Neill P. Symons

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation.

Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.

Tomographic Images of Klyuchevskoy Volcano P‐Wave Velocity

Three-dimensional structural images of the P-wave velocity below the edifice of the great Klyuchevskoy group of volcanoes in central Kamchatka are derived via tomographic inversion. The structures show a distinct low velocity feature extending from around 20 km depth to 35 km depth, indicating evidence of magma ponding near the Moho discontinuity. The extensive low velocity feature represents, at least to some degree, the source of the large volume of magma currently erupting at the surface near the Klyuchevskoy group.

Padé approximation in time-domain boundary conditions of porous surfaces

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.

Insight into the output of reverse-time migration: what do the amplitudes mean?

Summary With the purpose of attaching meaning to the waveforms imaged by reverse-time migration, we obtain an expression for the output of such an algorithm over a simple subsurface model of a dipping interface. We invoke the cross-correlation imaging condition and make extensive use of the stationary phase approximation to analyze the migrated image. Our result quantifies the meaning of the amplitudes output from reverse-time shot-profile migration and should have relevance for direct migration of passive seismic data and frequency-swept source signals. A numerical example of reverse-time migration supports our theoretical results.

Development of a high-fidelity simulation capability for battlefield acoustics.

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.

3D finite‐difference simulation of acoustic waves in turbulent moving media

A finite‐difference algorithm appropriate for modeling acoustic waves in a fully heterogeneous moving 3D media has been developed. The model is characterized by: acoustic velocity, density, and the three components of the background media velocity. The approach solves a set of coupled 1st order velocity‐pressure differential equations appropriate for an adiabatic divergence‐free background velocity. The equations are staggered in time and space and the algorithm uses second order temporal and fourth order spatial finite‐differences. Since approximations are not adopted in the solution of the equations all arrivals are modeled with fidelity providing the spatial and temporal grids are chosen appropriately. The algorithm can include either a pressure or velocity free surface on the bottom boundary and absorbing boundaries on other model flanks. Designed to run on large scale parallel computational platforms, the algorithm has been validated for four machine architectures. Comparisons are presented to an ana...

Comparison of Poroelastic And Elastic Full-Waveform AVO Responses

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.

Grid Search Algorithm For 3D Seismic Source Location

The spatial and temporal origin of a seismic energy source are estimated by minimizing (in the weighted least squares sense) the misfit between observed and predicted arrival times at a set of receiver stations. A search is conducted for the best source position within a 3D gridded volume of trial locations. Rapid calculation of predicted traveltimes is achieved by evaluating closed-form formulae appropriate for a homogeneous or 1D layered velocity model. The method is applicable to microseismic event location for mapping hydraulic fracturing in a petroleum reservoir.

3D Acoustic and Elastic Modeling with Marmousi2.

The Marmousi model is a synthetic 2D earth model developed from geologic aspects of the Cuanza basin of offshore Angola. It contains several structural features relevant in marine seismic exploration for petroleum: a water layer with a horizontal seabed, a sequence of dipping growth faults that offset and truncate sedimentary beds, anticlines, two salt sills, a near-horizontal erosional unconformity, and a deep petroleum reservoir. The model is commonly utilized to generate synthetic data for evaluating seismic reflection imaging algorithms. Recently, Martin et al. (2006) created a sophisticated elastic upgrade to the original acoustic Marmousi model, dubbed Marmousi2. Lithology-based formulae appropriate for shale, sandstone, marl, and salt are used to assign shear (S) wave speed and mass density values to the various layers, given the compressional (P) wave speed. Several gas-, oil-, and brine-saturated units are inserted into the layering. The new model is still 2D, although it is extended both laterally and vertically, and water depth is increased to 450 m to enable simulation of deep water seismic exploration experiments. Figure 1 displays the 2D Marmousi2 S-wave velocity distribution; the P-wave velocity and density models are structurally similar.

Seismic wave propagation in 3D randomly‐heterogeneous elastic media

Three-dimensional (3D) seismic wave propagation within a randomly-heterogeneous, isotropic elastic medium is simulated with an explicit, time-domain, finite-difference (FD) algorithm based on the velocity-stress system of elastodynamics. Geologically realistic earth models, containing spatially-correlated random variations in material properties, are readily generated with a wavenumber-domain algorithm. Calculated synthetic seismic data clearly show numerous effects associated with scattering of compressional, shear, and surface waves by the randomly distributed perturbations.