Christopher R. Bradley

Estimation of Q for Long-Period (>2 sec) Waves in the Los Angeles Basin

We simulate 0- to 0.5-Hz 3D wave propagation through the Southern California Earthquake Center seismic velocity reference model, version 2, for the 1994 Northridge earthquake in order to examine the effects of anelastic attenuation and amplification within the near-surface sediments. We use a fourth-order finite-difference staggered-grid method with the coarse-grained frequency-independent anelastic scheme of Day and Bradley (2001) and a variable slip distribution from kinematic inversion for the Northridge earthquake. We find that the near-surface material with S -wave velocity ( V s) as low as 500 m/sec significantly affects the long-period peak ground velocities, compared with simulations in which the S -wave velocity is constrained to 1 km/sec and greater. Anelastic attenuation also has a strong effect on ground-motion amplitudes, reducing the predicted peak velocity by a factor of up to 2.5, relative to lossless simulations. Our preferred Q model is Q s/ V s = 0.02 ( V s in meters per second) for V s less than 1–2 km/sec, and much larger Q s/ V s (0.1, V s in meters per second) for layers with higher velocities. The simple model reduces the standard deviation of the residuals between synthetic and observed natural log of peak velocity from 1.13 to 0.26, relative to simulations for the lossless case. The anelastic losses have their largest effect on short-period surface waves propagating in the Los Angeles basin, which are principally sensitive to Q s in the low-velocity, near-surface sediments of the basin. The low-frequency ground motion simulated here is relatively insensitive to Q p, as well as to the values of Q s at depths greater than roughly that of the 2-km/sec S -wave velocity isosurface.

Memory-Efficient Simulation of Anelastic Wave Propagation

Realistic anelastic attenuation can be incorporated rigorously into finite difference and other numerical wave propagation methods using internal or memory variables. The main impediment to the realistic treatment of anelastic attenuation in 3D is the very large computational storage requirement imposed by the additional variables. We previously proposed an alternative to the conventional memory-variable formulation, the method of coarse-grain memory variables, and demonstrated its effectiveness in acoustic problems. We generalize this memory-efficient formulation to 3D anelasticity and describe a fourth-order, staggered-grid finite-difference implementation. The anelastic coarse-grain method applied to plane wave propagation successfully simulates frequency-independent Q p and Q s . Apparent Q values are constant to within 4% tolerance over approximately two decades in frequency and biased less than 4% from specified target values. This performance is comparable to that achieved previously for acoustic-wave propagation, and accuracy could be further improved by optimizing the memory-variable relaxation times and weights. For a given assignment of relaxation times and weights, the coarse-grain method provides an eight-fold reduction in the storage requirement for memory variables, relative to the conventional approach. The method closely approximates the wavenumber-integration solution for the response of an anelastic half-space to a shallow dislocation source, accurately calculating all phases including the surface-diffracted SP phase and the Rayleigh wave. The half-space test demonstrates that the wave field-averaging concept underlying the coarse-grain method is effective near boundaries and in the presence of evanescent waves. We anticipate that this method will also be applicable to unstructured grid methods, such as the finite-element method and the spectral-element method, although additional numerical testing will be required to establish accuracy in the presence of grid irregularity. The method is not effective at wavelengths equal to and shorter than 4 grid cell dimensions, where it produces anomalous scattering effects. This limitation could be significant for very high-order numerical schemes under some circumstances (i.e., whenever wave-lengths as short as 4 grids are otherwise within the usable bandwidth of the scheme), but it is of no practical importance in our fourth-order finite-difference implementation.

Assessment of a Nonlinear Dynamic Rupture Inversion Technique Applied to a Synthetic Earthquake

Dynamic rupture inversion is a powerful tool for learning why and how faults fail, but much more work has been done in developing inversion methods than evaluating how well these methods work. This study examines how well a nonlinear rupture inversion method recovers a set of known dynamic rupture parameters on a syntheticfault based onthe2000westernTottori, Japanearthquake(Mw6.6).Rupture evolution on the fault is governed by a slip-weakening friction law. A direct-search method known as the neighborhood algorithm (Sambridge, 1999) is used to find optimal values of both the initial stress distribution and the slip-weakening distance on the fault, based on misfit values between known and predicted strong-motion displacement records. The yield stress and frictional sliding stress on the fault are held constant. A statistical assessment of the results shows that, for this test case, the inversion succeeds in locating all parameters to within ! 14% of their true values. With the model configuration used in this study, the parameters located in the central rupture area are better resolved than the parameters located at the sides and bottom of the fault. In addition, a positive linear correlation between the mean initial stress and the slip-weakening distance is identified. The investigation confirms that dy- namic rupture inversion is useful for determining rupture parameters on the fault, but that intrinsic trade-offs and poor resolution of some parameters limit the amount of information that can be unambiguously inferred from the results. In addition, this study demonstrates that using a statistical approach to assess nonlinear inversion results shows how sensitive the misfit measure is to the various parameters, and allows a level of confidence to be attached to the output parameter values.

Phenomenology and Modeling of Explosion‐Generated Shear Energy for the Source Physics Experiments

Abstract We present a mechanism for shear‐wave generation from buried explosions as part of the Source Physics Experiment (SPE) series. The SPE series includes sensitized heavy ammonium nitrate/fuel oil sources of various sizes detonated in a borehole in the jointed Climax stock granite. The cylinder‐shaped shots were grouted in the borehole to couple the energy to the rock. A high‐fidelity site model—with explicit inclusion of the cylindrical explosive, the grout‐filled borehole, and site joint sets—was included in a numerical simulation that mimics the near‐field velocity environment measured by an array of in‐ground accelerometers. This approach was accommodated through a coupled Euler–Lagrange code that allows simultaneous solving of a Euler domain to model the high‐deformation source region and a Lagrange domain that includes the complex geology with full contact. Specific laboratory‐measured geomechanical properties for the rock and the joint sets were included in the model. The simulations compare favorably to the data and provide a possible physical mechanism for unexpected shear motion through the release of stored shear strain on the joints. This research will advance our understanding of explosion‐generated shear‐wave energy from low‐yield nuclear tests.

Immobile Pore-Water Storage Enhancement and Retardation of Gas Transport in Fractured Rock

The effect of immobile pore-water on gas transport in fractured rock has implications for numerical modeling of soil vapor extraction, methane leakage, gaseous

The Combined Finite-Discrete Element Method applied to the Study of Rock Fracturing Behavior in 3D

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Geologic fracturing method and resulting fractured geologic structure

CO2 leakage from sequestration operations, radionuclide transport from underground nuclear explosions, and nuclear waste disposal. While the ability for immobile pore-water storage to effect gas transport has been recognized in the past, the details and specific scenarios leading to enhanced, retarded, or unaffected gas transport have not been explored. We performed numerical investigations into the enhancement and retardation of gas transport due to immobile pore-water storage in order to identify implications for gas transport applications. To do this, we developed a numerical approach to model gas transport with a single-phase flow solution coupled to the advection–dispersion equation modified to account for immobile pore-water storage. Other than the immobility of pore water, the formulation contains all other physics included in two-phase formulations (advective and diffusive gas transport in fractures and rock matrix and dissolution in immobile pore water). The assumption of immobile pore water is valid here since for many applications involving transport of soluble gases in fractured rock, the rate of aqueous transport is insignificant compared to gas transport. We verify our modeling approach with analytical solutions of: (1) 1D gas diffusion, (2) 1D gas advection, (3) barometric pumping of a fracture, and (4) gas transport with uniform fracture flow and diffusion into the matrix. We account for pore-water storage in our model by implementing a kinetic formulation of gas dissolution wherein the dissolved (aqueous) phase is considered an immobile constituent. Using this formulation, we model the effect of dissolution rate and saturation on the retardation of gas transport during pure diffusion and pure advection. We also demonstrate that although it is commonly believed that pore-water storage will always enhance gas transport in fractures during oscillatory flow (e.g., during reversing pressure gradients such as barometric pumping cycles), our simulations indicate that this may not always be the case. Our numerical investigations indicate that scenarios with lower effective diffusion coefficients (