Full-Waveform Inversion Using Partial Time Shifts

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Solution Overview

Problem

Conventional Full-Waveform Inversion (FWI) methods face challenges such as cycle-skipping, amplitude effects, and limited initial model requirements, which hinder the generation of accurate and high-resolution velocity models in seismic exploration.

Innovation Solution

The implementation of partial time shifts based on graph space optimal transport (OT) permutations is applied to seismic data or simulated data, enhancing kinematic information and robustness against cycle-skipping from the first iterations, regardless of the initial model quality.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If conventional least squares misfit function is used in FWI, then high-resolution velocity model can be achieved, but cycle-skipping occurs and requires good initial model

Engineering Contradiction:

Improvevelocity model resolutionVSAvoidcycle-skipping robustness

Core Design Contradiction:

Manufacturing precisionVSReliability

Solution Approach 1:

The patent introduces an enhanced kinematic transform as an intermediary step between the raw seismic data and the misfit calculation. This transform applies time shifts based on graph space optimal transport to align events before computing the misfit, thereby preventing cycle-skipping while maintaining the ability to achieve high-resolution models through conventional least squares optimization

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent performs preliminary time shift alignment using graph space optimal transport before the main FWI inversion process. By pre-aligning the kinematic information between observed and simulated data, the method creates a better starting point for the inversion that is less susceptible to cycle-skipping, allowing the subsequent least squares optimization to converge to high-resolution models

Inventive Principle:

Principle #10Preliminary action

2Reliability

If full time shifts are applied to align seismic data, then cycle-skipping is avoided, but computational complexity increases

Engineering Contradiction:

Improvecycle-skipping robustnessVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent applies only a portion of the full time shift derived from graph space optimal transport. Specifically, it uses a scaled version (e.g., 0.5 to 0.8 times the full shift) that is sufficient to align major kinematic features and avoid cycle-skipping, but not so large as to create excessive computational burden or misalign amplitude information

Inventive Principle:

Principle #16Partial or excessive action

Solution Approach 2:

The patent separates the time shift application into distinct stages: first applying a partial time shift based on enhanced kinematic transforms to align major events, then using the remaining misfit for conventional FWI optimization. This segmentation allows each stage to focus on specific aspects of the inversion problem, reducing overall computational complexity

Inventive Principle:

Principle #1Segmentation

Data Source

PatentUS11747499B2Full-waveform inversion using partial time shifts and enhanced kinematic transforms

Publication Date: 2023.09.05 CGG SERVICES SAS

AI summary

A permutation that optimizes correspondence between the seismic data and the simulated data is computed using a graph space optimal transport formulation-based misfit. The seismic data or simulated data are transformed into auxiliary data by applying a portion of time shifts computed from the optimal permutation before updating the structural model of the explored underground formation. The full-waveform inversion minimization of the distance between auxiliary data and the seismic data or simulated data to which partial time shifts have not been applied, may be embedded in a Kantorovich-Rubinstein norm.