- Copyright © 2003 Society of Exploration Geophysicists
In this article, we propose an inversion scheme to replace the adaptive subtraction approaches which are widely used in conventional two-step (prediction + subtraction) multiple elimination methods. This new method, named SIMP (simultaneous inversion for multiples and primaries), inverts seismic data using constraints (e.g., modeled multiples and/or geologic discriminants) for multiples and primaries simultaneously. SIMP incorporates pattern recognition and shaping filters into one concise and practically solvable formulation. Its main advantages are that no orthogonality between multiples and primaries is assumed and that wavelet information is not necessary for the inversion.
Figure 1 compares conventional prediction plus subtraction and the SIMP approaches. In the conventional method (Figure 1a), predicted multiples are generated first, the shaping filters are derived second, and finally the primary component is obtained by subtracting the multiples shaped by the filters from the input data. In one SIMP procedure (SIMP I, Figure 1b), the predicted multiples are generated first, but the shaping filters (not the multiples) and the primaries are inverted simultaneously by a constrained inversion approach. A general SIMP approach (SIMP II, Figure 1c) inverts for multiples and primaries simultaneously assuming proper constraints are available.
Modern multiple elimination methodologies are firmly rooted in the principles of wave theory. In general, these multiple removal schemes involve two basic steps: multiple prediction and adaptive subtraction. The multiple prediction can be model-driven or data-driven. During the prediction step, the kinematic part of the multiples (traveltimes) is obtained. The adaptive subtraction step aims to obtain the dynamic part of the multiples (e.g., amplitudes and waveform shaping).
Once multiple-model traces are predicted, based on the original seismic data and/or a subsurface model, they need to be “shaped” in order to “match” the actual multiples. This is usually achieved with …