Implicit interpolation in reverse‐time migration

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 906-917 ◽  
Author(s):  
Jinming Zhu ◽  
Larry R. Lines

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.

2014 ◽  
Vol 962-965 ◽  
pp. 2984-2987
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Ting Chen

Based on two-way acoustic wave equation, we present a method for computing angle-domain common-image gathers for reverse time migration. The method calculates the propagation direction of source wave-fields and receiver wave-fields according to expression of energy flow density vectors (Poynting vectors) of acoustic wave equation in space-time domain to obtain the reflection angle, then apply the normalized cross-correlation imaging condition to achieve the angle-domain common-image gathers. The angle gathers obtained can be used for migration velocity analysis, AVA analysis and so on. Numerical examples and real data examples demonstrate the effectiveness of this method.


2020 ◽  
Vol 223 (1) ◽  
pp. 77-93
Author(s):  
Peng Guo ◽  
Huimin Guan ◽  
George A McMechan

SUMMARY Seismic data recorded using a marine acquisition geometry contain both upgoing reflections from subsurface structures and downgoing ghost waves reflected back from the free surface. In addition to the ambiguity of propagation directions in the data, using the two-way wave equation for wavefield extrapolation of seismic imaging generates backscattered/turned waves when there are strong velocity contrasts/gradients in the model, which further increases the wavefield complexity. For reverse-time migration (RTM) of free-surface multiples, apart from unwanted crosstalk between inconsistent orders of reflections, image artefacts can also be formed along with the true reflector images from the overlapping of up/downgoing waves in the data and in the extrapolated wavefield. We present a wave-equation-based, hybrid (data- and model-domain) wave separation workflow, with vector seismic data containing pressure- and vertical-component particle velocity from dual-sensor seismic acquisition, for removing image artefacts produced by the mixture of up/downgoing waves. For imaging with free-surface multiples, the wavefield extrapolated from downgoing ghost events (reflected from the free surface) in the recorded data act as an effective source wavefield for one-order-higher free-surface multiples. Therefore, only the downgoing waves in the data should be used as the source wavefield for RTM with multiples; the recorded upgoing waves in the seismograms will be used for extrapolation of the time-reversed receiver wavefield. We use finite-difference (FD) injection for up/down separation in the data domain, to extrapolate the down- and upgoing waves of the common-source gathers for source and receiver wavefield propagation, respectively. The model-domain separation decomposes the extrapolated wavefield into upgoing (backscattered) and downgoing (transmitted) components at each subsurface grid location, to remove false images produced by cross-correlating backscattered waves along unphysical paths. We combine FD injection with the model-domain wavefield separation, for separating the wavefield into up- and downgoing components for the recorded data and for the extrapolated wavefields. Numerical examples using a simple model, and the Sigsbee 2B model, demonstrate that the hybrid up/down separation approach can effectively produce seismic images of free-surface multiples with better resolution and fewer artefacts.


Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA153-WCA158 ◽  
Author(s):  
Faqi Liu ◽  
Guanquan Zhang ◽  
Scott A. Morton ◽  
Jacques P. Leveille

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.


Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. T287-T300 ◽  
Author(s):  
Lasse Amundsen ◽  
Johan O. A. Robertsson

Methods for wavefield injection are used in, for instance, reverse time extrapolation of shot gathers in reverse time migration. For correct injection of recorded data without any ambiguity of the propagation direction, the wavefield-injection methodology requires pressure and particle velocity data such as multicomponent towed marine or seabed seismic recordings. We discovered that by carefully considering the models (medium parameters and boundary conditions) for injection, wavefield injection of multicomponent data can also be used to solve several long-standing challenges in marine seismic data processing by means of conventional time-space-domain finite-difference propagators. We outlined and demonstrated several of these important applications including up-down separation of wavefields (deghosting), direct-wave removal, source-signature estimation, multiple removal, and imaging using primaries and multiples. Only acoustic models are considered, but the concepts are straightforward to generalize to elastodynamic and electromagnetic models.


Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. T123-T129 ◽  
Author(s):  
Xiaolei Song ◽  
Sergey Fomel

We introduce a novel technique for seismic wave extrapolation in time. The technique involves cascading a Fourier transform operator and a finite-difference operator to form a chain operator: Fourier finite differences (FFD). We derive the FFD operator from a pseudoanalytical solution of the acoustic wave equation. Two-dimensional synthetic examples demonstrate that the FFD operator can have high accuracy and stability in complex-velocity media. Applying the FFD method to the anisotropic case overcomes some disadvantages of other methods, such as the coupling of qP-waves and qSV-waves. The FFD method can be applied to enhance accuracy and stability of seismic imaging by reverse time migration.


Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 589-600 ◽  
Author(s):  
Yafei Wu ◽  
George A. McMechan

A wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation. This transformed equation is solved directly with a finite‐difference scheme for both homogeneous and smooth inhomogeneous media. Wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step. The wavelet coefficients are extrapolated, rather than the wavefield itself. The numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite‐difference method because of the compact support of the wavelet bases. Poststack reverse‐time migration is implemented as an application. The resolution spaces of the wavelet transform provide a natural framework for multigrid analysis. Migrated images are constructed from various resolution spaces.


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