(Ph.D. Dissertation)

Hongchuan Sun, University of Utah

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A new migration method is formulated and applied to both synthetic and field data. This method, denoted as wavepath migration (WM), is developed for reducing computational costs and improving image quality compared to Kirchhoff migration (KM). The WM formula is derived by using the stationary-phase approximation of the diffraction stack integral. Unlike three-dimensional (3-D) KM, which migrates an observed reflection event to a quasi-ellipsoid in the image space, 3-D WM migrates the same event to a small Fresnel zone portion centered about the specular reflection point. Both the traveltime information and the ray's incidence angle are required by WM for locating the specular reflection point.

The WM algorithm is first applied to both poststack and prestack two-dimensional (2-D) seismic data for depth imaging. Compared to KM images, poststack WM images contain fewer migration artifacts, and have about the same or better resolution as the KM images, but the reflection events are typically weaker and the image continuity is somewhat worse. For a 2-D poststack migration example, the WM method is only one-third faster than KM. The results with prestack data show that WM images contain fewer migration artifacts and can usually define complex structures more accurately. All of the 2-D prestack examples show that the computational cost of WM is very similar to that of KM. However, by slant stacking the neighboring traces in the seismic section and subsampling the data, 2-D prestack WM can be 4-11 times faster than KM.

The WM method is further applied to both synthetic and field 3-D prestack data for depth imaging. The results with synthetic data show that WM generates fewer migration artifacts and can sometimes define complex structure better than KM. The results with field data show that WM can mostly reduce migration artifacts and can often resolve the reflection interfaces better than KM. The CPU comparison shows that, for both the synthetic and field data examples, WM can be more than an order-of-magnitude faster than KM. It is also shown that WM can account for different recording geometries, but it prefers a regular receiver distribution in order to more easily compute incidence angles. For a data set with irregular receiver distribution, trace interpolation is recommended for an accurate calculation of the incidence angles.

The WM method is finally applied to both synthetic and field 2-D data for velocity analysis. It is shown that, for the synthetic example, both the WM velocity analysis (WMVA) and the KM velocity analysis (KMVA) can successfully rebuild the layered model from an initial homogeneous model. For this simple example, WMVA is twice as fast as KMVA. The results with field data show that WMVA can effectively improve the velocity model, and the WMVA updated velocity correlates well with the KMVA updated velocity. For this 2-D marine data set, WMVA is six times faster than KMVA. This efficiency should be even better for the 3-D case.

In summary, I have developed a new migration method that promises to significantly reduce the imaging expense of 3-D data and also reduce the aliasing artifacts. The potential drawback is that its accuracy is sensitive to calculation of the incidence angle, which is a difficulty for noisy data. This problem can be mostly overcome by widening the migration Fresnel zone. The most practical use of this method will be to rapidly build velocity models by WMVA.