Wave Equation Migration Velocity Analysis

Like tomography, migration velocity analysis (MVA) is a velocity analysis method by iterative inversion. The difference between the two is at a ``strategic'' level: instead of trying to find the velocity model that will result in the given raw data, it tries to find the velocity through which prestack migrated data results in a perfectly focused image. The chapter pertaining to velocity analysis in () shows why dipping reflectors in laterally varying velocity media require the velocity analysis to be performed in the migrated domain (image domain) instead of the unmigrated domain (data domain).

MVA can be done with infinite-frequency (ray-based) operators () or with finite band (wave-equation) operators (). The advantages of the latter over the former are detailed in the WEMVA chapter of (). In particular, ray theory breaks down if its high frequency assumption does not hold (), as is the case with velocity anomalies of the size of those that generate the FEAVO effect. Multipathing is another instance when the wave equation methods are more appropriate. They also treat more correctly the amplitudes.

WEMVA proceeds as follows: the wavefield at a certain depth is downward continued a depth step through the known velocity model with an accurate (nonlinear) operator. The result is transformed to angle domain and an improved image is created by eliminating either the curvature of the events in angle-domain common image gathers (), or the FEAVO anomalies. An image perturbation ($\Delta$Image) is obtained by subtracting the two images, and is backprojected through an invertible operator in order to obtain a velocity update. The velocity model is updated and the cycle proceeds again until $\Delta$Image becomes negligible. Figure illustrates this process.

 

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Figure 1 Migration Velocity Analysis flowchart

WEMVA is at the forefront of research. As the comparison in the next section will show, it avoids all the shortcomings of the previous attempts.