HR: 17:15h
AN: S42J-04 INVITED     [PDF]
TI: Seismic FDTD Modeling of Surface Waves Over Grid-Transformed and Stair-Stepped Topographies
AU: * Ketcham, S
EM: Stephen.A.Ketcham@erdc.usace.army.mil
AF: US Army Engineer Research and Development Center, 72 Lyme Rd, Hanover, NH 03755 United States
AU: Moran, M
EM: Mark.L.Moran@erdc.usace.army.mil
AF: US Army Engineer Research and Development Center, 72 Lyme Rd, Hanover, NH 03755 United States
AU: Anderson, T
EM: Thomas.S.Anderson@erdc.usace.army.mil
AF: US Army Engineer Research and Development Center, 72 Lyme Rd, Hanover, NH 03755 United States
AU: Greenfield, R
EM: roy@essc.psu.edu
AF: Greenfield Associates, 600 Mckee St, State College, PA 16803 United States
AB: We are developing finite-difference time domain code to model 3D surface wave propagation caused by moving surface sources. Our applications require that we simulate surface wave propagation over real and sometimes steep terrain up to 1-km2 in area. Force inputs will have durations up to 1 minute and contain significant energy in the 15-45 Hz band. These features require that our code (1) have surface wave accuracy over topographical surfaces to ranges of several Rayleigh wavelengths, (2) be stable over long durations, and (3) run on supercomputers. We have implemented a grid transformation and the corresponding equations of motion and stress-strain-velocity. The transformation maps a rectangular, computational grid to a distorted grid with a topographical surface. The distorted grid conforms to the topographical surface. We have discretized the transformed equations of motion and stress-strain-velocity to calculate centered second order differences in space and time on the computational grid. We use conventional staggering of stress and particle velocity calculation points. To model a free surface, we adapt interface property averaging techniques to our transformed equations and approximate the stress release of a free surface by including a relatively thin layer of air above the ground. The ground-air interface is specified along the conformal topographical surface. Alternatively the interface can be located along a stair-stepped approximation of the topographical surface. The code therefore inherently allows for three transformation/free surface options: (1) transformed grid with ground-air interface that fully conforms to topography, (2) non-transformed rectangular grid with stair-stepped ground-air interface that discretely approximates topography, or (3) transformed grid with a hybrid interface, i.e., a conformal ground-air interface over part of surface and stair-stepped interface over the remainder. We have tested the accuracy and limitations of topography-conforming grid transformations by comparing results of surface-pulse-induced propagation over homogeneous elastic models with planar-sloped surfaces (slopes ranging from 0 to 1) to corresponding wavenumber-integration solutions. The comparisons show that receiver signal accuracy decreases with increasing slope and range. Acceptable accuracy is demonstrated in 25-percent-slope models out to 3-4 Raleigh wavelengths and in 50-percent-slope models out to 1-2 Raleigh wavelengths. Further comparisons with wavefields of models having non-transformed rectangular grids show that the topography-conforming grid transformations are more accurate for gentler slopes (e.g., 25 percent or less), while the fully rectangular grids with stair-stepped topography are best for steeper slopes, albeit with the well-recognized limitations of stair-stepped topographical models. These results suggest that using the hybrid topography modeling is desirable. e.g., we have synthesized a homogeneous elastic model with a grid-conforming 25-percent slope that is interrupted by a stair-stepped steep trench and a stair-stepped steep hill. Results from impulsive surface source analyses show underlying accuracy and minimal numerical noise, demonstrating the potential of the technique for surface sources on real topographies.
DE: 7255 Surface waves and free oscillations
DE: 7260 Theory and modeling
SC: Seismology [S]
MN: 2003 Fall Meeting