Frequency domain Finite Frequency domain Finite Difference Modelling : Difference Modelling :

ExamplesExamples

Wave equation discretizationAcoustic, second order in space, rotated operators, lumped mass

Accuracy at 4 grid points per wavelength:

99% (phase velocity)

97 % (group velocity)

Memory: O( n2 log n )

Memory: O( n3 )

Matrix solution

LU Decomposition to solve

Nested dissection to reduce storage

S u = L U u = f

(P S PT) (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 pointsLinear system: 640,000 complex equationsMemory: 500 Mbytes RAMTime: 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.