One-Return Wave Equation Migration for Salt Boundary Imaging
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Solution Overview
Problem
Conventional one-way wave equation migration methods fail to effectively image geologic structures with strong turning waves and duplex waves, such as overhanging salt boundaries and vertical faults, due to their inability to handle waves propagating beyond 90° and multiple reflections.
Innovation Solution
The one-return wave equation migration method extrapolates both down-going and up-going waves, using a two-pass approach with properly designed imaging conditions to reconstruct partial images from turning waves and duplex waves, producing depth images that include contributions from primary reflections, turning waves, and duplex waves.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional one-way wave equation migration is used, then computation is simple and fast, but turning waves and duplex waves are ignored resulting in poor imaging of overhanging salt boundaries and vertical faults
Solution Approach 1:
The wave field is segmented into down-going and up-going components using one-way wave equation propagators. The migration process is divided into two passes: first pass handles down-going waves, second pass handles up-going waves. This segmentation allows the method to capture turning waves and duplex waves while maintaining computational efficiency through specialized one-way propagators.
Solution Approach 2:
The method inverts the traditional migration approach by performing upward continuation in the second pass after downward continuation in the first pass. This two-way inversion allows up-going waves to be properly handled and turned waves to be captured, reversing the conventional single downward-pass approach while maintaining one-way propagator efficiency.
2Manufacturing precision
If reverse-time migration is used to image turning waves and duplex waves, then imaging quality improves, but computational cost and storage requirements increase significantly
Solution Approach 1:
The method extracts only the essential up-going and down-going wave components using one-way propagators, discarding the need for full two-way wave equation solving. This extraction approach captures turning waves and duplex waves while avoiding the excessive computational burden of reverse-time migration by working with simplified one-way equations.
Solution Approach 2:
The method changes the mathematical parameters by using one-way wave equation approximations instead of the full two-way hyperbolic wave equation. This parameter change maintains the ability to image turning waves and duplex waves while significantly reducing computational cost and storage requirements through the simplified one-way propagator formulation.
3Productivity
If conventional one-way migration downward continues source and receiver wavefields independently, then computation is efficient, but evanescent energy propagating upward is ignored
Solution Approach 1:
The method performs preliminary action by computing and storing the down-going wave field in the first pass, then using this stored field as input for the second pass upward continuation. This preliminary computation ensures that evanescent energy is captured and preserved, preventing information loss while maintaining computational efficiency through the two-pass structure.
Solution Approach 2:
The method ensures continuity of useful action by maintaining the connection between down-going and up-going wave fields through the two-pass process. The first pass computes down-going waves, and the second pass continuously processes up-going waves using the results from the first pass, ensuring no evanescent energy is lost while preserving computational efficiency.
Data Source
AI summary
A one-return wave equation migration is used to extrapolate both down-going and up-going waves. Followed by a properly designed imaging condition, the partial image contributed form turning waves is correctly reconstructed. Numerical examples show that this method can significantly enhance definition of an overhanging salt boundary and a geological structure with vertical features.