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Computer Implementation Of Efficient Transversely Isotropic Wave Propagators For Simulation, Reverse Time Depth Migration And Full Waveform Inversion

IP.com Disclosure Number: IPCOM000236677D
Publication Date: 2014-May-08
Document File: 6 page(s) / 34K

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Computer Implementation Of Efficient Transversely Isotropic Wave Propagators For Simulation, Reverse Time Depth Migration And Full Waveform Inversion

An efficient wave propagation algorithm is useful for doing wave field simulation, reverse time depth migration (RTM) and full waveform inversion (FWI).  These processes are typically applied to simulate and process seismic data while attempting to identify subsurface structures and subsurface properties for hydrocarbon exploration and development.  Efficient algorithms attempt to (1) provide solutions for wave field propagation that meet a specified level of accuracy for a specified medium parameterization (2) reduce the number of floating point operations (3) reduce the computer memory requirements (4) reduce computer memory cache misses (5) reduce the number of halo domain exchanges and the amount of halo data exchanged in a parallel programming domain-decomposed implementation and (6) provide adaptability enabling the use of specialized efficient computing hardware such as Graphical Processing Units (GPU).   For RTM and FWI applications, both forward and adjoint wave field simulation operators are needed to fully implement the algorithm.  An adjoint simulation operator propagates a wave field backward in time.   Adjoint operators are implemented for all methods described here.  Each algorithm described here for wave propagation needs to consider the type of medium and the wave mode of interest when searching for the most computationally advantageous approach. 

Efficiencies related to a stretched grid are most readily implemented in a set of coupled first-order coupled equations using precomputed Jacobians for the defined grid, but stretched-grid efficiencies can be added to second-order formulations as well.  A stretched-grid approach gains efficiency by operating on fewer grid points where the velocity model is fastest and by using a larger stability time step increment.  The use of a larger time step may require temporal numerical dispersion corrections (Stork, 2013) to maintain accuracy.

In general, a system of second-order differential equations is more computationally efficient than a system of coupled first-order equations, but requires an assumption of a constant medium parameter.   Second-order equations in stress or pressure would assume constant density and spatially-variable stiffness coefficients.   Second-order equations in particle displacement or particle velocity would assume spatially-constant stiffness parameters and spatially-variable density.   Usually the choice of constant density is preferred over a choice of constant stiffness.  Stiffness divided by density has units of velocity squared and the parameterization of spatially-variable stiffness with constant density accurately matches the spatially-variable velocity assumption.  Accurate simulated reflection amplitudes at a strong-contrast boundary such as a hard water bottom or a sediment/salt interf...