On the parallelization of the acoustic wave equation with absorbing boundary conditions

Many practical problems involve wave propagation through atmosphere, oceans, or terrestrial crust. Modeling and analysis of these problems is usually done in (semi)infinite domains, but numerical calculations obviously impose restriction to finite domains. To mimic the actual behavior in the (semi)infinite medium, artificial absorbing boundary conditions are imposed at the boundaries, whereby waves can only exit, but not enter the finite computational domain. Efficient absorbing boundary conditions are difficult to analyze and costly to run. In particular, it is of interest to assess whether the wave equation with (approximate or exact) absorbing boundary conditions admits a suitable diagonalization. This would open the possibility for parallelizing many important numerical codes used in applications. In this paper the authors propose a set of stable, local, absorbing boundary conditions for the discrete acoustic wave equation. They show that the acoustic wave equation with absorbing boundary conditions cannot be exactly diagonalized

Global optimization for multisensor fusion in seismic imaging

The accurate imaging of subsurface structures requires the fusion of data collected from large arrays of seismic sensors. The fusion process is formulated as an optimization problem and yields an extremely complex energy surface. Due to the very large number of local minima to be explored and escaped from, the seismic imaging problem has typically been tackled with stochastic optimization methods based on Monte Carlo techniques. Unfortunately, these algorithms are very cumbersome and computationally intensive. Here, the authors present TRUST--a novel deterministic algorithm for global optimization that they apply to seismic imaging. The excellent results demonstrate that TRUST may provide the necessary breakthrough to address major scientific and technological challenges in fields as diverse as seismic modeling, process optimization, and protein engineering

Constant-time solution to the Global Optimization Problem using Bruschweiler's ensemble search algorithm

A constant-time solution of the continuous Global Optimization Problem (GOP) is obtained by using an ensemble algorithm. We show that under certain assumptions, the solution can be guaranteed by mapping the GOP onto a discrete unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is applied. For adequate sensitivities of the measurement technique, the query complexity of the ensemble search algorithm depends linearly on the size of the function's domain. Advantages and limitations of an eventual NMR implementation are discussed.Comment: 14 pages, 0 figure

DeepNet: An Ultrafast Neural Learning Code for Seismic Imaging

A feed-forward multilayer neural net is trained to learn the correspondence between seismic data and well logs. The introduction of a virtual input layer, connected to the nominal input layer through a special nonlinear transfer function, enables ultrafast (single iteration), near-optimal training of the net using numerical algebraic techniques. A unique computer code, named DeepNet, has been developed, that has achieved, in actual field demonstrations, results unattainable to date with industry standard tools

Chemical detection using the airborne thermal infrared imaging spectrometer (TIRIS)

A methodology is described for an airborne, downlooking, longwave infrared imaging spectrometer based technique for the detection and tracking of plumes of toxic gases. Plumes can be observed in emission or absorption, depending on the thermal contrast between the vapor and the background terrain. While the sensor is currently undergoing laboratory calibration and characterization, a radiative exchange phenomenology model has been developed to predict sensor response and to facilitate the sensor design. An inverse problem model has also been developed to obtain plume parameters based on sensor measurements. These models, the sensors, and ongoing activities are described

Neural network accuracy measures and data transforms applied to the seismic parameter estimation problem

The accuracy of an artificial neural network (ANN) algorithm is a crucial issue in the estimation of an oil field reservoir`s properties from remotely sensed seismic data. This paper demonstrates the use of the k-fold cross validation technique to obtain confidence bounds on an ANN`s accuracy statistic from a finite sample set. In addition, we also show that an ANN`s classification accuracy is dramatically improved by transforming the ANN`s input feature space to a dimensionally smaller, new input space. The new input space represents a feature space that maximizes the linear separation between classes. Thus, the ANN`s convergence time and accuracy are improved because the ANN must merely find nonlinear perturbations to the starting linear decision boundaries. These techniques for estimating ANN accuracy bounds and feature space transformations are demonstrated on the problem of estimating the sand thickness in an oil field reservoir based only on remotely sensed seismic data

Oil reservoir properties estimation using neural networks

This paper investigates the applicability as well as the accuracy of artificial neural networks for estimating specific parameters that describe reservoir properties based on seismic data. This approach relies on JPL`s adjoint operators general purpose neural network code to determine the best suited architecture. The authors believe that results presented in this work demonstrate that artificial neural networks produce surprisingly accurate estimates of the reservoir parameters

Optimization and geophysical inverse problems

A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section