Seismic Imaging Waveform Inversion via Frequency Band Updates
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Solution Overview
Problem
Full waveform inversion based on generalized inversion theory requires significant computational resources and time, limiting its application due to the need for calculating large matrices and inverse matrices.
Innovation Solution
The method involves direct computation of the difference between actual and initial velocity models using the Lippmann-Schwinger equation and parameter perturbations, updating the reference velocity model across frequency bands without relying on the steepest descent method, and employing a waveform inverter to iteratively refine the subsurface structure imaging.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If full waveform inversion based on generalized inversion theory is used, then the velocity model can be iteratively updated to minimize the objective function, but the computational time and storage requirements increase significantly due to calculating Jacobian matrix, Hessian matrix, and inverse matrix
Solution Approach 1:
The patent extracts and eliminates the computationally intensive matrix calculation steps (Jacobian matrix, Hessian matrix, and inverse matrix computations) from the full waveform inversion process. By removing these unnecessary intermediate calculations, the method achieves velocity model updates without the prohibitive computational overhead, directly addressing the contradiction between accuracy and computational time
Solution Approach 2:
The patent inverts the traditional approach by directly computing velocity model updates without following the conventional path of calculating Jacobian and Hessian matrices first. Instead of the standard sequence (data → Jacobian → Hessian → inverse → update), the method uses an alternative mathematical formulation that achieves the same update goal through a more efficient computational pathway
2Measurement precision
If full waveform inversion based on generalized inversion theory is used, then the velocity model can be iteratively updated to minimize the objective function, but the storage requirements increase significantly due to calculating and configuring large matrices
Solution Approach 1:
The patent removes the requirement to store large Jacobian and Hessian matrices from the inversion process. By extracting these unnecessary storage demands and replacing them with a method that computes updates through more efficient mathematical operations, the patent significantly reduces memory and storage requirements while preserving velocity model accuracy
Solution Approach 2:
The patent inverts the traditional storage-intensive approach by using an alternative mathematical formulation that computes velocity updates without requiring the storage of large intermediate matrices. This inverted methodology achieves the same inversion goal with minimal storage requirements
3Measurement precision
If the steepest descent method is used for waveform inversion, then the velocity model can be updated iteratively, but the computational complexity and time increase
Solution Approach 1:
The patent extracts and eliminates the steepest descent iterative optimization process from the waveform inversion methodology. By removing this computationally complex iterative approach and replacing it with a direct update method, the patent reduces computational complexity while maintaining the ability to accurately update velocity models
Solution Approach 2:
The patent inverts the conventional iterative optimization approach by using a direct computational method that achieves velocity model updates without requiring repeated steepest descent iterations. This inverted strategy reduces computational complexity by eliminating the iterative loop while preserving update accuracy
Data Source
AI summary
A seismic imaging technology, and more specifically, an imaging technology for modelling a subsurface structure by updating a velocity model of each frequency band in the ascending, descending order or any random order of frequencyThe purpose of the present disclosure is to directly compute the difference between the velocity of the actual subsurface velocity and an initial guess of the velocity.According to one aspect of the present invention, a seismic imaging apparatus for performing iterative application of the direct waveform inversion to image a subsurface structure of an area to be measured may include a waveform inverter to update a reference velocity model while changing a frequency band in a set order, by using parameter perturbation that is obtained from a virtual scattering source and an updated reference wavefield.