Cross-Correlation Least-Squares RTM for Amplitude Constraints

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Solution Overview

Problem

Current least-squares reverse-time migration (LSRTM) methods face challenges in applying amplitude constraints to real datasets due to the earth's viscoelastic nature and difficulty in defining source strength, leading to imperfect amplitude matching and preprocessing complexities.

Innovation Solution

The introduction of a correlative least-squares reverse-time migration (CLSRTM) method that relaxes amplitude constraints by maximizing the cross-correlation of simulated and observed seismic data at zero lag, using a cross-correlation-based objective function and Newton's method for numerical convergence, allowing for improved stability and image quality.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional least-squares RTM (LSRTM) is applied to real datasets, then amplitude matching is attempted, but the earth's viscoelastic nature and difficulty in defining source strength lead to imperfect amplitude matching and preprocessing complexities

Engineering Contradiction:
Improveamplitude matching precisionVSAvoidpreprocessing complexity
Core Design Contradiction:
Measurement precisionVSDevice complexity

Solution Approach 1:

The patent extracts and removes the amplitude constraint requirement from the LSRTM process. By formulating the objective function based on cross-correlation rather than amplitude matching, the method eliminates the need for complex preprocessing steps related to amplitude correction, viscoelastic compensation, and source strength definition, while maintaining imaging quality.

Inventive Principle:
Principle #2Taking out (Extraction)

Solution Approach 2:

The patent changes the fundamental parameter being optimized in the least-squares formulation. Instead of minimizing amplitude differences between simulated and observed data, the method minimizes the cross-correlation difference, which is less sensitive to amplitude variations caused by viscoelastic effects and source strength uncertainties.

Inventive Principle:
Principle #35Parameter changes

2Productivity

If cross-correlation of forward propagated source wavefield with backward propagated receiver wavefield is used in RTM, then imaging is achieved, but amplitude distortions are caused by RTM crosstalk artifacts

Engineering Contradiction:
Improveimaging efficiencyVSAvoidamplitude accuracy
Core Design Contradiction:
ProductivityVSManufacturing precision

Solution Approach 1:

The patent introduces an iterative least-squares optimization process that uses feedback from the cross-correlation objective function. The imaging result is continuously refined by adjusting the reflectivity model based on the correlation mismatch between simulated and observed data, thereby reducing crosstalk artifacts and improving amplitude accuracy while maintaining imaging efficiency.

Inventive Principle:
Principle #23Feedback

3Manufacturing precision

If iterative least-squares migration (LSM) is used to reduce migration artifacts and improve lateral spatial resolution, then image quality improves, but computational cost increases

Engineering Contradiction:
Improvelateral spatial resolutionVSAvoidcomputational power
Core Design Contradiction:
Manufacturing precisionVSPower

Solution Approach 1:

The patent changes the objective function parameter from amplitude-based to cross-correlation-based. This modification maintains the iterative optimization framework's ability to improve lateral spatial resolution and reduce artifacts, while the cross-correlation metric converges more efficiently, reducing the computational power required for each iteration and the overall process.

Inventive Principle:
Principle #35Parameter changes

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

CLSRTM provides improved image quality with reduced migration artifacts and enhanced structural detail, especially in areas of poor illumination, and is capable of handling complex velocity distributions and anisotropic media, while tolerating some velocity inaccuracies.

Implementation Method 1

the numerical Green's functions from finite difference to the two-way wave equation

Methodology Applied
Scientific EffectWave propagation:

Implementation Method 2

One of the most common RTM imaging conditions is cross-correlation of the forward propagated source wavefield with the backward propagated receiver wavefield

Methodology Applied
Scientific EffectCross-correlation:

Data Source

PatentEP2787372B1Device and method for stable least-squares reverse time migration
Publication Date: 2019.11.06 CGG SERVICES SAS
  • EP2787372B1 patent drawingFigure 1
  • EP2787372B1 patent drawingFigure 2
  • EP2787372B1 patent drawingFigure 3A~3B

AI summary

Method for generating a final image of a subsurface of the earth, including the steps of receiving (1000) measured seismic data d of the subsurface; selecting (1002) an objective function E that is function of a reflectivity r of the subsurface; and calculating (1012), in a processor, the reflectivity r based on the measured seismic data d, the objective function E, simulated data d, a modeling operator M from a reverse time demigration (RTDM) process and an imaging operator MT from a reverse time migration (RTM) process.