Full-Waveform Inversion with Matching Matrices for Local-Minimum Avoidance
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Solution Overview
Problem
Existing full-waveform inversion methods based on the least squares error function are prone to trapping in local minimum values due to stringent precision requirements for the initial velocity model, leading to unsatisfactory inversion results.
Innovation Solution
A method involving the construction of a cost matrix to represent similarity between seismic traces, determination of a matching matrix and objective function, calculation of an adjoint source and gradient, and iterative updating of the initial velocity model to achieve convergence criteria, reducing precision requirements and avoiding local minima.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the least squares error function is used for full-waveform inversion, then the algorithm is simple to implement, but the inversion is prone to trapping in local minimum values when the initial velocity model precision is insufficient
Solution Approach 1:
The patent changes the objective function parameter from the traditional least squares error function to a matching matrix-based objective function. This transformation allows the inversion process to evaluate waveform matching quality more flexibly, enabling escape from local minima while maintaining computational feasibility through iterative optimization.
Solution Approach 2:
The patent introduces a matching matrix as an intermediary between the synthetic and observed seismic data. This matching matrix serves as a mediator that quantifies waveform similarity, allowing the inversion algorithm to progressively improve the velocity model by maximizing the matching degree without being constrained by the rigid assumptions of the least squares approach.
2Productivity
If the least squares error function is used, then the computational process is straightforward, but high precision initial velocity model is required to avoid local minima
Solution Approach 1:
The patent performs preliminary construction of a matching matrix that evaluates the overall waveform matching quality between synthetic and observed data. This preliminary assessment provides a more robust starting point for the inversion process, reducing the stringency of initial model requirements while maintaining computational efficiency through the matching matrix guidance.
Solution Approach 2:
The patent employs an iterative inversion process where the matching matrix is dynamically updated in each iteration based on the current velocity model. This dynamic adaptation allows the algorithm to progressively refine the velocity model from less precise initial conditions, transforming the static least squares approach into a flexible, adaptive process.
3Device complexity
If traditional least squares comparison is used, then the data comparison is simple, but the inversion result significantly deviates from actual circumstances when initial model precision is low
Solution Approach 1:
The patent transitions from the traditional one-dimensional least squares error comparison to a two-dimensional matching matrix framework that simultaneously considers waveform amplitude and timing relationships. This dimensional expansion provides a more comprehensive assessment of waveform matching quality, improving inversion accuracy while maintaining manageable computational complexity through systematic matrix operations.
Data Source
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AI summary
The present disclosure provides a full-waveform inversion method and device, and a storage medium. The method comprises: constructing a cost matrix according to observed seismic data and synthetic seismic data, each matrix element in the cost matrix being used for representing the similarity between a piece of seismic trace data in the synthetic seismic data and a piece of seismic trace data in the observed seismic data; according to the cost matrix, determining a matching matrix used for reflecting the best matching relationship between the observed seismic data and the synthetic seismic data, and calculating a target function; obtaining an adjoint field hypocenter according to the target function; determining the gradient according to the adjoint field hypocenter and a forward propagation wave field; and iteratively updating an initial velocity model according to the gradient and an iteration step size until preset convergence criteria are met.