Modeling flow in a pressure-sensitive, heterogeneous medium

Using an asymptotic methodology, including an expansion in inverse powers of {radical}{omega}, where {omega} is the frequency, we derive a solution for flow in a medium with pressure dependent properties. The solution is valid for a heterogeneous medium with smoothly varying properties. That is, the scale length of the heterogeneity must be significantly larger then the scale length over which the pressure increases from it initial value to its peak value. The resulting asymptotic expression is similar in form to the solution for pressure in a medium in which the flow properties are not functions of pressure. Both the expression for pseudo-phase, which is related to the 'travel time' of the transient pressure disturbance, and the expression for pressure amplitude contain modifications due to the pressure dependence of the medium. We apply the method to synthetic and observed pressure variations in a deforming medium. In the synthetic test we model one-dimensional propagation in a pressure-dependent medium. Comparisons with both an analytic self-similar solution and the results of a numerical simulation indicate general agreement. Furthermore, we are able to match pressure variations observed during a pulse test at the Coaraze Laboratory site in France

Trends of and factors associated with live-birth and abortion rates among HIV-positive and HIV-negative women

Little is known about fertility choices and pregnancy outcome rates among HIV-infected women in the current combination ART era

Implementation of the Conjugate Gradient Algorithm in DSO

Computation of the inner state parameters in DSO inversion requires solving a large normal matrix system. A combined conjugate gradient and Lanczos iterative technique can be used to both solve the system and approximate some of the spectrum of the normal operator. At each iteration of the conjugate gradient algorithm, a small tridiagonal matrix (of dimension equal to the number of iterations) is created which has extreme eigenvalues approximating those of the original matrix. A second matrix whose columns are the normalized residual vectors from the conjugate gradient algorithm allows the corresponding eigenvectors to be computed as well if desired. Implemented so that it can be applied to different DSO inversion problems, the conjugate gradient code provides the user with a tool to analyze the condition of the problem as well as the quality of the inversion results. Storage of the residual (Lanczos) vectors may be costly if large problems are being solved. Numerical experiments indic..

A Computationally Feasible Approximate Resolution Matrix for Seismic Inverse Problems

this paper. However, he did not form the model resolution matrix from the resulting approximate eigen information. Nolet and Snieder (1990) gave a theoretical overview of applying Paige and Saunders' (1982) LSQR algorithm to the continuous inverse problem. They did not give any numerical examples. Berryman described both a Lanczos method (1994a) and an LSQR-based method (1994b) for computing resolution. The Lanczos technique is very similar to the method discussed in this paper. Although he gave a small (4 \Theta 4) seismic tomography example of LSQR, he did not give a numerical example of the Lanczos method. Zhang and McMechan (1995) apply LSQR to a larger set of synthetic tomography problems

Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code

Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code

Viscoelastic Modeling and Inversion of a Marine Data Set

this paper. Ige

Simultaneous Determination of the Source-Time Function and Reflectivity via Inversion

No attempt to uncover the desired mechanical properties of the earth will be successful in reflection seismology without an accurate estimate of the source term in the wave equation model. In this paper we argue for using inversion to solve the source calibration problem while at the same time discerning the earth parameters. We show both mathematically and through a numerical example how highly effective inversion can be in this determination when reproducible sources provide redundancy in the seismic data