Wave-Equation Kirchhoff Migration for Complex Velocity Models
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Solution Overview
Problem
Conventional Kirchhoff migration techniques are inaccurate and unstable when dealing with large velocity variations and complex geological structures, as they rely on raytracing, which is not suitable for high-resolution, complex velocity models.
Innovation Solution
The use of a wave-equation Kirchhoff (WEK) technique that simulates low-frequency wave propagation to derive traveltimes and amplitudes, allowing for accurate Kirchhoff migration by forward-propagating a low-frequency wavefield and picking the arrival traveltime and maximum amplitude for each subsurface location.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If raytracing is used for Kirchhoff migration, then computational efficiency is improved, but accuracy deteriorates when dealing with large velocity variations and complex geological structures
Solution Approach 1:
The patent replaces the raytracing method (mechanical/geometric approach) with a wave-equation-based approach. Specifically, it uses the eikonal equation solved via finite-difference methods to compute traveltimes and the wave equation to compute amplitudes, substituting the geometric optics approximation with a full wavefield simulation that accurately handles complex velocity variations and geological structures.
Solution Approach 2:
The patent changes the fundamental parameters and equations used in Kirchhoff migration. Instead of using raytracing equations, it employs the eikonal equation for traveltime calculation and the wave equation for amplitude calculation. This parameter change allows the method to accurately handle large velocity variations and complex geological structures while maintaining computational feasibility through efficient numerical solvers.
2Measurement precision
If wave-equation methods are used to improve accuracy, then handling of complex velocity models is improved, but computational cost increases
Solution Approach 1:
The patent segments the computational task into distinct components: traveltime computation using the eikonal equation and amplitude computation using the wave equation. This segmentation allows each component to be solved with optimized numerical methods, reducing overall computational complexity while maintaining accuracy.
Solution Approach 2:
The patent applies partial wave-equation modeling by using the eikonal equation (a simplified form) for traveltime calculation and only the necessary wave equation components for amplitude calculation. This partial application reduces computational complexity compared to full wavefield simulation while still providing accurate results for complex velocity models.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach improves the accuracy of traveltime and amplitude calculations, effectively handling fine-scale geo-bodies and sharp velocity contrasts, resulting in higher-quality images compared to conventional ray-based Kirchhoff migration, while maintaining computational efficiency.
Implementation Method 1
forward-propagating a low-frequency wavefield from a shot location among the predefined source locations, deriving an arrival traveltime of a maximum amplitude of the low-frequency wavefield
Data Source
AI summary
Limitations in accuracy and computing power requirements impeding conventional Kirchhoff migration and reverse time migration are overcome by using the wave-equation Kirchhoff, WEK, technique with Kirchhoff migration. WEK technique includes forward-propagating a low-frequency wavefield from a shot location among pre-defined source locations, calculating an arrival traveltime of a maximum amplitude of the low-frequency wavefield, and applying Kirchhoff migration using the arrival traveltime and the maximum amplitude.