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At least 19 records

Modeling of Seismic Waves Through Geologic Metamaterials

This project conducted a modeling study on seismic invisibility cloaks that render geologic targets invisible to seismic waves, using the concept of seismic metamaterials. We present a parametric numerical study on the behaviors of seismic waves through cloaks with different design parameters as well as degrees of geologic heterogeneity. In addition, a seismic cloaking strategy is proposed for a future field-scale experiment at a real-world test bed. This feasibility study will guide future field experiment designs and ultimately allow us to conduct systematic field-scale tests employing Sandia’s existing resources and field expertise. The ultimate goal is to develop methods and design parameters of seismic invisibility cloaks to protect against natural and man-made seismic waves. Seismic cloaking has potential applications in several areas of national security, energy, and natural hazard reduction.

58 GEOSCIENCES↗

Field Demonstration of The Krauklis Seismic Wave In A Novel Mva Method For Geologic CO 2 Storage

The Energy & Environmental Research Center (EERC) conducted a feasibility study of a new, low-impact geophysics monitoring method designed to incrementally track the saturation front of CO 2 injected into a reservoir. The method leverages a new way of transmitting energy from the surface to the reservoir and employs a new subsurface signal called the Krauklis wave (K-wave) and other guided waves for seismic monitoring. The EERC partnered with Seismos, Inc., the company that holds the exclusive technology license for this method, to advance development of K-wave technology, and Denbury Onshore, LLC, to field-test the system. The system was field-tested at Denbury’s Bell Creek oil field, currently undergoing CO 2 -based enhanced oil recovery (EOR) in southeastern Montana. The K-wave system uses a wellhead-mounted source to propagate energy down the wellbore in the form of a tube wave and through the well perforations into the reservoir. Part of the energy transmitted through the perforations into the reservoir converts to slow moving K-waves and/or other guided waves that are expected to propagate through the formation to neighboring wells. The propagated signal would induce tube waves in the neighboring wells that return to the surface to be recorded with a wellhead-mounted receiver. The propagation time of the signal is directly affected by the presence of CO 2 between the wells, so the difference in transit time of the returning signal between pre- and postinjection data sets could be used to help define the lateral extent of a CO 2 saturation front. Objectives of the study were to demonstrate, validate, and evaluate the K-wave method’s ability to monitor the morphology of injected CO 2 and estimate saturation distribution. Results from the demonstration were to be compared to conventional 4-D surface seismic methods, dynamic reservoir simulations, and CO 2 breakthrough data to validate the technology and provide useful information that may result in improvements. Prior to mobilizing for the full-scale K-wave baseline survey, a field test was conducted to better understand wellhead hardware configurations and test the response from the Bell Creek reservoir using three wells. Useful operational information resulted but signal from the first-generation gas release/gas injection source was not recorded in neighboring wells. After the initial field test, numerical modeling of the K-wave method was initiated using parameters specific to the Bell Creek Field. Modeling results indicated that the fundamental concepts behind the K-wave method exhibited problems and revealed a significantly greater attenuation of the signal at the wellbore perforations than expected, totaling on the order of 10-8 from source well to receiver well over a 400-m well spacing. Modeling also showed that greater source frequency bandwidth was needed to produce guided waves within a 30-foot-thick reservoir layer such as that at Bell Creek and that reservoir layer seismic velocity would need to be slower than the velocities of the bounding layers in order to act as a wave guide opposite to what exists at Bell Creek. Modeling results prompted a second field test with a stronger, second-generation displacement source developed in the interim. Concurrent with the second field test, a 3-D seismic survey was acquired to serve as a baseline for project validation and to serve as a monitor data set for the portion of the project area where CO 2 injection had already commenced. The new source was tested using a four-well geometry and failed to produce a detectable signal, which appeared to confirm modeling results and indicated that the Bell Creek Field is not an ideal site for the K-wave test. It was concluded that a source with sufficient strength and bandwidth could not be built to overcome the factors discovered by the modeling within a reasonable amount of time. Several other sites undergoing CO 2 -based EOR were also evaluated; however, none of these sites was amenable because of geology, limitations of source and receiver hardware, or the advanced state of the CO 2 flood. In addition, two other configurations of the source and receiver layout were considered; however, these design modifications either changed the scope of the project or did not meet the goals of the Carbon Storage Program. In consultation with the U.S. Department of Energy (DOE) Project Manager and Technology Manager, a no-go decision was invoked to forego additional expenditures as the technology would not meet current project objectives. Project activities to date have moved the technology forward by developing modeling equations that can be applied elsewhere, advanced the state of wellhead sensors and sources, and spurred improvements to field operations. The 3-D seismic survey in the project area and the dynamic reservoir simulations done as part of this study have provided value for ongoing and future synergistic activities at Bell Creek related to DOE carbon storage goals.

54 ENVIRONMENTAL SCIENCES↗

Modeling and simulation of earthquake soil structure interaction excited by inclined seismic waves

Presented is an application of wave potential formulation (WPF) together with domain reduction method (DRM) to modeling earthquake soil structure interaction (ESSI) behavior in horizontally layered ground under inclined incident seismic waves. Wave potential formulation is used to develop a spatially varying, inclined seismic wave field from incident Primary (P) and Secondary (S) waves that propagate through layered ground. Developed seismic wave field is then used to develop effective forces for Domain Reduction Method that are then used for analyzing ESSI response of a soil structure system. Developed methodology, called WPF-DRM, is verified using analytic solution for a free field response of layered ground subjected to inclined incident waves. Developed WPF-DRM methodology is illustrated through analysis of an ESSI response of a deeply embedded structure, a small modular reactor (SMR) subjected to incident S wave polarized in vertical plane (SV) with variation in inclinations and frequencies. Presented example highlights the influences of incident wave inclination and frequency on ESSI response of analyzed SMR.

58 GEOSCIENCES↗

A modular methodology for time-domain stochastic seismic wave propagation

Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

58 GEOSCIENCES↗

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscale basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.

58 GEOSCIENCES↗

Effects of Shallow-Velocity Reductions on 3D Propagation of Seismic Waves

Abstract We perform 3D simulations of seismic wavefields to clarify effects of strong reductions of shallow velocities on long-period seismic waves. The simulations use a reference Community Velocity Model of southern California and a modified version with strong velocity reductions in the top 500 m of the Los Angeles basin. Differences between wavefields generated by 10 earthquakes in the reference and perturbed models are analyzed. Velocity changes are estimated by measuring relative time shifts between reference and perturbed seismograms using wavelet cross-correlation spectra. The results indicate that strong localized temporal velocity drops near the surface, such as those observed during strong ground motions, may generate regional perturbations of wavefields at periods up to 20 s. These perturbations may be misinterpreted as generated by temporal changes at seismogenic depths. The results also have important implications for waveform tomography studies.

Geochemistry & Geophysics↗

Analysis of Seismic Wave Amplification in Sedimentary Basins Using 3D Wavefield Simulations: Nenana Basin, Central Alaska

We investigate seismic wave amplification in Nenana basin, central Alaska, using 3D seismic wavefield simulations. We quantify frequency-dependent amplification by comparing synthetic seismograms among four different seismic velocity models: (a) a tomographic model, (b) a tomographic model with the uppermost 6.5 km replaced by a 1D basin profile, (c) a tomographic model with an embedded ellipsoidal basin, and (d) a tomographic model with an embedded realistic basin. For each model we perform wavefield simulations accurate up to 2 Hz for a set of 10 different earthquakes, which provide a range of frequencies and incident angles for waves interacting with the basin. Average amplification ratios are four on the horizontal components and seven on the vertical component. The dominant influence of the amplification is the 3D geometry of the basin, not the slow-velocity profile near the surface. Our synthetic amplification ratios are in general agreement with amplification estimates obtained from 14 stations that recorded the same set of earthquakes. Our approach offers a general strategy for documenting frequency-dependent basin amplification for a region with realistic basin structures and local earthquakes.

Geosciences↗

Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation [Slides]

We have developed a series of multiscale finite-element methods for simulating seismic wave propagation in complex media. The most important feature of multiscale finite-element methods is using medium- and mesh-dependent multiscale basis functions. For different wave equations, or for wave equation modeling in different domains, we design different local spectral/linear problems to compute multiscale basis functions. Multiscale basis functions can accurately capture the fine-scale medium information for coarse-scale modeling problems. Numerical examples have demonstrated the efficiency and accuracy of our multiscale finite-element method framework for wave equation modeling. Future works aim at further improving the efficiency using more levels of information encapsulation, and address more realistic physics problems.

58 GEOSCIENCES↗

Azimuthally Dependent Seismic-Wave Coherence at the Source Physics Experiment Large-N Array

Abstract We report on 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 analyze 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 indicates 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.

58 GEOSCIENCES↗

Seismic Wave Coherence as a Function of Propagation Azimuth at the Large-N Array, Source Physics Experiment

The Large-N array of the Source Physics Experiment (SPE) consisted, in part, of 496 vertical component geophones that recorded the seismic wave field produced by the SPE-5 buried chemical explosion. Preliminary observations of the data showed a large degree of azimuthally dependent seismic scattering, particularly for post-P wave arrivals, hindering surface wave analysis. We document and quantify the azimuthal dependence of the wave field scattering in order to guide future coherent wave field processing methods. Specifically, we form three linear arrays, with different nominal source-receiver azimuths, by extracting a subset of the Large-N stations. For each linear array, we evaluate wave field coherence as a function of frequency and inter-station distance. For P waves, we observe that there is a strong azimuthal dependence of wave coherence, with the highest degree of scattering occurring in a northwest/southeast propagation direction. This suggests that there are structural elements beneath the Large-N array that affect the direct source to receiver body wave ray path. We also observe that the scattering of the post-P energy displays a coherence that is dependent on both frequency and azimuthal direction. This energy is preferentially coherent in the southwest-to-northeast propagation direction, consistent with the strike of the steeply dipping fault (Boundary fault) adjacent to the northeast side of the Large-N array, but only at low frequencies (<10 Hz). At higher frequencies, the azimuthally dependent wave coherence diminishes, suggesting that the scattering of high frequency portion of the post-P wave field is independent of the large-scale geologic structure at this site.

58 GEOSCIENCES↗

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗

Simulations of Seismic Wave Propagation on Mars

In this paper, we present global and regional synthetic seismograms computed for 1D and 3D Mars models based on the spectral-element method. For global simulations, we implemented a radially-symmetric Mars model with a 110 km thick crust. For this 1D model, we successfully benchmarked the 3D seismic wave propagation solver SPECFEM3D_GLOBE against the 2D axisymmetric wave propagation solver AxiSEM at periods down to 10 s. We also present higher-resolution body-wave simulations with AxiSEM down to 1 s in a model with a more complex 1D crust, revealing wave propagation effects that would have been difficult to interpret based on ray theory. For 3D global simulations based on SPECFEM3D_GLOBE, we superimposed 3D crustal thickness variations capturing the distinct crustal dichotomy between Mars’ northern and southern hemispheres, as well as topography, ellipticity, gravity, and rotation. The global simulations clearly indicate that the 3D crust speeds up body waves compared to the reference 1D model, whereas it significantly changes surface waveforms and their dispersive character depending on its thickness. We also perform regional simulations with the solver SES3D based on 3D crustal models derived from surface composition, thereby addressing the effects of various distinct crustal features down to 2 s. The regional simulations confirm the strong effects of crustal variations on waveforms. Finally, we conclude that the numerical tools are ready for examining more scenarios, including various other seismic models and sources.

58 GEOSCIENCES↗

Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth

SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Geochemistry & Geophysics↗

Solving Seismic Wave Equations on Variable Velocity Models With Fourier Neural Operator

Here, in the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning (DL) enables solving partial differential equations (PDEs), including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn the frequency domain seismic wavefields under the context of variable velocity models. We also propose a new framework paralleled FNO (PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

58 GEOSCIENCES↗

Dissipation-preserving spectral element method for damped seismic wave equations

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Pararhombi: Parallel Implementation of 3-D Seismic Wave Propagation in Orthorhombic Media

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.

58 GEOSCIENCES↗

Pararhombi: Parallel Implementation of 3-D Seismic Wave Propagation in Orthorhombic Media

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.

58 GEOSCIENCES↗