Back to results
US 10,241,222 B2Granted
Seismic elastic wave simulation for tilted transversely isotropic media using adaptive lebedev staggered grid
AssigneeLandmark Graphics Corporation
InventorsFan Jiang, Shengwen Jin
Life of this patent
Estimating the term…
Abstract
Disclosed are systems and methods for numerically simulating seismic-wave propagation in tilted transversely isotropic (TTI) media, using an adaptive Lebedev staggered grid. In various embodiments, the adaptive grid includes multiple horizontal zones having different associated grid spacings, which may be determined based on a vertical wave-velocity model. The numerical simulation may involve iteratively solving a set of finite-difference equations including finite-difference coefficients that vary spatially depending on the grid spacing. Additional embodiments and features are described.
Claims17
A method, comprising:
- defining positions of at least one seismic source and at least one seismic receiver relative to a tilted transversely isotropic (TTI) medium;
- defining an adaptive Lebedev staggered grid over at least a portion of the TTI medium, the grid comprising a plurality of horizontal zones with associated grid spacings, a grid spacing associated with at least one of the zones differing from a grid spacing associated with another one of the zones;
- and
- using a processor, calculating propagation of a seismic wave emitted by the at least one seismic source through the TTI medium and receipt thereof at the receiver by solving a set of elastic wave equations discretized over the adaptive Lebedev staggered grid, wherein the elastic wave equations discretized over the grid comprise finite-difference equations of at least second order,
- wherein the finite difference equations comprise finite difference coefficients, the method further comprising calculating the finite-difference coefficients based on the grid spacings, and
- wherein the finite-difference coefficients are variable within an overlap region comprising adjacent portions of two of the horizontal zones, and wherein the finite-difference coefficients are constant within each of the horizontal zones outside the overlap region.
3 more elements
A system, comprising:
- at least one seismic source for emitting a seismic wave into a TTI medium;
- at least one seismic receiver configured to detect a seismic wave propagating through TTI medium;
- and
- a computational facility configured to:
- receive information about positions of the at least one seismic source and the at least one seismic receiver relative to the rock formation,
- define an adaptive Lebedev staggered grid over at least a portion of the rock formation, the grid comprising a plurality of horizontal zones with associated grid spacings, a grid spacing associated with at least one of the zones differing from a grid spacing associated with another one of the zones,
- based at least in part on a computational model of the TTI medium, calculate propagation of a seismic wave emitted by the at least one seismic source through the formation and detection thereof at the receiver by solving a set of elastic wave equations discretized over the adaptive Lebedev staggered grid, and
- compare the detected seismic wave with the calculated seismic wave at the receiver and, when a difference between the detected and calculated seismic waves exceeds a specified threshold, adjusting the computational model by adjusting at least one field parameter thereof, wherein the elastic wave equations discretized over the grid comprise finite-difference equations of at least second order,
- wherein the finite difference equations comprise finite difference coefficients and calculating the finite-difference coefficients based on the grid spacings,
- wherein the finite-difference coefficients are variable within an overlap region comprising adjacent portions of two of the horizontal zones, and
- wherein the finite-difference coefficients are constant within each of the horizontal zones outside the overlap region.
8 more elements
Dependencies are inferred from the claim text.