In this report, we describe how to estimate the time-variable components of the seismic moment tensor and compare these estimates to the more conventional analysis that incorporates an assumption of the source time function (STF) across all components of the seismic moment tensor. The advantage of our method is that we are able to independently estimate the time-evolution of each component of the seismic moment tensor, which may help to resolve the complex source phenomena associated with buried explosions. By performing an eigen decomposition of the time-evolving seismic moment tensor components, we are able to plot the seismic mechanism as a trajectory on a lune diagram. This technique enables interpretation of the seismic mechanism as a function of time, as opposed to the more conventional analysis which assumes that the seismic mechanism is time invariant. Finally, we describe the differences between the seismic moment and the seismic moment rate STFs, how to implement each one in inversion schemes, and the relative strengths/weaknesses of each. Our key take-away is that we are able to distinguish nearly-overlapping sources with highly different mechanisms, such as an explosion immediately following an earthquake, by estimating moment rate from seismic data through a STF-invariant inversion for the full time-variable moment tensor.
In this report, we assess the data recorded by a Distributed Acoustic Sensing (DAS) cable deployed during the Source Physics Experiment, Phase II (DAG) in comparison with the data recorded by nearby 4.5-Hz geophones. DAS is a novel recording method with unprecedented spatial resolution, but there are significant concerns around the data fidelity as the technology is ramped up to more common usage. Here we run a series of tests to quantify the similarity between DAS data and more conventional data and investigate cases where the higher spatial resolution of the DAS can provide new insights into the wavefield. These tests include 1D modeling with seismic refraction and bootstrap uncertainties, assessing the amplitude spectra with distance from the source, measuring the frequency dependent inter-station coherency, estimating time-dependent phase velocity with beamforming and semblance, and measuring the cross-correlation between the geophone and the particle velocity inferred from the DAS. In most cases, we find high similarity between the two datasets, but the higher spatial resolution of the DAS provides increased details and methods of estimating uncertainty.
This report details a method to estimate the energy content of various types of seismic body waves. The method is based on the strain energy of an elastic wavefield and Hooke’s Law. We present a detailed derivation of a set of equations that explicitly partition the seismic strain energy into two parts: one for compressional (P) waves and one for shear (S) waves. We posit that the ratio of these two quantities can be used to determine the relative contribution of seismic P and S waves, possibly as a method to discriminate between earthquakes and buried explosions. We demonstrate the efficacy of our method by using it to compute the strain energy of synthetic seismograms with differing source characteristics. Specifically, we find that explosion-generated seismograms contain a preponderance of P wave strain energy when compared to earthquake-generated synthetic seismograms. Conversely, earthquake-generated synthetic seismograms contain a much greater degree of S wave strain energy when compared to explosion-generated seismograms.
In this report, we assess the data recorded by a Distributed Acoustic Sensing (DAS) cable deployed during the Source Physics Experiment, Phase II (DAG) in comparison with the data recorded by nearby 4.5-Hz geophones. DAS is a novel recording method with unprecedented spatial resolution, but there are significant concerns around the data fidelity as the technology is ramped up to more common usage. Here we run a series of tests to quantify the similarity between DAS data and more conventional data and investigate cases where the higher spatial resolution of the DAS can provide new insights into the wavefield. These tests include 1D modeling with seismic refraction and bootstrap uncertainties, assessing the amplitude spectra with distance from the source, measuring the frequency dependent inter-station coherency, estimating time-dependent phase velocity with beamforming and semblance, and measuring the cross-correlation between the geophone and the particle velocity inferred from the DAS. In most cases, we find high similarity between the two datasets, but the higher spatial resolution of the DAS provides increased details and methods of estimating uncertainty.
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.
This final report summarizes the work completed under the Laboratory Directed Research and Development (LDRD) project “Seismic Spatial Gradients as a Machine Learning-Based Classifier for Explosion Monitoring.” The overarching goal of the project was to explore the efficacy of using machine learning-based classification algorithms where the input data are the spatial gradient of the seismic wavefield collected at a single point on the Earth’s surface. The methods that I describe here are in direct contrast to conventional methods of seismic discrimination which typically rely on a spatially extended network of instruments and physics-based wavefield attributes such as, for example, the ratio between $\textit{P}$ and $\textit{S}$ waves. Rather, we use the spatial gradient of the seismic wavefield observed at a single point on the Earth’s surface and data processing approaches inspired by the machine learning community. We tested two algorithms, a neural network and a modified version of principal component analysis termed Spectrally Filtered Principal Component Analysis (SFPCA). To test these algorithms, we first conducted a series of numerical tests using synthetic data and then conducted a small-scale controlled field experiment. The tests using synthetic data showed that both algorithms had high success rates on gradiometric data, even when simulated noise was added to the signal. Furthermore, we found that using seismic spatial gradients increased the performance of our discrimination algorithms when compared to using just the traditional translational motion seismic data. The tests with field data also showed a high degree of discriminative success.
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.
We present a new method to discriminate between earthquakes and buried explosions using observed seismic data. The method is different from previous seismic discrimination algorithms in two main ways. First, we use seismic spatial gradients, as well as the wave attributes estimated from them (referred to as gradiometric attributes), rather than the conventional three-component seismograms recorded on a distributed array. The primary advantage of this is that a gradiometer is only a fraction of a wavelength in aperture com¬pared with a conventional seismic array or network. Second, we use the gradiometric attributes as input data into a machine learning algorithm. The resulting discrimination algorithm uses the norms of truncated principal components obtained from the gradio- metric data to distinguish the two classes of seismic events. Using high-fidelity synthetic data, we show that the data and gradiometric attributes recorded by a single seismic gra¬diometer performs as well as a conventional distributed array at the event type discrimi¬nation task.
This report describes a proof-of-concept method of seismic source discrimination using seismic gradiometry and a common machine learning technique. The tests described here are purely numerical, using synthetic seismic data and well understood mathematical techniques. The primary innovation described here is the application of a richer seismic data set derived from seismic gradiometry. Seismic gradiometry is a method to estimate the time variable spatial gradient of the wavefield to compute various wavefield attributes such as slowness, dynamic strain, and rotational motions. With the addition of these wavefield attributes, we are afforded up to twenty "compo- nents" of time series data measured at a single point on, or in, the Earth. This is in direct contrast to conventional three-component seismic data collected at several locations using a seismic network. Using the gradiometrically-derived wavefield components directly in a single-layer neural network, I show that it is possible to discriminate between three common seismic source types (earthquakes, explosions, and opening fractures) for various noise conditions and gradiometry configurations.
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.