Domain Freezing in Joint Inversion for Geophysical Modeling
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Solution Overview
Problem
Geophysical joint inversion of multiple data types often faces convergence issues due to non-linearity, particularly with seismic reflection data lacking low-frequency content, leading to poor convergence properties and getting stuck in local minima.
Innovation Solution
The method involves 'freezing' specific domains such as model parameters, frequency, and spatial domains during the inversion process, allowing for sequential phases where only a portion of the data is inverted, gradually increasing complexity and resolution, and using low-frequency data initially to stabilize the inversion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple data types are inverted simultaneously with many model parameters, then the inversion can estimate multiple geological properties (porosity, fluid type), but the computational cost increases and convergence becomes difficult due to non-linearity
Solution Approach 1:
The inversion process is divided into multiple sequential phases, each inverting a subset of data types and model parameters. For example, electromagnetic data may be inverted first to estimate conductivity, followed by seismic data inversion to estimate acoustic impedance, with later phases combining multiple data types. This segmentation reduces the number of parameters inverted simultaneously, lowering computational complexity while still achieving multi-parameter estimation through the sequence of phases.
Solution Approach 2:
Low-frequency portions of seismic data are inverted first to establish a long-wavelength baseline model before inverting high-frequency data. This preliminary inversion of low-frequency data provides a stable starting model that reduces non-linearity effects in subsequent high-frequency inversions, improving convergence properties while maintaining the ability to resolve fine details.
2Measurement precision
If high-frequency seismic data is inverted directly, then high resolution geological features can be resolved, but the inversion gets stuck in local minima due to strong non-linearity
Solution Approach 1:
Low-frequency portions of seismic data are inverted first to establish a long-wavelength baseline model before inverting high-frequency data. This preliminary inversion of low-frequency data provides a stable starting model that reduces non-linearity effects in subsequent high-frequency inversions, improving convergence properties while maintaining the ability to resolve fine details.
Solution Approach 2:
The inversion process uses iterative phases that periodically alternate between inverting different data types and model parameters. Each phase updates the model based on available data, then the next phase builds upon this updated model with additional data types or parameter sets, creating a periodic cycle of refinement that progressively improves resolution while maintaining convergence.
Data Source
AI summary
Method for estimating geological properties in a subsurface region using multiple types of geophysical data (21). An initial physical properties model 22 is constructed. Some parameters in the model are frozen (23) and optionally portions of the model wave number and spatial domains (24) and the data frequency and data time domains (25), are also frozen. Then, a joint inversion (26) of the multiple data types is performed to calculate an update to the model only for the portions that are not frozen. The converged model (27) for this inversion is used as a new starting model, and the process is repeated (28), possibly several times, unfreezing more parameters and data each time until the desired spatial and parameter resolution (29) has been achieved.