Gaining a proper understanding of how Earth structure and other near-source properties affect estimates of explosion yield is important to the nonproliferation mission. The yields of explosion sources are often based on seismic moment or waveform amplitudes. Quantifying how the seismic waveforms or estimates of the source characteristics derived from those waveforms are influenced by natural or man-made structures within the near-source region, where the wavefield behaves nonlinearly, is required to understand the full range of uncertainty in those yield estimates. We simulate tamped chemical explosions using a nonlinear, shock physics code and couple the ground motions beyond the elastic radius to a linear elastic, full waveform seismic simulation algorithm through 3D media. In order to isolate the effects of simple small-scale 3D structures on the seismic wavefield and linear seismic source estimates, we embed spheres and cylinders close to the fully- tamped source location within an otherwise homogenous half-space. The 3 m diameters spheres, given their small size compared to the predominate wavelengths investigated, not surprisingly are virtually invisible with only negligible perturbations to the far-field waveforms and resultant seismic source time functions. Similarly, the 11 m diameter basalt sphere has a larger, but still relatively minor impact on the wavefield. However, the 11 m diameter air-filled sphere has the largest impact on both waveforms and the estimated seismic moment of any of the investigated cases with a reduction of ~25% compared to the tamped moment. This significant reduction is likely due in large part to the cavity collapsing from the shock instead of being solely due to diffraction effects . Although the cylinders have the same diameters as the 3 m spheres, their length of interaction with the wavefield produces noticeable changes to the seismic waveforms and estimated source terms with reductions in the peak seismic moment on the order of 10%. Both the cylinders and 11 m diameter spheres generate strong shear waves that appear to emanate from body force sources.
With geologic data from over 950 boreholes, Yucca Flat basin, residing on the Nevada National Security Site, has excellent borehole control on stratigraphy. These data were used to create a Geologic Framework Model (GFM) of the basin. Of these boreholes, 188 have corresponding downhole seismic survey data, which were used to determine average P-wave velocities of the geologic units and create a GFM seismostratigraphic model (GFM-SS). With the acquisition of six new active-source large-N datasets in Yucca Flat, we can now quantitatively assess the accuracy of the GFM-SS previously controlled only by borehole data. For each of the six datasets, we subset the GFM to the region of interest and create a forward model of P-wave travel times for the GFM-SS given the large-N source-receiver geometries. We first made trial-and-error adjustments to the unit velocities (while keeping the layer geometry intact) to improve the travel-time residuals. We then implemented a simulated annealing approach to find the optimal velocity model for each dataset. Our results indicate that the borehole-controlled model overestimates alluvium velocities across Yucca Flat. This result persists even when we make smaller GFM-SS models that are local to individual large-N experiments. We hypothesize that this result is a combination of shorter ray paths and the resulting lack of interaction with large-scale features (such as faults), as well as less attenuation of high frequencies in the borehole data. Both the current GFM-SS and the updated model based on median velocities that we present here overgeneralize local unit velocities, which can be quite heterogeneous in Yucca Flat.
We used the CTH shock physics code to simulate the explosion of an 18-t chemical explosive at a depth of 250 m. We used the CTH in the two-dimensional axisymmetric (cylindrical) geometry (2DC) and most simulations included fully tamped explosions in wet tuff. Our study focused on parametric studies of three of the traditional strength models available in CTH, namely, geologic-yield, elastic perfectly-plastic von Mises, and Johnson-Cook strength (flow stress) models. We processed CTH results through a code that generates Reduced Displacement Potential (RDP) histories for each simulation. Since RDP is the solution of the linear wave equation in spherical coordinates, it is mainly valid at far-enough distance from the explosion the elastic radius. Among various parameters examined, we found the yield strength to have the greatest effect on the resulting RDP, where the peak RDP reduces almost linearly in log-log space as the yield strength increases. Moreover, an underground chemical explosion results in a cavity whose final diameter is inversely proportional to the material yield strength, i.e., as the material's yield strength increases the resulting final cavity radius decreases. Additionally, we found the choice of explosive material (COMP-C4 versus COMP-B) has minor effects on the peak RDP, where denser COMP-C4 shows higher peak RDP than the less dense COMP-B by a factor of ~1.1. In addition to wet tuff, we studied explosions in dry tuff, salt, and basalt, for a single strength model and yield strength value. We found wet tuff has the highest peak RDP value, followed by dry tuff, salt, and basalt. 2DC simulations of explosions in 11 m radius spherical, hemispherical, and cylindrical cavities showed the RDP signals have much lower magnitude than tamped explosions, where the cavity explosions mimicked nearly decoupled explosions.
Rock Valley, in the southern end of the Nevada National Security Site, hosts a fault system that was responsible for a shallow (< 3 km below surface ) magnitude 3.7 earthquake in May 1993. In order to better understand this system, seismic properties of the shallow subsurface need to be better constrained. In April and May of 2021, accelerated weight drop (AWD) active-source seismic data were recorded in order to measure P- and S-wave travel-times for the area. This report describes the processing and phase picking of the recorded seismic waveforms. In total, we picked 7,982 P-wave arrivals at offsets up to ~2500 m, and 4,369 S-wave arrivals at offsets up to ~2200 m. These travel-time picks can be inverted for shallow P-wave and S-wave velocity structure in future studies.
An active source experiment using an accelerated weight drop was conducted in Rock Valley, Nevada National Security Site, during the spring of 2021 in order to characterize the shallow seismic structure of the region. P-wave first arrival travel times picked from this experiment were used to construct a preliminary 3-D compressional wave speed model over an area that is roughly 4 km wide east-west and 8 km north-south to a depth of about 500-600 m below the surface, but with primary data concentration along the transects of the experimental lines. The preliminary model shows good correlation with basic geology and surface features, but geological interpretation is not the focus of this report. We describe the methods used in the tomographic inversion of the data and show results from this preliminary P-wave model.
Most earth materials are anisotropic with regard to seismic wave-speeds, especially materials such as shales, or where oriented fractures are present. However, the base assumption for many numerical simulations is to treat earth materials as isotropic media. This is done for simplicity, the apparent weakness of anisotropy in the far field, and the lack of well-characterized anisotropic material properties for input into numerical simulations. One approach for addressing the higher complexity of actual geologic regions is to model the material as an orthorhombic medium. We have developed an explicit time-domain, finite-difference (FD) algorithm for simulating three-dimensional (3D) elastic wave propagation in a heterogeneous orthorhombic medium. The objective of this research is to investigate the errors and biases that result from modeling a non-isotropic medium as an isotropic medium. This is done by computing “observed data” by using synthetic, anisotropic simulations with the assumption of an orthorhombic, anisotropic earth model. Green’s functions for an assumed isotropic earth model are computed and then used an inversion designed to estimate moment tensors with the “observed” data. One specific area of interest is how shear waves, which are introduced in an anisotropic model even for an isotropic explosion, affect the characterization of seismic sources when isotropic earth assumptions are made. This work is done in support of the modeling component of the Source Physics Experiment (SPE), a series of underground chemical explosions at the Nevada National Security Site (NNSS).
Seismic source modeling allows researchers both to simulate how a source that induces seismic waves interacts with the Earth to produce observed seismograms and, inversely, to infer what the time histories, sizes, and force distributions were for a seismic source given observed seismograms. In this report, we discuss improvements made in FY21 to our software as applies to both the forward and inverse seismic source modeling problems. For the forward portion of the problem, we have added the ability to use full 3-D nonlinear simulations by implementing 3-D time varying boundary conditions within Sandia’s linear seismic code Parelasti. Secondly, on the inverse source modeling side, we have developed software that allows us to invert seismic gradiometer-derived observations in conjunction with standard translational motion seismic data to infer properties of the source that may improve characterization in certain circumstances. First, we describe the basic theory behind each software enhancement and then demonstrate the software in action with some simple examples.
This report summarizes work completed under the Laboratory Directed Research and Development (LDRD) project "Uncertainty Quantification of Geophysical Inversion Using Stochastic Differential Equations." Geophysical inversions often require computationally expensive algorithms to find even one solution, let alone propagating uncertainties through to the solution domain. The primary purpose of this project was to find more computationally efficient means to approximate solution uncertainty in geophysical inversions. We found multiple computationally efficient methods of propagating Earth model uncertainty into uncertainties in solutions of full waveform seismic moment tensor inversions. However, the optimum method of approximating the uncertainty in these seismic source solutions was to use the Karhunen-Love theorem with data misfit residuals. This method was orders of magnitude more computationally efficient than traditional Monte Carlo methods and yielded estimates of uncertainty that closely approximated those of Monte Carlo. We will summarize the various methods we evaluated for estimating uncertainty in seismic source inversions as well as work toward this goal in the realm of 3-D seismic tomographic inversion uncertainty.
Underground explosions nonlinearly deform the surrounding earth material and can interact with the free surface to produce spall. However, at typical seismological observation distances the seismic wavefield can be accurately modeled using linear approximations. Although nonlinear algorithms can accurately simulate very near field ground motions, they are computationally expensive and potentially unnecessary for far field wave simulations. Conversely, linearized seismic wave propagation codes are orders of magnitude faster computationally and can accurately simulate the wavefield out to typical observational distances. Thus, devising a means of approximating a nonlinear source in terms of a linear equivalent source would be advantageous both for scenario modeling and for interpretation of seismic source models that are based on linear, far-field approximations. This allows fast linear seismic modeling that still incorporates many features of the nonlinear source mechanics built into the simulation results so that one can have many of the advantages of both types of simulations without the computational cost of the nonlinear computation. In this report we first show the computational advantage of using linear equivalent models, and then discuss how the near-source (within the nonlinear wavefield regime) environment affects linear source equivalents and how well we can fit seismic wavefields derived from nonlinear sources.
We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.
We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.
The complex postdetonation geologic structures that form after an underground nuclear explosion are hard to constrain because increased heterogeneity around the damage zone affects seismic waves that propagate through the explosion site. Generally, a vertical rub-ble-filled structure known as a chimney is formed after an underground nuclear explosion that is composed of debris that falls into the subsurface cavity generated by the explosion. Compared with chimneys that collapse fully, leaving a surface crater, partially collapsed chimneys can have remnant subsurface cavities left in place above collapsed rubble. The 1964 nuclear test HADDOCK, conducted at the Nevada test site (now the Nevada National Security Site), formed a partially collapsed chimney with no surface crater. Understanding the subsurface structure of these features has significant national security applications, such as aiding the study of suspected underground nuclear explosions under a treaty verification. In this study, we investigated the subsurface architecture of the HADDOCK legacy nuclear test using hybrid 2D–3D active source seismic reflection and refraction data. The seismic data were acquired using 275 survey shots from the Seismic Hammer (a 13,000 kg weight drop) and 65 survey shots from a smaller accelerated weight drop, both recorded by ∼ 1000 three-component 5 Hz geophones. First-arrival, P-wave tomographic modeling shows a low-velocity anomaly at ∼ 200 m depth, likely an air-filled cavity caused by partial collapse of the rock column into the temporary post-detonation cavity. A high-velocity anomaly between 20 and 60 m depth represents spall-related compaction of the shallow alluvium. Hints of low velocities are also present near the burial depth ( ∼ 364 m). The reflection seismic data show a prominent subhorizontal reflector at ∼ 300 m depth, a short-curved reflector at ∼ 200 m, and a high-amplitude reflector at ∼ 50 m depth. Comparisons of the reflection sections to synthetic data and borehole stratigraphy suggest that these features correspond to the alluvium–tuff contact, the partial collapse cavity, and the spalled layer, respectively.
As a part of the series of Source Physics Experiments (SPE) conducted on the Nevada National Security Site in southern Nevada, we have developed a local-to-regional scale seismic velocity model of the site and surrounding area. Accurate earth models are critical for modeling sources like the SPE to investigate the role of earth structure on the propagation and scattering of seismic waves. We combine seismic body waves, surface waves, and gravity data in a joint inversion procedure to solve for the optimal 3D seismic compres-sional and shear-wave velocity structures and earthquake locations subject to model smoothness constraints. Earthquakes, which are relocated as part of the inversion, provide P-and S-body-wave absolute and differential travel times. Active source experiments in the region augment this dataset with P-body-wave absolute times and surface-wave dispersion data. Dense ground-based gravity observations and surface-wave dispersion derived from ambient noise in the region fill in many areas where body-wave data are sparse. In general, the top 1–2 km of the surface is relatively poorly sampled by the body waves alone. However, the addition of gravity and surface waves to the body-wave data-set greatly enhances structural resolvability in the near surface. We discuss the method-ology we developed for simultaneous inversion of these disparate data types and briefly describe results of the inversion in the context of previous work in the region.
We document azimuthally dependent seismic scattering at the Source Physics Experiment (SPE) using the large-N array. The large-N array recorded the seismic wavefield produced by the SPE-5 buried chemical explosion, which occurred in April 2016 at the Nevada National Security Site, U.S.A. By selecting a subset of vertical-component geophones from the large-N array, we formed 10 linear arrays, with different nominal source-receiver azimuths as well as six 2D arrays. For each linear array, we evaluate wavefield coherency as a function of frequency and interstation distance. For both the P arrival and post-P arrivals, the coherency is higher in the northeast propagation direction, which is consistent with the strike of the steeply dipping Boundary fault adjacent to the northwest side of the large-N array. Conventional array analysis using a suite of 2D arrays suggests that the presence of the fault may help explain the azimuthal dependence of the seismic-wave coherency for all wave types. This fault, which separates granite from alluvium, may be acting as a vertically oriented refractor and/or waveguide.
Many geologic materials and minerals are seismically anisotropic, with the most general anisotropic material having up to 21 independent elastic coefficients. This report outlines the development of a 3-D, generally anisotropic, linear elastic full waveform finite-difference solver. First, a mathematical description of the solution equations will be described. The finite-difference implementation of these equations will then be shown. Finally, a comparison of results from this new solver to other solutions will be provided as verification that the new algorithm can accurately replicate these solutions. ACKNOWLEDGEMENTS The author also acknowledges the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (DNN R&D), and the Source Physics Experiment (SPE) working group, a multi-institutional and interdisciplinary group of scientists and engineers.
ParelastiFWl is a python-based frontend to the seismic full waveform inversion process using Sandia Geophysics Department's 3-D isotropic elastic full waveform simulation code, Parelasti. The arguments one provides to ParelastiFWl guide the full waveform inversion process, including resolution of the inversion grid and basic regularization. This report outlines the user flags and ParelastiFWI usage to control the full waveform inversion procedure. ACKNOWLEDGEMENTS The author also acknowledges the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (DNN R&D), and the Source Physics Experiment (SPE) working group, a multi-institutional and interdisciplinary group of scientists and engineers.
We invert far-field infrasound data for the equivalent seismoacoustic timedomain moment tensor to assess the effects of variable atmospheric models and source phenomena. The infrasound data were produced by a series of underground chemical explosions that were conducted during the Source Physics Experiment (SPE), which was originally designed to study seismoacoustic signal phenomena. The first goal of this work is to investigate the sensitivity of the inversion to the variability of the estimated atmospheric model. The second goal is to determine the relative contribution of two presumed source mechanisms to the observed infrasonic wavefield. 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 available, regional-scale atmospheric observations. 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 for each chemical explosion event, based on 10 yrs of meteorological data: an average model, which averages the atmospheric conditions for 10 yrs prior to each SPE event, as well as two extrema models. To parameterize the inversion, we assume that the source of infrasonic energy results from the linear combination of explosion-induced surface spall and linear seismic-to-elastic mode conversion at the Earth’s free surface. 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 1) the majority of the observed acoustic energy is produced by the spall and/or 2) our modeling of the elastic energy, and the subsequent conversion to acoustic energy, is too simplistic.
As part of the Source Physics Experiment (SPE) Phase I shallow chemical detonation series, multiple surface and borehole active-source seismic campaigns were executed to perform high- resolution imaging of seismic velocity changes in the granitic substrate. Cross-correlation data processing methods were implemented to efficiently and robustly perform semi-automated change detection of first-arrival times between campaigns. The change detection algorithm updates the arrival times, and consequently the velocity model, of each campaign. The resulting tomographic imagery reveals the evolution of the subsurface velocity structure as the detonations progressed. ACKNOWLEDGEMENTS The authors thank Dan Herold, Bob White, Kale Mc Lin, Ryan Emmit, Maggie Townsend, Curtis Obi, Fred Helsel, Rebekah Lee, Liam Toney, Matt Geuss, and Josh Feldman for their direct and invaluable contributions to this work. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Note that a more detailed manuscript for this work is being prepared for publication in the Bulletin of the Seismological Society of America (BSSA).
This document serves to guide a researcher through the process of running the Weather Research and Forecasting (WRF) model and incorporating observations into coarse resolution reanalysis products to model atmospheric conditions at high (50 m) resolution. This documentation is specific to WRF and the WRF Preprocessing System (WPS) version 3.8.1 and the Objective Analysis (OBSGRID) code released on April 8, 2016. Output from WRF serves as an input into the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS) which performs staggered-grid finite difference modeling of the acoustic velocity pressure system to produce Green's functions through these atmospheric models.
Full waveform inversion allows the seismologist to utilize an entire waveform and all the information it contains to help image the 3-D structure of the interior of the earth. This report summarizes the basic theory that has been developed in full waveform seismic inversion, primarily related to computation of sensitivity kernels. It then describes the implementation of this theory using Sandia Geophysics Department's Parelasti code, a 3-D full waveform elastic simulation algorithm. Finally, the code is validated using synthetics from simple homogeneous elastic earth models.
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.
During the initial phase of this Department of Energy (DOE) Geothermal Technologies Office (GTO) SubTER project, we conducted a series of high-energy stimulations in shallow wells, the effects of which were evaluated with high resolution seismic imaging campaigns designed to characterize induced fractures. The high-energy stimulations use a novel explosive source that limits damage to the borehole, which was paramount for change detection seismic imaging and re-fracturing experiments. This work provided evidence that the high-energy stimulations were generating self-propping fractures and that these fracture locations could be imaged at inch scales using high-frequency seismic tomography. While the seismic testing certainly provided valuable feedback on fracture generation for the suite of explosives, it left many fracture properties (i.e. permeability) unresolved. We present here the methodology for the second phase of the project, where we are developing and demonstrating emerging seismic and electrical geophysical imaging technologies that have been designed to 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 is being 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 fracture stimulation and fluid flow.
During the initial phase of this SubTER project, we conducted a series of high resolution seismic imaging campaigns designed to characterize induced fractures. Fractures were emplaced using a novel explosive source 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. permeability) unresolved. We present here the methodology for the second phase of the project, where we will develop and demonstrate emerging seismic and electrical geophysical imaging technologies 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 will be 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 fracture stimulation and fluid flow.
Muons are subatomic particles capable of penetrating the earth's crust several kilometers. Muons have been used to image the Pyramid of Khafre of Giza, various volcanoes, and smaller targets like cargo. For objects like a volcano, the detector is placed at the volcano's base and muon fluxes for paths through the volcano are recorded for many days to weeks.
Seismic attenuation is defined as the loss of the seismic wave amplitude as the wave propagates excluding losses strictly due to geometric spreading. Information gleaned from seismic waves can be utilized to solve for the attenuation properties of the earth. One method of solving for earth attenuation properties is called t*. This report will start by introducing the basic theory behind t* and delve into inverse theory as it pertains to how the algorithm called tstarTomog inverts for attenuation properties using t* observations. This report also describes how to use the tstarTomog package to go from observed data to a 3-D model of attenuation structure in the earth.
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.
P- and S-body wave travel times collected from stations in and near the state of Nevada were inverted for P-wave velocity and the Vp/Vs ratio. These waves consist of Pn, Pg, Sn and Sg, but only the first arriving P and S waves were used in the inversion. Travel times were picked by University of Nevada Reno colleagues and were culled for inclusion in the tomographic inversion. The resulting tomographic model covers the entire state of Nevada to a depth of {approx}90 km; however, only the upper 40 km indicate relatively good resolution. Several features of interest are imaged including the Sierra Nevada, basin structures, and low velocities at depth below Yucca Mountain. These velocity structure images provide valuable information to aide in the interpretation of geothermal resource areas throughout the state on Nevada.
Summary: 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-difference algorithm efficiency, while simultaneously minimizing numerical inaccuracy.
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 synthetic seismic data.