Seismic Wave Simulation via Staircase Discretization Superposition

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Solution Overview

Problem

The finite difference method struggles with computational instability and reduced accuracy when simulating seismic wave propagation across strong discontinuous interfaces in medium parameters, requiring grid refinement and parameter smoothing, which increases computational burden and reduces accuracy.

Innovation Solution

A model parameter design method that discretizes the discontinuous interface using the staircase approximation method, applying a threshold judgment criteria to obtain multiple results, and superimposing these results using the principle of linear superposition to achieve stable and accurate simulations without grid refinement or parameter smoothing.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If grid refinement is applied at the discontinuous interface, then computational stability is improved, but computation work and time consumption increase

Engineering Contradiction:

Improvecomputational stabilityVSAvoidcomputation efficiency

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

The discontinuous interface is segmented into multiple discrete grid nodes, with each node independently processed through threshold judgment. This segmentation allows the interface to be handled at the grid node level without requiring global grid refinement, thus maintaining computational efficiency while ensuring stability at the interface.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent applies local quality by treating the discontinuous interface differently from the surrounding medium. Specifically, grid nodes at the interface are identified through threshold judgment and processed with special constitutive relations, while the rest of the medium uses standard finite difference methods. This localized treatment ensures stability where needed without increasing overall computational burden.

Inventive Principle:

Principle #3Local quality

2Reliability

If parameter smoothing is applied at the discontinuous interface, then computational stability is improved, but simulation accuracy is reduced

Engineering Contradiction:

Improvecomputational stabilityVSAvoidwave propagation accuracy

Core Design Contradiction:

ReliabilityVSMeasurement precision

Solution Approach 1:

Instead of smoothing parameters to achieve stability (the conventional approach), the patent inverts the approach by using threshold judgment to precisely identify interface nodes and applying discontinuous constitutive relations directly. This inversion maintains both stability and accuracy by respecting the true discontinuous nature of the interface rather than artificially smoothing it.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The patent changes the parameter representation at the interface by using threshold-based binary classification (interface vs. non-interface nodes) rather than continuous parameter smoothing. The constitutive relations are changed to account for the discontinuous nature of the interface, allowing accurate representation of sharp parameter changes without smoothing.

Inventive Principle:

Principle #35Parameter changes

3Measurement precision

If grid refinement is applied, then simulation accuracy is improved, but memory consumption increases

Engineering Contradiction:

Improveinterface simulation accuracyVSAvoidmemory space

Core Design Contradiction:

Measurement precisionVSQuantity of substance

Solution Approach 1:

The interface is segmented into discrete grid nodes identified by threshold judgment, allowing accurate interface representation without refining the entire computational grid. This segmentation approach confines the special treatment to only the interface nodes, avoiding the memory overhead of global grid refinement while maintaining interface accuracy.

Inventive Principle:

Principle #1Segmentation

4Reliability

If parameter smoothing is applied, then computational stability is improved, but computation time increases

Engineering Contradiction:

Improvenumerical simulation stabilityVSAvoidcomputation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent inverts the conventional smoothing approach by directly representing the discontinuous interface through threshold judgment and discontinuous constitutive relations. This inversion eliminates the need for computationally expensive smoothing operations while maintaining numerical stability through proper handling of interface nodes.

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS20230350088A1Model parameter design method and device for simulating propagation of seismic waves at any discontinuous interface

Publication Date: 2023.11.02 INSTITUTE OF GEOLOGY AND GEOPHYSICS CHINESE ACADEMY OF SCIENCES

AI summary

The present invention discloses a model parameter design method and device for simulating propagation of seismic waves at any discontinuous interface, including: reading source wavelet and model parameters; selecting a space step and a time step according to the model parameters, and setting a space order of the finite difference numerical simulation; discretizing the discontinuous interface in the medium, and according to the threshold judgment criteria, obtaining many staircase discretization results for the discontinuous interface; conducting a forward modeling on the obtained multiple results of staircase discretization for the discontinuous interface by using the finite difference method, and setting parameters of the forward modeling; and obtaining the final simulation results by the superposition of the forward modeling results of different staircase-discretization of the discontinuous interface. The present invention can greatly improve the calculation efficiency.