Multi-scale manifold learning for seismic waveform inversion
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Solution Overview
Problem
Current Full Waveform Inversion (FWI) methods in seismology face challenges in accurately estimating subsurface properties using acoustic/elastic energy due to the complexity of heterogeneous earth materials, particularly in minimizing data misfit through optimization techniques.
Innovation Solution
The method involves fitting a recursive sequence of convex nonnegative cones generated by multidimensional Bernstein polynomials to observed data using a quasi-Newton optimization method, which represents wave equation coefficients as combinations of Bernstein polynomials and updates the subsurface structure model by minimizing data misfit, employing spectral element methods and explicit Newmark time integrators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard FWI optimization techniques are used to minimize data misfit, then subsurface parameter estimation is achieved, but the method struggles with heterogeneous earth materials and complex geological structures
Solution Approach 1:
The patent transforms the subsurface parameter estimation problem by changing the parameterization approach from direct physical property estimation to Bernstein polynomial coefficient estimation. This parameter transformation enables the optimization to handle heterogeneous materials more effectively while maintaining accuracy in subsurface parameter estimation.
Solution Approach 2:
The patent segments the complex subsurface model into multiple Bernstein polynomials of different degrees. By dividing the estimation problem into hierarchical segments (low-degree to high-degree polynomials), the method can progressively capture complex geological heterogeneities while maintaining computational tractability.
2Manufacturing precision
If high-resolution subsurface modeling is performed to improve imaging accuracy, then detailed subsurface structure is obtained, but computational complexity and data misfit minimization difficulty increase
Solution Approach 1:
The patent applies segmentation by hierarchically increasing Bernstein polynomial degrees from low to high. This progressive refinement allows the model to achieve high-resolution subsurface imaging capability while managing computational complexity through staged optimization rather than attempting high-resolution estimation all at once.
Solution Approach 2:
The patent performs preliminary optimization using low-degree Bernstein polynomials to establish a baseline subsurface model before progressing to higher-degree polynomials. This preliminary action simplifies the overall computational task by breaking down the complex high-resolution inversion into manageable sequential steps.
Data Source
AI summary
A method for analyzing acoustic/elastic waves to determine subsurface structure of the earth includes receiving a plurality of observations of a seismic acoustic/elastic wave-field from a plurality of sensors; generating a plurality of Bernstein grids of differing resolutions; calculating a data misfit of the plurality of observations with respect to an initial subsurface structure model defined in terms of conic combinations of Bernstein polynomials on a lowest resolution Bernstein grid, and mapping the data misfit from the Bernstein grid onto a Lagrangian grid; updating the subsurface structure model by minimizing the data misfit between the plurality of observations and observations obtained by a simulation; increasing resolution of the Bernstein grid and recomputing the updated subsurface structure model on the increased resolution Bernstein grid; and mapping the recomputed subsurface structure model onto the Lagrangian grid.