Spatial resolution is associated with the temporal resolution, but mat be limited due to “diffraction” aperture or inaccurate velocities. Velocity errors occur when data are processed to a datum in violation of the hyperbolic assumption. These errors may be very small and are assumed to be negligible, especially with CMP processing. Prestack migrations gather data from many CMP gathers, and any relative velocity errors degrade the spatial resolution. We demonstrate this spatial resolution loss and recovery using a real 2D data set that contains faulting events. In addition, the resolution of the faults may be further focused, depending on their angle of obliquity to the 2D line.
High spatial resolution data for a research project was acquired in the Hussar area of Alberta Canada. The sedimentary layers in the area are relatively horizontal, with a surface elevation that had a range of 100 m. A vertical component of the data was extracted and conventionally processes with a standard prestack migration. The results were typical of the area and displayed no faulting.
The data were also processed to form common scatterpoint (CSP) gathers, prestack migration gathers that are formed without moveout correction, (Bancroft et.al. 1994 and 1998). Velocity analysis of each gather provides a unique velocity at each CMP location. Moveout correction, scaling, muting, and stacking produced a prestack migration that appeared to contain faulted structure. The 2D data was further analyzed to evaluate the obliquity of the fault planes, relative to the angle of the 2D line, by modifying the velocities. These results showed improved focusing of the fault planes, identifying the angles of obliquity. It should be noted that vertical displacement across the faults is very small, but the character of the reflection changes significantly across the fault as demonstrated in Figure 1a. Note the character change between CMP 536 at 636 at 2 sec. near the bottom of the figure. This data was processed to a maximum time of 4.0 sec. Figure 1b shows the same area, processed with a poststack finite difference migration to a maximum time of 2.0 secs.
The resolution of seismic data can be significantly improved after migration. This can be achieved with a simple trace deconvolution in areas with a simple geology such as a sedimentary basin, or a more complex deconvolution if the structure is complex. There are considerable objections to this process; some are identified and discussed, then reasons for its use are presented. Two examples of deconvolution after migration are presented.
Different acquisition geometries of the baseline and monitor seismic surveys produce different patterns of acquisition footprints. The resulting time lapse image shows the differences in artifacts, which may dominate the changes in the reflectivity model due to the production from or injection into the reservoirs. Synthetic data is used to show how different acquisition geometries between baseline and monitor surveys lead to different Kirchhoff migration artifacts for the same reflectivity model.
The least squares prestack Kirchhoff migration (LSPSM) is performed separately on the baseline and monitor data to attenuate these effects and provide comparable high resolution images for both pre- and poststack time lapse studies. A joint least squares Kirchhoff prestack migration (LSPSM) of both baseline and monitor data is introduced which attenuates the migration artifacts and returns high resolution LSPSM and/or time lapse images.
Equivalent Offset Migration (EOM) is based on the pre-stack Kirchhoff time migration (PSTM) method. It first maps the energies of the scatter points onto an intermediate Common Scatter Point (CSP) gathers, then after successfully applying a Normal Move Out (NMO) correction will output the migrated image. Assuming negligible lateral velocity gradient, the CSP data are sorted along the normal hyperbolic paths and serve as a useful tool for velocity inversion. The scatter point response below the dipping interface is a tilted hyperbola. Using the constructed wavefront we established the relationship between the tilted and normal hyperbolae. Similar relationship is obtained by simulation of CSP responses. We improved the focusing of the separated energy in the semblance plots by removing the tilt effects. As a result, the accuracy of migration velocity inversion enhanced and the focusing of output image of time migration are improved.