# David F. Aldridge's research while affiliated with Sandia National Laboratories and other places

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## Publications (57)

We establish analogies between equivalent source theory in seismology (moment-tensor and single-force sources) and acoustics (monopoles, dipoles and quadrupoles) in the context of volcanic eruption signals. Although infrasound (acoustic waves < 20 Hz) from volcanic eruptions may be more complex than a simple monopole, dipole or quadrupole assumptio...

We investigate a novel application of Fréchet derivatives for time-lapse mapping of deep, electrically–enhanced fracture systems with a borehole to surface DC resistivity array. The simulations are evaluated for a cased horizontal wellbore embedded in a homogeneous halfspace, where measurements are evaluated near, mid–range, and far from the well h...

Hydraulic fracture stimulation of low permeability reservoir rocks is an established and cross-cutting technology for enhancing hydrocarbon production in sedimentary formations and increasing heat exchange in crystalline geothermal systems. Whereas the primary measure of success is the ability to keep the newly generated fractures sufficiently open...

Seismic waves propagating within the Earth are small perturbations in
stress and strain superimposed on an existing three-dimensional (3D)
stress field. This ambient stress state, commonly referred to as
"tectonic stress" or "pre-stress", may be significant in or near zones
of active tectonic deformation, such as the Nevada Test Site. The effect
of...

An analytical expression for the pressure wavefield radiated from an explosion seismic source with an amplitude distribution in the form of a 3D Gaussian function is developed. This expression provides a useful reference solution for validating various numerical seismic wave propagation algorithms.

A Rayleigh wave propagates laterally without dispersion in the vicinity of the plane stress-free surface of a homogeneous and isotropic elastic halfspace. The phase speed is independent of frequency and depends only on the Poisson ratio of the medium. However, after temporal and spatial discretization, a Rayleigh wave simulated by a 3D staggered-gr...

An efficient numerical algorithm for treating earth models composed of fluid and solid portions is obtained via straightforward modifications to a 3D time-domain finite-difference algorithm for simulating isotropic elastic wave propagation.

Long term geologic sequestration of carbon dioxide (CO2) is considered a viable approach for removing large amounts of excess carbon from the earth's surface environment. As CO2 is injected into a subsurface porous formation, it displaces (or mixes with) in situ pore fluids. Seismic reflection and transmission responses of the formation depend on t...

We examine seismic records of repeating explosions from Pavlof volcano, Alaska, during its 2007 eruption. Repetitive explosions are typical of Strombolian-style eruptions and allow measurement of relative time shifts between similar late-arriving phases using the technique called coda wave interferometry (Snieder et al., 2002). The measurements ena...

Dispersion and attenuation relations are derived for both the continuous and discrete velocity-memory-stress systems governing 3D anelastic wave propagation in a standard linear solid. Phase speed and attenuation factor curves extracted from these relations enable optimal selection of spatial and temporal gridding intervals to achieve finite-differ...

The velocity-memory-stress time-domain finite-difference system is a common method of modeling seismic wave propagation in anelastic media. This formulation is based upon the assumption of a standard linear solid rheology which allows the conversion of the original integro-differential system of equations into purely differential equations. Underst...

Sound waves propagating in porous media are subject to strong dissipation and dispersion. This paper elaborates upon several recent publications by the authors regarding the time-domain description of these effects. The foundation is a relaxational description of the viscous and thermal dissipation in a rigid porous medium, which is shown to posses...

Stable and accurate numerical modeling of seismic wave propagation in the vicinity of high-contrast interfaces is achieved with straightforward modifications to the conventional, rectangular-staggered-grid, finite-difference (FD) method. Improvements in material parameter averaging and spatial differencing of wavefield variables yield high-quality...

Numerical calculation of synthetic seismograms for 1D layered earth models remains a significant aspect of amplitude-offset investigations, surface wave studies, microseismic event location approaches, and reflection interpretation or inversion processes. Compared to 3D finite-difference algorithms, memory demand and execution time are greatly redu...

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 appr...

In atmospheric acoustics, formulation of a reactive, time‐domain boundary condition (TDBC) at the ground surface is a challenging problem since many commonly used models of the ground are noncausal and have a slowly decaying response. A correctly formulated TDBC can significantly simplify finite‐difference time‐domain simulation of outdoor sound pr...

A time-domain formulation for sound propagation in rigid-frame porous media, including waveform attenuation and dispersion, is developed. The new formulation is based on inversion of the relaxation functions from a previous model [Wilson DK, Ostashev VE, Collier SL. J Acoust Soc Am 2004;116:1889–92], thereby casting the convolution integrals in a f...

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...

We use the phrase seismic gradiometry to refer to the developing
research area involving measurement, modeling, analysis, and
interpretation of spatial derivatives (or differences) of a seismic
wavefield. In analogy with gradiometric methods used in gravity and
magnetic exploration, seismic gradiometry offers the potential for
enhancing resolution,...

Sequestration of CO2 in depleted oil reservoirs, saline aquifers, or
unminable coal sequences may prove to be an economical and
environmentally safe means for long-term removal of carbon from the
atmosphere. Requirements for storage of CO2 in subsurface geologic
repositories (e.g., less than 0.1% per year leakage) pose significant
challenges for ge...

A time-domain boundary condition (TDBC) for acoustic reflections from a rigid-frame porous material is derived. The TDBC is the time-domain counterpart of the familiar, linear, frequency-dependent surface impedance for locally reacting surfaces. Although the TDBC is developed from a rather simple, two-parameter phenomenological model, it is shown t...

To quantitatively assess material properties in porous media and their associated scale dependence, we simulate acoustic wavefield resonances in numerical models derived from microtomographic data gathered for sintered glass bead packs. The 3D wave propagation simulations utilize a staggered-grid finite-difference (FD) formulation of the first orde...

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...

Three-dimensional (3D) seismic wave propagation is simulated in the newly-developed Marmousi2 elastic model, using both acoustic and elastic finite-difference (FD) algorithms. Although acoustic and elastic ocean-bottom particle velocity seismograms display distinct differences, only subtle variations are discernable in pressure seismograms recorded...

Numerical solution of partial differential equations by explicit,
time-domain, finite-difference (FD) methods entails approximating
temporal and spatial derivatives by discrete function differences. Thus,
the solution of the difference equation will not be identical to the
solution of the underlying differential equation. Solution accuracy
degrades...

Previously, a set of time-domain equations for broadband sound propagation in rigid-framed porous materials [Wilson et al., J. Acoust. Soc. Am. 116, 1889-1892 (2004)] was derived by modeling viscous and thermal diffusion in the pores as relaxational processes. In this paper, the time-domain relaxational model is shown to be analogous to a phenomeno...

This paper describes development and application of a high-fidelity, seismic/acoustic simulation capability for battlefield sensors. The purpose is to provide simulated sensor data so realistic that they cannot be distinguished by experts from actual field data. This emerging capability provides rapid, low-cost trade studies of unattended ground se...

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...

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 lin...

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 ima...

Three-dimensional seismic wave propagation within a heterogeneous, isotropic poroelastic medium is simulated with an explicit, time-domain, finite-difference algorithm. A system of thirteen, coupled, first-order partial differential equations is solved for the velocity vector components, stress tensor components, and pressure associated with solid...

In previous work, a set of time‐domain equations for sound propagation in a rigid porous medium, including viscous and thermal dissipation effects, was derived [Ostashev et
al., J. Acoust. Soc. Am. 115, 2624 (2004)]. From those equations, time‐domain counterparts to frequency‐domain impedance boundary conditions (BCs) were also derived. In this pap...

A scalable parallel algorithm has been developed for three-dimensional acoustic wave propagation through a dynamic atmospheric environment, which includes the effects of spatially and temporally varying wind and temperature fields and ground impedance. A set of coupled, first-order velocity-pressure partial differential equations are implemented. S...

The finite difference time domain (FDTD) simulations of sound propagation in the atmosphere and idealized turbulent media were discussed. The FDTD was performed with input fields generated by a large-eddy simulation (LES). The acoustic FDTD was used in combination with kinematically generated turbulence fields to test theoretical predictions for wa...

Acoustic wave propagation in a three-dimensional heterogeneous moving atmosphere 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...

Significant untapped domestic petroleum resources exist within oil-saturated high-porosity zones of the Central Basin Platform (CBP) geologic province of the Permian Basin in Texas and New Mexico. However, high-porosity inclusions are relatively small and deeply-buried, rendering detection and characterization via conventional surface seismic refle...

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 f...

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...

Most previous analytical and numerical studies of sound propagation in a
moving atmosphere have been based on wave equations for the sound
pressure and on various parabolic approximations to the wave equations.
However, these equations cannot be used as starting equations for
recently proposed direct numerical simulation (DNS) of sound propagation...

Reverse-time seismic wave propagation is readily demonstrated with a time-domain finite-difference (FD) algorithm that numerically solves the velocity-stress differential equations of 3D isotropic elastodynamics. True reverse-time propagation is achieved via a three-step procedure: (1) save velocity vector and stress tensor components of an outward...

Numerical simulation of seismic wave propagation in three spatial dimensions may require substantial computational memory and execution time. A 3D time-domain finite-difference (FD) algorithm that solves the velocity-stress equations of isotropic elastodynamics requires at least 48N bytes of memory, where N is the number of spatial gridpoints. The...

A general approach toward solving the 3D full waveform seismic inverse problem entails iteratively refining a candidate earth model until an acceptable match is obtained between predicted and observed data. On each iteration, we calculate spatially distributed updates to the current model parameters by solving a large system of linear algebraic equ...

Exact mathematical expressions for the sensitivity of elastic wavefield data, with respect to small perturbations in mass density and Lame parameters, are derived by applying the reciprocity principle to solutions of the velocity-stress differential equations of isotropic elastodynamics. The formulae are valid for various types of sources (forces,...

The air/earth interface is accurately represented in a 3D finite-difference elastic wave propagation algorithm merely by assigning material properties of air to the spatial grid nodes above the earth's surface. Computational stability is maintained by making the boundary gradational. Synthetic seismic traces calculated by this approach compare favo...

The standard linear solid that best approximates a desired seismic quality factor function Q(ω) over a specified frequency interval is determined by a grid search inversion algorithm.

Reciprocity conditions are developed for all combinations of two point seismic energy sources (body forces, body moments, and/or surface tractions) located within a linear, time-invariant, and local anelastic continuum.

Wave propagation within a 3D anacoustic (attenuative and dispersive) fluid is simulated using a combination of finite-difference and finite-integration numerical techniques. Calculated responses compare favorably with those obtained via the memory variable approach.

The West Pearl Queen is a depleted oil reservoir that has produced approximately 250,000 bbl of oil since 1984. Production had slowed prior to CO injection, but no previous secondary or tertiary recovery methods had been applied. The initial project involved reservoir characterization and field response to injection of CO; the field experiment cons...

By providing highly realistic simulations of sound propagation through complex atmospheric and terrain en-vironments, finite-difference time-domain (FDTD) tech-niques can potentially reduce development time and im-prove the battlefield performance of acoustic sensors. In this paper, we summarize recent progress in improving two key aspects of acous...

In many parts of the United States, as well as other regions of the world, competing demands for fresh water or water suitable for desalination are outstripping sustainable supplies. In these areas, new water supplies are necessary to sustain economic development and agricultural uses, as well as support expanding populations, particularly in the S...

The concept of a frequency-dependent ground impedance has been widely adopted, particularly for cal-culation methods that solve for the sound field on a frequency-by-frequency basis. But recent interest in finite-difference, time-domain (FDTD) calculations of outdoor propagation motivates a time-domain ap-proach to modeling sound interactions with...

## Citations

... (c) Broadband waveform attributed to a hydrothermal reservoir at Aso reported by Kaneshima et al. (1996). (a) Reproduced from Kawakatsu et al. (1992); (b) reproduced from Neuberg et al. (1994); (c) reproduced from Kaneshima et al. (1996) audio range acoustic signals > 20 Hz, but later infrasound (< 20 Hz) studies built extensively upon this concept (e.g., Firstov and Kravchenko 1996;Vergniolle et al. 1996;Johnson 2003, Vergniolle andCaplan-Auerbach 2006;Matoza et al. 2009a;Caplan-Auerbach et al. 2010;Kim et al. 2012;Ripepe et al. 2013;Lamb et al. 2015;Delle Donne et al. 2016;Haney et al. 2018;Iezzi et al. 2019aIezzi et al. , 2022Perttu et al. 2020b). In a reexamination of the original formulation of Woulff and McGetchin (1976) in the context of the current understanding of jet noise, Matoza et al. (2013b) concluded that the formulation of Woulff and McGetchin (1976) can lead to large errors when inferring eruption parameters from acoustic data and thus requires modification. ...

... Tang & Lee 2015;Pan et al. 2018). In lieu of incorporating the Hessian, parameter trade-off can be limited through a combination of data-driven inversion strategies (Shipp & Singh 2002;Sears et al. 2008;Prieux et al. 2013a,b) and appropriate model parametrization (Tarantola 1986;Plessix & Cao 2011;Köhn et al. 2012;Gholami et al. 2013;Operto et al. 2013;Alkhalifah & Plessix 2014;Krebs et al. 2016). Understanding the parameter trade-off is necessary for accurate model appraisal, particularly when first-order optimization methods are used. ...

... The radially directed fields from the casing, and the length of the intermediate zone, have practical implications in the context of well-logging because they delineate the region in which measurements can be made to acquire information about the formation resistivity outside the well. Within the intermediate zone, fields behave like those due to a transmission line (Kaufman, 1990), and multiple authors have adopted modeling strategies that approximate the well and surrounding medium as a transmission line (Kong et al., 2009;Aldridge et al., 2015). ...

... This approximation will begin to break down if the size of the prism approximating the casing has a larger area than the true casing. To overcome this, several alternative approaches have been developed, including replacing the casing with a distribution of charges (Weiss et al., 2016) or dipoles (Cuevas, 2014). Other modelling approaches include using a resistor network approach (Yang et al., 2016), OcTree meshes to locally refine around the casing (Haber et al., 2016), and the development of hierarchical finite element approach (Weiss, 2017), among others. ...

... The simplest is the inclusion of a density contrast to mimic an air layer, at the expense of numerical accuracy. For elastic wave propagation, Bartel et al. (2000) find that some smoothing of the extreme density contrast is required for numerical stability. Boore (1972), Robertsson (1996), Mittet (2002), Bohlen and Saenger (2006), and Zeng et al. (2012) consider variants of the vacuum approach. ...

... where A is a source magnitude scalar with SI unit "N" for force-density source and "N · m" for moment-density source. The spatial function sðx; x s Þ can be a Gaussian function (Aldridge et al., 2011): sðx; ...

... In the context of non-linearities, Lecoanet et al. (2015) studied gravity wave generated by interface or Reynolds stress forcing in a coupled ocean/atmosphere model. Taking into account non-linearities they solved the 2D incompressible Navier-Stokes equations in a Fourier domain along x and over a Chebyshev grid along z. Wilson et al. (2004) studied 3D acoustic inviscid wave propagation based on finite differences and included turbulence and wind in their modelling. They provided a tool to study scattering phenomena affecting atmospheric remote-sensing systems. ...

... The task was completed in Refs. [1,2,8,10,12,[19][20][21][24][25][26]. First, we derived the exact formula for the sound scattering cross-section per unit volume, σ, in a turbulent atmosphere [8,20]. ...

... Three-dimensional poroelasticity simulation has become somewhat common in recent years due to the increasingly powerful computers available. Recent works on three-dimensional computational poroelasticity on regular grids include those of Naumovich [37], who used a staggered-grid finite volume method on regular, rectilinear grids for isotropic media, and Aldridge et al. [1], who used a staggered-grid finite difference approach. Three-dimensional work capable of using irregular grids includes that of de la Puente et al. [18], who employed a discontinuous Galerkin method on triangular and tetrahedral meshes, and the spectral element work of Morency and Tromp [36]. ...

... Second , QWs were employed to study sound scattering due to atmospheric turbulence behind noise barriers (Wilson et al., 2004a ), which is an important problem in noise control. Third, QWs were used to model atmospheric turbulence in finite-difference time-domain simulations of sound propagation outdoors (Marlin et al., 2003; Van Renterghem, 2003; Wilson et al., 2003 ), which is a very promising method in computational atmospheric acoustics. Fourth, QWs were employed in the solution of a forward problem in acoustic tomography of the atmosphere (Vecherin et al., 2004; Wilson et al., 2004b ). ...