Acoustic Wave Equation Reflectivity Parameterization

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Solution Overview

Problem

Current seismic imaging techniques, such as least-squares reverse time migration (LSRTM) and full-waveform inversion (FWI), face limitations in accurately building high-resolution velocity and reflectivity models of subterranean formations, particularly in deep-water surveys, due to the need for density models and first-order Born approximations, which restrict the simulation of reflection events and introduce inaccuracies.

Innovation Solution

A novel parameterization of the acoustic wave equation that simulates transmitted and reflected components without requiring density models or high velocity contrasts, enabling the use of reflection events to update velocity and reflectivity models, and improving computational efficiency by using a smooth velocity model in FWI and LSRTM.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If density models and first-order Born approximations are used in current seismic imaging techniques, then the simulation of reflection events can be performed, but the accuracy of velocity and reflectivity models is restricted and inaccuracies are introduced

Engineering Contradiction:
Improveaccuracy of velocity and reflectivity modelsVSAvoidsimulation accuracy of reflection events
Core Design Contradiction:
Measurement precisionVSReliability

Solution Approach 1:

The patent changes the fundamental parameters of the wave equation from the conventional acoustic wave equation (using density and first-order Born approximations) to a new parameterization that directly incorporates velocity and reflectivity. This parameter change eliminates the need for density models and first-order approximations, allowing for accurate simulation of reflection events with steep dips and high velocity contrasts while improving the accuracy of velocity and reflectivity models.

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent substitutes the conventional mechanical approximation approach (first-order Born approximation) with a more accurate wave equation parameterization that directly models the physics of wave propagation and reflection. This substitution replaces the approximate mechanical system with a more rigorous mathematical model that accurately captures the behavior of seismic waves in complex subterranean formations.

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

2Productivity

If conventional acoustic wave equation is used, then computational procedures are simplified, but the penetration depth of velocity model updates is limited and resolution of seismic images is reduced

Engineering Contradiction:
Improvecomputational efficiencyVSAvoidresolution of seismic images
Core Design Contradiction:
ProductivityVSMeasurement precision

Solution Approach 1:

The patent changes the parameterization of the wave equation to use smooth velocity models as the foundation, rather than relying on dense velocity models required by conventional approaches. This parameter change allows computational procedures to remain efficient while extending the penetration depth of velocity model updates and improving the resolution of seismic images, as the smooth velocity model enables more effective wave propagation simulation through deep subterranean formations.

Inventive Principle:
Principle #35Parameter changes

3Reliability

If density models are required in current techniques, then reflection events can be simulated, but the complexity of the imaging process increases and computational efficiency decreases

Engineering Contradiction:
Improvesimulation capability of reflection eventsVSAvoidcomplexity of imaging process
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent extracts and removes the requirement for density models from the seismic imaging process. By reparameterizing the wave equation to directly use velocity and reflectivity as fundamental parameters, the invention eliminates the need for density models entirely, thereby reducing the complexity of the imaging process while maintaining the capability to simulate reflection events accurately.

Inventive Principle:
Principle #2Taking out (Extraction)

Solution Approach 2:

The patent changes the fundamental parameters from density-based modeling to velocity and reflectivity-based modeling. This parameter transformation simplifies the imaging process by removing the need to compute and store density models, reducing computational complexity while preserving the ability to simulate reflection events through the modified wave equation parameterization.

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

This approach allows for the generation of accurate high-resolution velocity and reflectivity models, extending the penetration depth of velocity model updates and improving the resolution of seismic images, enabling better identification of oil and natural gas reservoirs without the need for density models, and enhancing computational efficiency.

Implementation Method 1

The acoustic energy generated by a seismic source spreads out in all directions. A portion of the acoustic energy travels down through the water and into a subterranean formation to propagate as sound waves within the subterranean formation.

Methodology Applied
Scientific EffectAcoustic wave propagation: Sound

Implementation Method 2

At each interface between different types of liquid, rock and sediment, a portion of the sound wave is refracted, a portion is transmitted, and another portion is reflected into the body of water to propagate as a reflected wavefield toward the water surface.

Methodology Applied
Scientific EffectAcoustic reflection: Reflection

Implementation Method 3

Each streamer contains many seismic receivers or sensors that detect pressure and/or particle motion wavefields of the sound waves.

Methodology Applied
Scientific EffectPressure wave detection: Sound

Data Source

PatentEP4042210B1Determining properties of a subterranean formation using an acoustic wave equation with a reflectivity parameterization
Publication Date: 2024.12.04 PGS GEOPHYSICAL AS
  • EP4042210B1 patent drawingFigure 1A
  • EP4042210B1 patent drawingFigure 1B
  • EP4042210B1 patent drawingFigure 2

AI summary

Methods and systems described herein are directed to determining properties of a subterranean formation using an acoustic wave-equation with a novel formulation in terms of a velocity model and a reflectivity model of the subterranean formation. The acoustic wave equation may be used with full-waveform inversion to build high-resolution velocity and reflectivity models of a subterranean formation. The acoustic wave equation may be also used with least-squares reverse time migration in the image and space domains, to build a reflectivity model of the subterranean formation with enhanced resolution and amplitude fidelity. The velocity and reflectivity models of materials that form the subterranean formation reveal the structure and lithology of features of the subterranean formation and may reveal the presence of oil and natural gas reservoirs.