Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems.

Area of Science:

• Geophysics
• Computational Science
• Inverse Problems

Background:

• Inverse problems, especially in geophysics, are often underdetermined due to high model complexity and limited, noisy data.
• This underdetermination leads to non-unique solutions, where multiple models fit the observed data within error bounds.
• Nonlinear inverse problems exhibit complex cost-function topographies with disconnected valleys representing equivalent solutions.

Purpose of the Study:

• To apply particle swarm optimization (PSO) for sampling the equivalence region in nonlinear inverse problems.
• To demonstrate the utility of PSO for uncertainty assessment in geophysical gravity inversion.
• To show efficient uncertainty quantification in a sampling-while-optimizing framework.

Main Methods:

• Utilizing particle swarm optimization (PSO) as a sampling methodology.
• Focusing on nonlinear inverse problems, specifically gravity inversion in sedimentary basins.
• Analyzing geophysical models sampled by PSO members to characterize nonlinear uncertainty.

Main Results:

• PSO effectively samples the region of equivalence in nonlinear inverse problems.
• The methodology allows for efficient uncertainty assessment in geophysical applications.
• Exploratory PSO members provide valuable data for inferring nonlinear uncertainty descriptors.

Conclusions:

• Particle swarm optimization is a viable and efficient tool for uncertainty analysis in underdetermined nonlinear inverse problems.
• This approach facilitates a deeper understanding of solution non-uniqueness in geophysical exploration.
• The sampling-while-optimizing strategy offers a practical way to quantify uncertainty in complex modeling scenarios.