Stabilizing Reverse Time Demigration Equation for Seismic Multiples
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Solution Overview
Problem
Existing methods for predicting multiples using Reverse Time Demigration (RTDM) face numerical instability when generalizing from One-Way Wave Equation Demigration (OWEDM) to RTDM, which affects the accuracy and stability of computing surface and interbed multiples in seismic data processing.
Innovation Solution
A method is introduced that stabilizes the RTDM equation by adding a coupling term based on a reflectivity term acting as a linear source, converting it into a pseudo-density function, and solving the resulting stabilized equation to reconstruct wavefields and generate a modeled seismic image, allowing for the prediction of both surface and interbed multiples with improved numerical stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a straightforward generalization from One-Way Wave Equation Demigration (OWEDM) to Reverse Time Demigration (RTDM) is attempted, then the capability to predict multiples is extended, but numerical instability occurs
Solution Approach 1:
The patent modifies the RTDM equation by changing the parameter representation from reflectivity to pseudo-density, and introduces a coupling term to transform the unstable generalization into a numerically stable formulation that maintains the extended capability to predict multiples
2Reliability
If the RTDM equation is stabilized by adding a coupling term and converting reflectivity to pseudo-density, then numerical stability is improved, but the computational complexity increases
Solution Approach 1:
The patent introduces pseudo-density as an intermediary variable that mediates between the reflectivity term and the wave equation, allowing the stabilization of the RTDM equation while maintaining a manageable computational framework through the coupling term
Data Source
AI summary
Methods and systems for generating a stable reverse time demigration (RTDM) equation for predicting wave phenomena such as reflections, refractions and multiples are described. A coupling term is added to an RTDM equation and reflectivity associated with the coupling term is replaced with a pseudo-density function derived from a nonlinear equation. The resultant coupled and stabilized RTDM equation is then used to predict the desired wave phenomena based on the applied seismic image.