Many earth materials and minerals are seismically anisotropic; however, due to the weakness of anisotropy and for simplicity, the earth is often approximated as an isotropic medium. Specific circumstances, such as in shales, tectonic fabrics, or oriented fractures, for example, require the use of anisotropic simulations in order to accurately model the earth. This report details the development of a new massively parallel 3-D full seismic waveform simulation algorithm within the principle coordinate system of an orthorhombic material, which is a specific form of anisotropy common in layered, fractured media. The theory and implementation of Pararhombi is described along with verification of the code against other solutions.
We invert far field infrasound data for the equivalent seismo-acoustic time domain moment tensor to assess the effects of variable atmospheric models as well as to quantify the relative contributions of two presumed source phenomena. The infrasound data was produced by a series of underground chemical explosions that were conducted during the Source Physics Experiment, (SPE) which was originally designed to study explosion-generated seismo-acoustic signal phenomena. The goal of the work presented herein is two-fold: the first goal is to investigate the sensitivity of the estimated time domain moment tensors to variability of the estimated atmospheric model. The second goal is to determine the relative contribution of two possible source mechanisms to the observed in- frasonic wave field. Rather than using actual atmospheric observations to estimate the necessary atmospheric Green's functions, we build a series of atmospheric models that rely on publicly avail- able, regional atmospheric observations and the assumption that the acoustic energy results from a linear combination of an underground isotropic explosion and surface spall. The atmospheric observations are summarized and interpolated onto a 3D grid to produce a model of sound speed at the time of the experiment. For each of four SPE acoustic datasets that we invert, we produced a suite of three atmospheric models, based on ten years of regional meteorological observations: an average model, which averages the atmospheric conditions for ten years prior to each SPE event, as well as two extrema models. We find that the inversion yields relatively repeatable results for the estimated spall source. Conversely, the estimated isotropic explosion source is highly variable. This suggests that the majority of the observed acoustic energy is produced by the spall source and/or our modeling of the elastic energy propagation, and it's subsequent conversion to acoustic energy via linear elastic-to-acoustic coupling at the free surface, is too simplistic.
Due to the weight of overburden and tectonic forces, the solid earth is subject to an ambient stress state. This stress state is quasi-static in that it is generally in a state of equilibrium. Typically, seismology assumes this ambient stress field has a negligible effect on wave propagation. However, two basic theories have been put forward to describe the effects of ambient stress on wave propagation. Dahlen and Tromp (2002) expound a theory based on perturbation analysis that largely supports the traditional seismological view that ambient stress is negligible for wave propagation. The second theory, espoused by Korneev and Glubokovskikh (2013) and supported by some experimental work, states that perturbation analysis is inappropriate since the elastic modulus is very sensitive to the ambient stress states. This brief report reformulates the equations given by Korneev and Glubokovskikh (2013) into a more compact form that makes it amenable to statement in terms of a pre-stress form of Hooke's Law. Furthermore, this report demonstrates the symmetries of the pre-stress modulus tensor and discusses the reciprocity relationship implied by the symmetry conditions.
Due to the weight of overburden and tectonic forces, the solid earth is subject to an ambient stress state. This stress state is quasi-static in that it is generally in a state of equilibrium. Typically, seismology assumes this ambient stress field has a negligible effect on wave propagation. However, two basic theories have been put forward to describe the effects of ambient stress on wave propagation. Dahlen and Tromp (2002) expound a theory based on perturbation analysis that largely supports the traditional seismological view that ambient stress is negligible for wave propagation. The second theory, espoused by Korneev and Glubokovskikh (2013) and supported by some experimental work, states that perturbation analysis is inappropriate since the elastic modulus is very sensitive to the ambient stress states. This brief report reformulates the equations given by Korneev and Glubokovskikh (2013) into a more compact form that makes it amenable to statement in terms of a pre-stress form of Hooke's Law. Furthermore, this report demonstrates the symmetries of the pre-stress modulus tensor and discusses the reciprocity relationship implied by the symmetry conditions.
Waves propagating through natural materials such as ocean water encounter spatial variations in material properties that cannot easily be predicted or known in advance. Deterministic wave simulation algorithms must assume that all properties throughout the model space are precisely known. However, a stochastic wave simulation tool can parameterize the material as a stochastic medium with a certain probability distribution and correlation length. This report documents the addition of spatial stochastic variability into Paracousti-UQ, Sandia Geophysics Department's 3-D full waveform acoustic algorithm within stochastic media. The ability of the code to replicate Monte Carlo solutions in 1-D spatially variable media is also evaluated.
Marine hydrokinetic (MHK) devices generate electricity from the motion of tidal and ocean currents, as well as ocean waves, to provide an additional source of renewable energy available to the United States. These devices are a source of anthropogenic noise in the marine ecosystem and must meet regulatory guidelines that mandate a maximum amount of noise that may be generated. In the absence of measured levels from in situ deployments, a model for predicting the propagation of sound from an array of MHK sources in a real environment is essential. A set of coupled, linearized velocity-pressure equations in the time-domain are derived and presented in this paper, which are an alternative solution to the Helmholtz and wave equation methods traditionally employed. Discretizing these equations on a three-dimensional (3D), finite-difference grid ultimately permits a finite number of complex sources and spatially varying sound speeds, bathymetry, and bed composition. The solution to this system of equations has been parallelized in an acoustic-wave propagation package developed at Sandia National Labs, called Paracousti. This work presents the broadband sound pressure levels from a single source in two-dimensional (2D) ideal and Pekeris wave-guides and in a 3D domain with a sloping boundary. Furthermore, the paper concludes with demonstration of Paracousti for an array of MHK sources in a simple wave-guide.
Resolving the time dependent terms in the seismic moment tensor provides important informa- tion that can be used to interpret the source process of an explosion, including the separation of isotropic explosion terms from shear forces and potentially isolated force couples. In this report, we detail our method of inverting three component seismic data for the seismic moment tensor. We review possible seismic source models from the simplest isotropic explosion type source to those incorporating the six independent moment tensor terms. The inversion we describe is formulated in the frequency domain, and results in estimates of time dependent moment tensor components. The inversion relies on an accurate estimate of the Green's functions of the Earth. However, given the complexity of the Earth, we explore the effects of inaccuracies in the presumed Earth model used to estimate the Green's functions needed for the inversion. Specifically, we explore the effects of stochastic variations in the Earth models on the inversion results. These tests are syn- thetic throughout, and show that adding stochastic density/velocity heterogeneity in the presumed Earth model results in reduced amplitude seismic moment tensor estimates, as well as degrading the data misfit. We suggest two mitigation strategies. First, produce a suite of Green's functions using different realizations of the stochastic field within the Earth Model. Secondly, perform the in- version in the power spectral domain, eliminating all phase information. Finally, we analyze actual seismic data collected in winter 2017/2018. The seismic data was collected at in active geothermal well site outside of Winnimucca, NV, and was produced during well stimulation operations. In general, the inversion results were poor, with a high degree of data misfit. We hypothesize that the poor results are a function of a poorly constrained Earth model as well as noisy, high-frequency data being used in the inversion.
This report shows the results of constructing predictive atmospheric models for the Source Physics Experiments 1-6. Historic atmospheric data are combined with topography to construct an atmo- spheric model that corresponds to the predicted (or actual) time of a given SPE event. The models are ultimately used to construct atmospheric Green's functions to be used for subsequent analysis. We present three atmospheric models for each SPE event: an average model based on ten one- hour snap shots of the atmosphere and two extrema models corresponding to the warmest, coolest, windiest, etc. atmospheric snap shots. The atmospheric snap shots consist of wind, temperature, and pressure profiles of the atmosphere for a one-hour time window centered at the time of the predicted SPE event, as well as nine additional snap shots for each of the nine preceding years, centered at the time and day of the SPE event.
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.
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).
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.
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.