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Summary 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. Introduction 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.
Rapid Estimates of Converted Wave Velocities Using Prestack Migration
Guirigay, Thais (CREWES) | Bancroft, John C. (CREWES) | Isaac, Helen (CREWES)
Summary new approach is presented for estimating the velocities of converted wave data that is based on prestack migration by equivalent offset to form common conversion point gathers. These gathers are used to form an initial estimate of the converted wave velocity Vc, that can then be used for the full accurate process of equivalent offset migration of converted wave data. Equivalent offset common conversion point gathers are formed using the P-wave and S-wave velocities and the double-square-root equation. The formation of these gathers requires approximate values for the P-wave and S-wave velocities, but after their formation, accurate velocities can be picked and the prestack migration completed with moveout correction.
ABSTRACT A method is presented for identifying the source of a locally circular or spherical wavefront given the traveltimes at arbitrary locations. For 2D data, the center of the circular wavefront is computed from three traveltimes recorded at three arbitrary locations. Applications to 3D data requires four traveltimes recorded at four arbitrary locations. This method is suited for a number of applications such as mapping traveltimes that are computed along sparse raypaths to gridded traveltimes, the monitoring of microseismic events caused by fraccing, or to the possible prediction of landslides in geologically unstable areas. The analytic solutions for both 2D and 3D produce two solutions from which one must be chosen based on neighbouring conditions or by using another known traveltime and its location.
ABSTRACT The surface consistent equations always have one or more singular values, depending on the configuration of the seismic survey. These singular values slow convergence, add uncertainty, and make it difficult to resolve the long wavelengths in the solution. Multigrid methods possess a greater ability to resolve long wavelength terms than Gauss-Seidel methods that are currently in use. These improved solutions are calculated at little or no additional computational cost. While total convergence is not guaranteed, multigrid methods seem to be able to universally improve the quality of surface consistent decomposition. There are some limitations we reach in solving the surface consistent equations. An attempt is made to further justify our previous conclusion (Millar and Bancroft, 2004) that some of the long wavelength drift that can plague Gauss-Seidel solutions is theoretically avoidable. In more or less the same amount of computer time using multigrid techniques we are getting more accurate synthetic solutions. We see how the quality of our solution depends on the geometry of the survey, and the role singular values play in the solution. Lastly, we explore the challenges of including of a time variant term in the equations as well.
As a new concept of residual statics analysis, Tjan and et al (1994) and Larner (1998) introduced a method of forming An intermediate step of equivalent offset migration (EOM) reference traces using prestack depth migration and its produces prestack migration gathers that provide reference inverse process, called de-migration. This method is traces for residual statics analysis. This method can be used designed for high complexity structural data where normal for data where prestack time migration is able to produce moveout assumption is seriously violated. This method is reasonable images, even those areas where the hyperbolic highly sensitive to the velocity for migration and demigration.
A prestack time migration is presented that is simple, efficient, and provides detailed velocity information. It is based on Kirchhoff prestack time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps: the first is a gathering process that forms common scatterpoint CSP gathers; the second is a focusing process that applies a simplified Kirchhoff migration on the CSP gathers, and consists of scaling, filtering, normal moveout NMO correction, and stacking. A key concept of the method is a reformulation of the double squareroot equation of sourcescatterpointreceiver traveltimes into a single square root. The single square root uses an equivalent offset that is the surface distance from the scatterpoint to a colocated source and receiver. Input samples are mapped into offset bins of a CSP gather, without time shifting, to an offset defined by the equivalent offset. The single squareroot reformulation gathers scattered energy to hyperbolic paths on the appropriate CSP gathers. A CSP gather is similar to a common midpoint CMP gather as both are focused by NMO and stacking. However, the CSP stack is a complete Kirchhoff prestack migrated section, whereas the CMP stack still requires poststack migration. In addition, the CSP gather has higher fold in the offset bins and a much larger offset range due to the gathering of all input traces within the migration aperture. The new method gains computational efficiency by delaying the Kirchhoff computations until after the CSP gather has been formed. The high fold and large offsets of the CSP gather enables precise focusing of the velocity semblance and accurate velocity analysis. Our algorithm is formulated in the spacetime domain, which enables prestack migration velocity analysis to be performed at selected locations and permits prestack migration of a 3-D volume into an arbitrarily located 2-D line.
Forel, D. and Gardner, G., 1988, A three-dimensional perspective on two-dimensional dip moveout: Geophysics, 53, All variables at the right hand side of this equation are 604-610.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (0.73)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.71)
Bancroft, J. C., Geiger, H. D., Wang, S., and Foltinek, D. S., 1995, Prestack migration by equivalent offset and CSP gathers: an update, CREWES 1995 Research Report.