Seismic Internal Multiple Prediction via PDE Segmentation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for attenuating internal multiples in seismic data processing, such as inverse scattering series, are computationally expensive, making them impractical for 3D seismic imaging applications.
Innovation Solution
A partial differential equation (PDE)-based approach that uses cascaded double-square-root one-way wave equations to efficiently predict and attenuate internal multiples, which is mathematically equivalent to conventional inverse scattering series but significantly more computationally efficient.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional inverse scattering series is used to predict internal multiples, then all internal multiples can be predicted simultaneously in one run, but the computational cost becomes significantly higher and prohibitive for 3D seismic imaging applications
Solution Approach 1:
The patent segments the inverse scattering series computation into multiple smaller partial differential wave equations that can be solved sequentially. Instead of solving one large complex equation for all internal multiples simultaneously, the method divides the problem into separate equations for different wave propagation paths (e.g., source to first reflector, first to second reflector, second to receiver), solving each segment independently to achieve the same result with reduced computational burden
Solution Approach 2:
The patent transforms the computational approach by moving from the frequency-wavenumber domain to the space-time domain. This dimensional transformation allows the use of finite difference methods to solve partial differential equations directly in the spatial and temporal dimensions, avoiding the computationally expensive Fourier transforms and iterative solutions required by conventional inverse scattering series in the frequency domain
2Reliability
If conventional inverse scattering series is applied to 3D seismic data, then internal multiple attenuation is achieved, but the computational time and resources become prohibitive
Solution Approach 1:
The patent divides the 3D internal multiple prediction problem into separate partial differential equations for different reflection paths. Each equation models a specific wave propagation sequence (e.g., source→reflector1→reflector2→receiver), allowing the system to solve simpler individual equations rather than one massive 3D inverse scattering problem, thereby reducing computational time while maintaining attenuation effectiveness
Solution Approach 2:
The patent replaces the conventional inverse scattering series mathematical framework with an alternative system based on partial differential wave equations solved via finite difference methods. This substitution changes the computational mechanics from frequency-domain iterative solutions to time-domain direct propagation simulations, achieving the same multiple attenuation goal with significantly reduced computational time for 3D data
Data Source
AI summary
Methods for processing seismic data are described. The method includes: obtaining seismic data; solving a series of partial differential wave equations, wherein a first partial differential wave equation describes propagation of a seismic wave going from a first reflector to a second reflector, wherein a second partial differential wave equation describes propagation of a seismic wave going from a second reflector to a third reflector, and wherein a third partial differential wave equation describes propagation of a seismic wave going from a third reflector to a seismic receiver, wherein outputting predicted internal multiples for further imaging or attenuation.