Seismic waveform simulation for models with fluctuating interfaces

The contrast of elastic properties across a subsurface interface imposes a dominant influence on the seismic wavefield, which includes transmitted and reflected waves from the interface. Therefore, for an accurate waveform simulation, it is necessary to have an accurate representation of the subsurface interfaces within the numerical model. Accordingly, body-fitted gridding is used to partition subsurface models so that the grids coincide well with both the irregular surface and fluctuating interfaces of the Earth. However, non-rectangular meshes inevitably exist across fluctuating interfaces. This non-orthogonality degrades the accuracy of the waveform simulation when using a conventional finite-difference method. Here, we find that a summation-by-parts (SBP) finite-difference method can be used for models with non-rectangular meshes across fluctuating interfaces, and can achieve desirable simulation accuracy. The acute angle of non-rectangular meshes can be relaxed to as low as 47°. The cell size rate of change between neighbouring grids can be relaxed to as much as 30%. Because the non-orthogonality of grids has a much smaller impact on the waveform simulation accuracy, the model discretisation can be relatively flexible for fitting fluctuating boundaries within any complex problem. Consequently, seismic waveform inversion can explicitly include fluctuating interfaces within a subsurface velocity model

QUANTIFYING UNCERTAINTIES IN GROUND MOTION SIMULATIONS FOR SCENARIO EARTHQUAKES ON THE HAYWARD-RODGERS CREEK FAULT SYSTEM USING THE USGS 3D VELOCITY MODEL AND REALISTIC PSEUDODYNAMIC RUPTURE MODELS

This project seeks to compute ground motions for large (M>6.5) scenario earthquakes on the Hayward Fault using realistic pseudodynamic ruptures, the USGS three-dimensional (3D) velocity model and anelastic finite difference simulations on parallel computers. We will attempt to bound ground motions by performing simulations with suites of stochastic rupture models for a given scenario on a given fault segment. The outcome of this effort will provide the average, spread and range of ground motions that can be expected from likely large earthquake scenarios. The resulting ground motions will be based on first-principles calculations and include the effects of slip heterogeneity, fault geometry and directivity, however, they will be band-limited to relatively low-frequency (< 1 Hz)

A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces

A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem

The Prospect of using Three-Dimensional Earth Models To Improve Nuclear Explosion Monitoring and Ground Motion Hazard Assessment

The last ten years have brought rapid growth in the development and use of three-dimensional (3D) seismic models of earth structure at crustal, regional and global scales. In order to explore the potential for 3D seismic models to contribute to important societal applications, Lawrence Livermore National Laboratory (LLNL) hosted a 'Workshop on Multi-Resolution 3D Earth Models to Predict Key Observables in Seismic Monitoring and Related Fields' on June 6 and 7, 2007 in Berkeley, California. The workshop brought together academic, government and industry leaders in the research programs developing 3D seismic models and methods for the nuclear explosion monitoring and seismic ground motion hazard communities. The workshop was designed to assess the current state of work in 3D seismology and to discuss a path forward for determining if and how 3D earth models and techniques can be used to achieve measurable increases in our capabilities for monitoring underground nuclear explosions and characterizing seismic ground motion hazards. This paper highlights some of the presentations, issues, and discussions at the workshop and proposes a path by which to begin quantifying the potential contribution of progressively refined 3D seismic models in critical applied arenas