Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and Finite-difference, time-domain ͑FDTD͒ calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium ͑with an emphasis on the atmosphere͒ are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.

The availability of regional earthquake data from the Pacific Northwest Seismograph Network (PNSN), together with active source data from the Seismic Hazards Investigation in Puget Sound (SHIPS) seismic experiments, has allowed us to construct a new high‐resolution 3‐D, P wave velocity model of the crust to a depth of about 30 km in the central Puget Lowland. In our method, earthquake hypocenters and velocity model are jointly coupled in a fully nonlinear tomographic inversion. Active source data constrain the upper 10–15 km of the model, and earthquakes constrain the deepest portion of the model. A number of sedimentary basins are imaged, including the previously unrecognized Muckleshoot basin, and the previously incompletely defined Possession and Sequim basins. Various features of the shallow crust are imaged in detail and their structural transitions to the mid and lower crust are revealed. These include the Tacoma basin and fault zone, the Seattle basin and fault zone, the Seattle and Port Ludlow velocity highs, the Port Townsend basin, the Kingston Arch, and the Crescent basement, which is arched beneath the Lowland from its surface exposure in the eastern Olympics. Strong lateral velocity gradients, consistent with the existence of previously inferred faults, are observed, bounding the southern Port Townsend basin, the western edge of the Seattle basin beneath Dabob Bay, and portions of the Port Ludlow velocity high and the Tacoma basin. Significant velocity gradients are not observed across the southern Whidbey Island fault, the Lofall fault, or along most of the inferred location of the Hood Canal fault. Using improved earthquake locations resulting from our inversion, we determined focal mechanisms for a number of the best recorded earthquakes in the data set, revealing a complex pattern of deformation dominated by general arc‐parallel regional tectonic compression. Most earthquakes occur in the basement rocks inferred to be the lower Tertiary Crescent formation. The sedimentary basins and the eastern part of the Olympic subduction complex are largely devoid of earthquakes. Clear association of hypocenters and focal mechanisms with previously mapped or proposed faults is difficult; however, seismicity, structure, and focal mechanisms associated with the Seattle fault zone suggest a possible high‐angle mode of deformation with the north side up. We suggest that this deformation may be driven by isostatic readjustment of the Seattle basin.

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Appendix 1. Abbreviated list of airgun shotpoint locations, FFID numbers, and shot times Appendix 2. Reftek and OBS station locations and elevations Appendix 3. List of timing used for Reftek stations 56 Appendix 4. List of stations having problems with spurious 12-second shifts Appendix 5. List of location of Reftek station data on archival tapes

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.