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.
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