Full-waveform seismic reflection responses of an isolated porous sandstone layer are simulated with three-dimensional (3D) isotropic poroelastic and isotropic elastic finite-difference (FD) numerical algorithms. When the pore-filling fluid is brine water with realistic viscosity, there is about a ∼10% difference in synthetic seismograms observed in an AVO recording geometry. These preliminary results suggest that equivalent elastic medium modeling is adequate for general interpretive purposes, but more refined investigations (such as AVO waveform analysis) should account for poroelastic wave propagation effects.
Acoustic wave propagation in a three-dimensional atmosphere that is spatially heterogeneous, time-varying, and/or moving is accurately simulated with a numerical algorithm recently developed under the DOD Common High Performance Computing Software Support Initiative (CHSSI). Sound waves within such a dynamic environment are mathematically described by a set of four, coupled, first-order partial differential equations governing small-amplitude fluctuations in pressure and particle velocity. The system is rigorously derived from fundamental principles of continuum mechanics, ideal-fluid constitutive relations, and reasonable assumptions that the ambient atmospheric motion is adiabatic and divergence-free. An explicit, finite-difference time-domain (FDTD) numerical scheme is used to solve the system for both pressure and particle velocity wavefields. Dependent variables are stored on staggered spatial and temporal grids, and centered FDTD operators possess 2nd-order and 4th-order space/time accuracy. We first present results of a test that shows the accuracy of our algorithm by comparison with analytic formulations. We then present a contrast and comparison of the sound character at a series of distances from a point source activated with a causal source. We are able to investigate the effects of turbulence, complex meteorology (including wind effects), a topographically variable ground surface, and a partially reflective ground surface.
This document is intended to serve as a users guide for the time-domain atmospheric acoustic propagation suite (TDAAPS) program developed as part of the Department of Defense High-Performance Modernization Office (HPCMP) Common High-Performance Computing Scalable Software Initiative (CHSSI). TDAAPS performs staggered-grid finite-difference modeling of the acoustic velocity-pressure system with the incorporation of spatially inhomogeneous winds. Wherever practical the control structure of the codes are written in C++ using an object oriented design. Sections of code where a large number of calculations are required are written in C or F77 in order to enable better compiler optimization of these sections. The TDAAPS program conforms to a UNIX style calling interface. Most of the actions of the codes are controlled by adding flags to the invoking command line. This document presents a large number of examples and provides new users with the necessary background to perform acoustic modeling with TDAAPS.
Findings are presented from the first year of a joint project between the U.S. Army Engineer Research and Development Center, the U.S. Army Research Laboratory, and the Sandia National Laboratories. The purpose of the project is to develop a finite-difference, time-domain (FDTD) capability for simulating the acoustic signals received by battlefield acoustic sensors. Many important effects, such as scattering from trees and buildings, interactions with dynamic atmospheric wind and temperature fields, and nonstationary target properties, can be accommodated by the simulation. Such a capability has much potential for mitigating the need for costly field data collection and furthering the development of robust identification and tracking algorithms. The FDTD code is based on a carefully derived set of first-order differential equations that is more general and accurate than most current sound propagation formulations. For application to three-dimensional problems of practical interest in battlefield acoustics, the code must be run on massively parallel computers. Some example computations involving sound propagation in a moving atmosphere and propagation in the presence of trees and barriers are presented.
The mathematical description of acoustic wave propagation within a time- and space-varying, and moving, linear viscous fluid is formulated as a system of coupled linear equations. This system is rigorously developed from fundamental principles of continuum mechanics (conservation of mass, balance of linear and angular momentum, balance of entropy) and various constitutive relations (for stress, entropy production, and entropy conduction) by linearizing all expressions with respect to the small-amplitude acoustic wavefield variables. A significant simplification arises if the fluid medium is neither viscous nor heat conducting (i.e., an ideal fluid). In this case the mathematical system can be reduced to a set of five, coupled, first-order partial differential equations. Coefficients in the systems depend on various mechanical and thermodynamic properties of the ambient medium that supports acoustic wave propagation. These material properties cannot all be arbitrarily specified, but must satisfy another system of nonlinear expressions characterizing the dynamic behavior of the background medium. Dramatic simplifications in both systems occur if the ambient medium is simultaneously adiabatic and stationary.
The spatial and temporal origin of a seismic energy source are estimated with a first grid search technique. This approach has greater likelihood of finding the global rninirnum of the arrival time misiit function compared with conventional linearized iterative methods. Assumption of a homogeneous and isotropic seismic velocity model allows for extremely rapid computation of predicted arrival times, but probably limits application of the method to certain geologic environments and/or recording geometries. Contour plots of the arrival time misfit function in the vicinity of the global minimum are extremely useful for (i) quantizing the uncertainty of an estimated hypocenter solution and (ii) analyzing the resolving power of a given recording configuration. In particular, simultaneous inversion of both P-wave and S-wave arrival times appears to yield a superior solution in the sense of being more precisely localized in space and time. Future research with this algorithm may involve (i) investigating the utility of nonuniform residual weighting schemes, (ii) incorporating linear and/or layered velocity models into the calculation of predicted arrival times, and (iii) applying it toward rational design of microseismic monitoring networks.
Inversion of head wave arrival times for three-dimensional (3D) planar structure is formulated as a constrained parameter optimization problem, and solved via linear programming techniques. The earth model is characterized by a set of homogeneous and isotropic layers bounded by plane, dipping interfaces. Each interface may possess arbitrary strike and dip. Predicted data consists of traveltimes of critically refracted waves formed on the plane interfaces of the model. The nonlinear inversion procedure is iterative; an initial estimate of the earth model is refined until an acceptable match is obtained between observed and predicted data. Inclusion of a priori constraint information, in the form of inequality relations satisfied by the model parameters, assists the algorithm in converging toward a realistic solution. Although the 3D earth model adopted for the inversion procedure is simple, the algorithm is quite useful in two particular contexts: (i) it can provide an initial model estimate suitable for subsequent improvement by more general techniques (i.e., traveltime tomography), and (ii) it is an effective analysis tool for investigating the power of areal recording geometries for detecting and resolving 3D dipping planar structure.
Traveltimes of head waves propagating within a three-dimensional (3D) multilayered earth are described by straightforward mathematical formulae. The earth model consists of a set of homogeneous and isotropic layers bounded by plane interfaces. Each interface (including the surface) may possess arbitrary strike and dip. In this model, the source-to-receiver raypath of a critically refracted wave consists of a set of straight line segments, not confined to a single plane. Algebraic derivations of the traveltime expressions are greatly simplified by using a novel 3D form of Snell's law of refraction. Various generalizations of the basic traveltime equation extend its applicability to arbitrary source-receiver recording geometries and/or mode-converted waves. Related expressions for the traveltimes of reflected waves and one-way transmitted waves propagating in the same layered earth model are obtained as byproducts of the analysis. The expressions contain a set of unit raypath orientation vectors that depend implicitly on source and receiver coordinates. Hence, the equations cannot be characterized as closed-form in the mathematical sense. However, for critically refracted waves, these vectors can be obtained by a minimal amount of numerical raytracing. The traveltime formulae are useful for a variety of forward modeling and inversion purposes.