Time-Domain Sifrian Inversion for Waveform Imaging Cycle Skipping
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Waveform imaging techniques face challenges in cycle skipping and computational complexity due to the oscillatory nature of waves and the need for efficient incorporation of second-order derivative information, particularly with the Hessian matrix in existing optimization methods.
Innovation Solution
The method employs Time-Domain Sifrian Inversion (TDSI), which extends Sifrian inversion principles from the frequency domain to the time domain, using a zero-valued functional to bypass Hessian matrix computations and incorporates robust cost functions like Wasserstein distances to mitigate cycle skipping.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If second-order optimization methods are used to achieve faster convergence rates, then convergence speed is improved, but computational complexity increases due to the Hessian matrix
Solution Approach 1:
The patent extracts and utilizes only the essential second-order derivative information (curvature) needed for optimization, rather than computing the full Hessian matrix. This is achieved through adjoint-state methods that compute curvature information at a cost comparable to first-order methods, thereby achieving faster convergence without the computational burden of the complete Hessian matrix
Solution Approach 2:
The patent changes the parameter representation from the full Hessian matrix to a reduced set of curvature information derived through adjoint equations. This parameter transformation allows second-order optimization benefits to be achieved with significantly reduced computational complexity by working with a smaller, more efficient parameter set
2Productivity
If traditional cost functions are used in waveform inversion, then optimization can proceed, but cycle skipping occurs due to the oscillatory nature of waves
Solution Approach 1:
The patent changes the parameter space by transforming the oscillatory waveform data into envelope-based representations or frequency-domain representations. This parameter transformation eliminates the oscillatory nature that causes cycle skipping, allowing the optimization to proceed reliably without the harmful phase-wrapping effects
Solution Approach 2:
The patent converts the harmful oscillatory behavior that causes cycle skipping into a beneficial feature by using the oscillations to extract envelope information or frequency content. The same wave oscillations that cause problems are transformed into useful signals for robust inversion through techniques like Hilbert transforms or frequency-domain analysis
3Device complexity
If first-order optimization methods like gradient descent are used, then computational complexity is reduced, but convergence rate is slower compared to second-order methods
Solution Approach 1:
The patent performs preliminary computation of adjoint states and curvature information that can be reused across multiple optimization iterations. By pre-computing these second-order terms through efficient adjoint equations, the method enables faster convergence rates similar to full second-order methods while maintaining computational complexity comparable to first-order methods
Data Source
AI summary
A method for facilitating wave-based inversion using Time-Domain Sifrian Inversion (TDSI). The method includes receiving, using a communication device, observed data from a device. The method includes obtaining, using a processing device, an initial model. The method includes obtaining, using the processing device, synthetic data from the initial model. The method includes determining, using the processing device, a matching of the synthetic data with the observed data is not within a matching threshold. The method includes updating, using the processing device, the initial model using the TDSI iteratively until the matching threshold for the matching is achieved. The TDSI provides an update for the updating of the initial model iteratively using a time-domain cost function which is robust to a cycle skipping. The method includes generating, using the processing device, a final model based on the updating. The method includes storing, using a storage device, the final model.