Publications

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Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fraction of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

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During the initial phase of this SubTER project, we conducted a series of high resolution seis- mic imaging campaigns designed to characterize induced fractures. Fractures were emplaced using a novel explosive source, designed at Sandia National Laboratories, that limits damage to the borehole. This work provided evidence that fracture locations could be imaged at inch scales using high-frequency seismic tomography but left many fracture properties (i.e. per- meability) unresolved. We present here the results of the second phase of the project, where we developed and demonstrated emerging seismic and electrical geophysical imaging tech- nologies that characterize 1) the 3D extent and distribution of fractures stimulated from the explosive source, 2) 3D fluid transport within the stimulated fracture network through use of a contrasting tracer, and 3) fracture attributes through advanced data analysis. Focus was placed upon advancing these technologies toward near real-time acquisition and processing in order to help provide the feedback mechanism necessary to understand and control frac- ture stimulation and fluid flow. Results from this study include a comprehensive set of 4D crosshole seismic and electrical data that take advantage of change detection methodologies allowing for perturbations associated with the fracture emplacement and particulate tracer to be isolated. During the testing the team also demonstrated near real-time 4D electri- cal resistivity tomography imaging and 4D seismic tomography using the CASSM approach with a temporal resolution approaching 1 minute. All of the data collected were used to develop methods of estimating fracture attributes from seismic data, develop methods of as- similating disparate and transient data sets to improve fracture network imaging resolution, and advance capabilities for near real-time inversion of cross-hole tomographic data. These results are illustrated here. Advancements in these areas are relevant to all situations where fracture emplacement is used for reservoir stimulation (e.g. Enhanced Geothermal Systems (EGS) and tight shale gases).

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Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

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Paracousti is a parallelized acoustic wave propagation simulation package developed at Sandia National Laboratories. It solves the linearized coupled set of acousto-dynamic partial differential equations using finite-difference approximations that are second order accurate in time and fourth order accurate in space. Paracousti simulates sound wave propagation within realistic 3-D earth, static atmosphere and hydroacoustic models, including 3-D variations in medium densities and acoustic sound speeds and topography or bathymetry. It can also incorporate attenuative media such as would be expected from physical mechanisms such as molecular dissipation. This report explains the usage of the Paracousti algorithm.

This report outlines recent enhancements to the TDAAPS algorithm first described by Symons et al., 2005. One of the primary additions to the code is the ability to specify an attenuative media using standard linear fluid mechanisms to match reasonably general frequency versus loss curves, including common frequency versus loss curves for the atmosphere and seawater. Other improvements that will be described are the addition of improved numerical boundary conditions via various forms of Perfectly Matched Layers, enhanced accuracy near high contrast media interfaces, and improved physics options.

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