Frequency domain Finite Difference Modelling : Examples

Wave equation discretization Acoustic, second order in space, rotated operators, lumped mass Accuracy at 4 grid points per wavelength: 99% (phase velocity) 97 % (group velocity)

Memory: O( n 2 log n ) Memory: O( n 3 ) Matrix solution ! ! LU Decomposition to solve Nested dissection to reduce storage S u = L U u = f (P S P T ) (P u) = P f L x =f U = xu

Wide angle (crustal) example Size: 250 km x 40 km, 120 sources 500 x 80 (at 10 Hz, 5000 m/s) 2000 x 320 = 640,000 grid points Linear system: 640,000 complex equations Memory: 500 Mbytes RAM Time: 3 minutes per frequency, 128 frequencies 7.2 hours for all frequencies, all sources (Reduced time) Equivalent time domain FD modelling: Time: One source, 30 minutes (no reduced time) 120 sources, 2.5 days (Assumes same accuracy FD, same Mflop machine)

Sub-salt Gulf of Mexico: 2-D Gridded velocity model, from well logs, checkshots and manual interpretation of stack

Neptune sub-salt: Real data shot gather from Northern end of model

Neptune sub-salt: Synthetic shot gather from Northern end of model

Neptune sub-salt: Synthetic shot gather from Northern end of model: “target only” data.

Neptune sub-salt: Synthetic shot gather from Northern end of model: “target only” data, with ray trace times from sub-salt unconformity.