Reflection seismic data consist of primary reflections, coherent and incoherent noises. One of the objectives of seismic data processing is to enhance the quality of the real signals by attenuating different kinds of noises. Multiples constitute one of the most troublesome forms of coherent noises in exploration seismology. Multiple reflections often destructively interfere with the desired primary reflections so identification and interpretation of the primary events would be difficult. So, the problem of multiple attenuation in reflection seismograms has always been of great importance. Radon transform that is based on a process which integrates the data along different curved surfaces, is a robust tool for suppressing multiples from seismic data. Like all transform filter pairs, the Radon transform first forward transforms the data into a model parameter domain where the crossing primaries and multiples would be better separated. In the most common multiple attenuation process, multiples are windowed in the transform domain and reconstructed in the original domain using an inverse Radon transform. Then, the modeled multiples are subtracted from the original data to obtain a gather with primaries only.
Based on the form of the integrating surface, there are three types of Radon transforms: linear, hyperbolic and parabolic. The Parabolic Radon is a common tool in multiple attenuation based on the velocity discrimination. In this method, the first step is to replace hyperbolic events in a CMP gather with parabolas by applying NMO correction using velocities of primaries. Then the parabolic Radon domain is generated by summing the data along a set of parabolic paths, parameterized by a curvature, q, which intersect the zero-offset axis at the time ?. This procedure is repeated for each intercept time sample. Ideally, an approximately parabolic event should map into a point in the parabolic Radon domain. So the primaries and multiples would be separable in the new domain. Due to applying NMO correction using the velocities of primary events, the energy of primaries maps to events at around 0 ms moveout in the transform domain, while under-corrected multiples should map to higher moveouts. For attenuating the multiples, it is necessary to produce a model containing only the multiple events. This is done by filtering the primary energy in the Radon domain and then inverse transforming the remaining part of the Radon domain which contains multiples, back to the offset domain. In the final step the multiples-only gather is subtracted from the original data.
The parabolic Radon has different benefits that make it attractive. It achieves multiple attenuation equally at all offsets. Moreover, it does not require knowing the exact velocities of multiples and primaries and it needs no knowledge of the multiple generation mechanism. The most important limitation of the method is that multiples must have sufficient moveout discrimination in order to be attenuated. Experiences have shown that while in synthetic data very fine discrimination may be modeled, in real data with their variable amplitudes and waveforms and additive noise, at least 30 ms moveout is required for the transform to be effective.
In this paper, the parabolic Radon transform with its application in multiple suppression has been studied and MATLAB programming has been implemented. The code was successfully applied on different synthetic 2D models consisting of various multiple reflections, such as water-bottom multiples, simple multiples and interbed multiples, that interfere with primary reflections at near or far offsets. This code was also examined on a 2D real seismic data set. The validation of the program has been verified by comparing the obtained results with the results of Geocluster software.