Forward Modeling

The vertical boundary model in Figure 3.1 is used to generate both crosswell and RVSP data. P-wave velocities are 5000 m/s and 5500 m/s, the P- to S-wave velocity ratio is 1.5, and a constant density is used. Parallel source and receiver wells bracket the model for the crosswell simulation. The RVSP simulation uses the same sources as for the crosswell simulation but the receivers are along the top of the model. Synthetic seismograms were computed using a 2-D elastic wave modeling code, placing sources and receivers at one meter intervals. The model grid size is 20 centimeters and the time interval is 10 microseconds. Although source frequencies above 2000 Hz are often used in hardrock crosswell experiments; I chose a 1500 Hz vertical-component line source and 6000 time steps. The line source is orthogonal to the model space and therefore geometric spreading occurs in only two dimensions. Both vertical- and horizontal-component data were generated and recorded. A common-shot gather for a source at 100 meters depth and receivers on the surface (RVSP) is shown in Figure 3.2. Seismograms from both crosswell and RVSP data sets are then migrated using both Kirchhoff (French, 1974; Gardner, 1974) and wavepath migration algorithms (Sun and Schuster 1999a; 1999b; 2000) in combination with reduced-time migration.

Figure 3.1: Vertical boundary model used to generate synthetic crosswell and RVSP data. Density is constant for the entire 100 m$^2$ model and a 1500 Hz Z-component source was used. Sources for both crosswell and RVSP simulations are on the left at one meter intervals (101 total). Receivers (101) at one meter intervals are distributed along the right for the crosswell simulation, and across the top for the RVSP simulation.

Figure 3.2: Synthetic RVSP seismogram for a source at 100 m depth. The source frequency is 1500 Hz, receiver spacing is 1 m, and the total record length is 0.06 seconds.