عنوان مقاله [English]
نویسندگان [English]چکیده [English]
A useful method to increase the signal/noise ratio of refracted waves is Common-Midpoint Refraction (CMPR) seismics. Consider a plane wave traveling from the source location A to a receiver point B (or vice versa). The distance between the two locations A and B is denoted as x. If the reference point is the CMP between A and B the relation is valid and one can write its travel time equation based on the ray parameters and vertical slowness (Diebold and Stoffa, 1981). For such a model, Slotnick (1936) obtained an equation which is the basic equation for depth conversion in CMPR method.
With this technique, the shallow underground can be described in detail using all information (amplitude, frequency, phase characteristics) of the wavetrain following the first break (first-break phase). Thus, the layering can be determined and faults, weak zones, and clefts can be identified. This will be done by stacking a trace in a domain. Since the stacking data along the straight line of the Radon transformation is used to suppress reflected wave groups and surface waves in CMPR method, the Radon transformation must be restricted to refracted waves only. After Radon transformation, an intercept-time section is made.
The following difficulties occur when dealing with CMPR seismics.
1. The data will be sorted as CMP-offset gathers. Therefore, the distance between two traces is twice the distance between two shot points. Thus, optimum stacking velocities for the partial Radon transformation in CMPR seismics cannot be determined.
2. Local variations in refractor velocities are difficult to record.
3. In routine CMPR seismics, the traveltime branch of the total refracted signal is stacked. Therefore, local irregularities of interest cannot be detected.
These disadvantages are rectified using a combination of CMPR seismics with the Generalized Reciprocal Method (GRM; Palmer, 1986). This joint application is possible because of the close relationship between both methods in their kinematical descriptions.
Gebrande (1986) described a technique to construct CMP traveltime curves using the data from only one forward and one reverse shot. Using this technique, the CMP intercept time would be in the form of an equation which have some similarities in comparison to in GRM. These similarities and their relationships are helpful in rectifying certain disadvantages in the CMPR method.
Velocities and optimum offsets determined by the GRM can be used directly in the partial Radon transformation in CMPR. The result of this process is an intercept-time section which can be converted directly to a depth section.
In the partial Radon transformation of joint CMPR seismics with the GRM, the stacked events are only those that belong to the critical offset in the CMP-offset gather. These events are principally the critical reflected waves. Therefore, the migration of the intercept-time section must employ a post-stack method such as Kirchhoff migration. After migrating time section it can be converted to depth section using its individual equation.
Using two models for numerical investigation, the efficiency of the method is tested, and the results are shown.