Multi-parameter Full Wavefield Inversion Line Search
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Solution Overview
Problem
Full wavefield inversion methods face high computational costs and slow convergence due to the expense of computing the Hessian matrix, especially when dealing with multi-parameter inversions where parameter classes have different sensitivities, leading to suboptimal search directions.
Innovation Solution
The alternating one/two pass line search method approximates second-order information through successive line searches, allowing for simultaneous updates of multiple parameter classes without explicit Hessian matrix information, using alternating or two-pass line search approaches to properly scale gradients and improve convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If second-order methods (using Hessian or its approximation) are used to improve convergence rate and balance gradients of different parameter classes, then convergence speed and parameter scaling are improved, but computational cost increases significantly due to the expense of computing the inverse Hessian
Solution Approach 1:
The patent segments the Hessian computation into separate updates for different parameter classes (velocity, anisotropy, attenuation) rather than computing the full Hessian matrix. Each parameter class gradient is preconditioned independently using approximate Hessian information, dividing the computational task into manageable parts that reduce overall computational cost while maintaining convergence benefits.
Solution Approach 2:
The patent changes the parameter representation by working with gradient vectors and search directions in model space rather than explicitly computing and inverting the Hessian matrix. The method uses parameter class-specific scaling factors that are updated iteratively based on gradient information, avoiding the expensive Hessian inversion while achieving similar parameter balancing effects.
2Use of energy by moving object
If gradient-based first-order methods are used to reduce computational cost, then computational efficiency is improved, but convergence speed becomes slow
Solution Approach 1:
The patent performs preliminary computation of gradient vectors for each parameter class before the main inversion loop. These gradient vectors are then reused and updated iteratively with minimal additional computation, allowing the method to achieve second-order convergence characteristics while maintaining first-order computational efficiency. The search directions are pre-computed and refined through iterative updates rather than requiring full Hessian computations at each step.
3Manufacturing precision
If the Hessian or its approximation is used to properly scale gradients for different parameter classes, then search direction quality is improved, but the method becomes less robust when the objective function is not quadratic or convex
Solution Approach 1:
The patent implements dynamic updating of search directions and scaling factors based on the current gradient information and objective function behavior. Rather than relying on a fixed Hessian approximation that may be inaccurate for non-convex problems, the method adaptively adjusts parameter class scaling and search directions at each iteration, making the inversion process more robust to non-quadratic and non-convex objective functions while maintaining search direction quality.
Data Source
AI summary
Method for simultaneously inverting full-wavefield seismic data (51) for multiple classes of physical property parameters (e.g., velocity and anisotropy) by computing the gradient (53), i.e. search direction (54), of an objective function for each class of parameters, then applying (preferably exhaustive) first-pass independent line searches to each parameter class to obtain the corresponding step size (55) along the search direction for each parameter class; then without yet updating the model, using the step sizes to define a relative scaling between gradients of all parameter classes. Next, each scaled search direction is recombined to form a new search direction (56), and a new second-pass line search is performed along the new search direction (57), and all parameters are simultaneously updated with the resulting step size (58). Alternatively to the preceding alternating two-pass embodiment, the model may be updated after each first-pass line search, and no second-pass line search is performed.