Exact wavefield reconstruction on finite-difference grids with minimal memory requirements

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. T303-T309 ◽  
Author(s):  
Marlies Vasmel ◽  
Johan O. A. Robertsson
Keyword(s):  
Finite Difference ◽  
Point Sources ◽  
Multiple Point ◽  
Spatial Accuracy ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Numerical Precision ◽  
Dipole Sources

Wavefield injection in finite-difference (FD) grids can be described by the method of multiple point sources. The method teaches how synthetically generated wavefields and wavefield constituents can be reconstructed from surface recordings using a combination of monopole and dipole sources on an injection surface surrounding the model. We show how to properly record surface wavefields and inject point sources in staggered FD grids, in a way that is consistent with the order of spatial accuracy of the FD scheme. The description is general and can be used for schemes of any order. Only one or two surface wavefields are required to reconstruct the original wavefields or wavefield constituents to numerical precision, independent of the order of spatial accuracy of the FD stencil. We have applied the method for the separation of up- and downgoing wavefields and for source wavefield reconstruction for reverse time migration. Our implementation enables accurate source wavefield reconstruction with optimally minimal memory requirements.

scholarly journals Local Explosion Detection and Infrasound Localization by Reverse Time Migration Using 3-D Finite-Difference Wave Propagation

2021 ◽  
Vol 9 ◽  
Author(s):  
David Fee ◽  
Liam Toney ◽  
Keehoon Kim ◽  
Richard W. Sanderson ◽  
Alexandra M. Iezzi ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Finite Difference ◽  
Grid Point ◽  
Reverse Time ◽  
Computationally Efficient ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Straight Line ◽  
Active Vent ◽  
Time Reversal Mirror

Infrasound data are routinely used to detect and locate volcanic and other explosions, using both arrays and single sensor networks. However, at local distances (<15 km) topography often complicates acoustic propagation, resulting in inaccurate acoustic travel times leading to biased source locations when assuming straight-line propagation. Here we present a new method, termed Reverse Time Migration-Finite-Difference Time Domain (RTM-FDTD), that integrates numerical modeling into the standard RTM back-projection process. Travel time information is computed across the entire potential source grid via FDTD modeling to incorporate the effects of topography. The waveforms are then back-projected and stacked at each grid point, with the stack maximum corresponding to the likely source. We apply our method to three volcanoes with different network configurations, source-receiver distances, and topography. At Yasur Volcano, Vanuatu, RTM-FDTD locates explosions within ∼20 m of the source and differentiates between multiple vents. RTM-FDTD produces a more accurate location for the two Yasur subcraters than standard RTM and doubles the number of detected events. At Sakurajima Volcano, Japan, RTM-FDTD locates the source within 50 m of the active vent despite notable topographic blocking. The RTM-FDTD location is similar to that from the Time Reversal Mirror method, but is more computationally efficient. Lastly, at Shishaldin Volcano, Alaska, RTM and RTM-FDTD both produce realistic source locations (<50 m) for ground-coupled airwaves recorded on a four-station seismic network. We show that RTM is an effective method to detect and locate infrasonic sources across a variety of scenarios, and by integrating numerical modeling, RTM-FDTD produces more accurate source locations and increases the detection capability.

Implicit interpolation in reverse‐time migration

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 906-917 ◽  
Author(s):  
Jinming Zhu ◽  
Larry R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Real Data ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Difference Wave ◽  
Time Migration ◽  
Seismic Acquisition ◽  
Recorded Data

Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.

Elastic reverse‐time migration

Geophysics ◽  
1987 ◽  
Vol 52 (10) ◽  
pp. 1365-1375 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Difference ◽  
Vertical Component ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Two Component ◽  
Synthetic Test ◽  
Data Extrapolation

Elastic, prestack, reverse‐time, finite‐difference migration of two‐component seismic surface data requires data extrapolation and application of an imaging condition. Data extrapolation involves synchronous driving of the vertical‐component and horizontal‐component finite‐difference meshes with the time reverse of the recorded vertical and horizontal traces, respectively. Extrapolation uses the coupled elastic wave equation for variable velocity solved with a second‐order, explicit finite‐difference scheme. The imaging condition at any point in the grid is the one‐way traveltime from the source to that point. Elastic migrations of both synthetic test data and real two‐component common‐source gathers produce simpler images than acoustic migrations because of the coalescing of double reflections (compressional waves and shear waves) into single loci.

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