inversion Project. We use coarse grain parallelism to dynamically distribute simulations over several workstations. When doing modeling, this strategy works efficiently, allowing us to reach an speedup of almost 4.5 on a cluster of 6 IBM RS6000 workstations. When doing inversion, however, we are currently limited to speedups of 2.4 on 3 workstations

An Infeasible Point Method for Minimizing the Lennard-Jones Potential

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44788/1/10589_2004_Article_140555.pd

Assessing the cost of global biodiversity and conservation knowledge

Knowledge products comprise assessments of authoritative information supported by stan-dards, governance, quality control, data, tools, and capacity building mechanisms. Considerable resources are dedicated to developing and maintaining knowledge productsfor biodiversity conservation, and they are widely used to inform policy and advise decisionmakers and practitioners. However, the financial cost of delivering this information is largelyundocumented. We evaluated the costs and funding sources for developing and maintain-ing four global biodiversity and conservation knowledge products: The IUCN Red List ofThreatened Species, the IUCN Red List of Ecosystems, Protected Planet, and the WorldDatabase of Key Biodiversity Areas. These are secondary data sets, built on primary datacollected by extensive networks of expert contributors worldwide. We estimate that US$160million (range: US$116–204 million), plus 293 person-years of volunteer time (range: 278–308 person-years) valued at US$14 million (range US$12–16 million), were invested inthese four knowledge products between 1979 and 2013. More than half of this financingwas provided through philanthropy, and nearly three-quarters was spent on personnelcosts. The estimated annual cost of maintaining data and platforms for three of these knowl-edge products (excluding the IUCN Red List of Ecosystems for which annual costs were notpossible to estimate for 2013) is US$6.5 million in total (range: US$6.2–6.7 million). We esti-mated that an additional US$114 million will be needed to reach pre-defined baselines ofdata coverage for all the four knowledge products, and that once achieved, annual mainte-nance costs will be approximately US$12 million. These costs are much lower than those tomaintain many other, similarly important, global knowledge products. Ensuring that biodi-versity and conservation knowledge products are sufficiently up to date, comprehensiveand accurate is fundamental to inform decision-making for biodiversity conservation andsustainable development. Thus, the development and implementation of plans for sustain-able long-term financing for them is critical

Efficient Free-Surface Kirchhoff Modeling

The aim of this work is to introduce a new scheme to apply Kirchhoff modeling efficiently to a 2-D acoustic model with a free surface and with irregular source and receiver locations. We consider as data all the traveltimes and amplitudes of each ray connecting points below some datum depth and points over this depth. We derive a new expression for the Kirchhoff formula which uses these computed traveltimes and amplitudes only. Given accurate components, the primary reflection seismograms computed via this new approach for the Kirchhoff method is remarkably accurate and less expensive than the usual technique. We also compare Kirchhoff seismograms with those produced from the same model by finite-difference solution of the linearized acoustic wave equation. Keywords: Kirchhoff modeling, High frequency approximations. AMS Subject Classification: 78A05, 86A15. Dept. of Applied Mathematics, State University of Campinas, CP 6065, 13081-970 Campinas (SP), Brazil ([email protected]), an..