A Semi-analytic but Biased Uncertainty Assessment Method using Sample Extensions, Analysed for Nonlinear Travel Time Tomography
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908460789006336 |
|---|---|
| author | Zhao, Xuebin Curtis, Andrew |
| author_facet | Zhao, Xuebin Curtis, Andrew |
| contents | Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior probability distribution functions (pdf's). To obtain robust inference results often requires millions of model parameter value samples to be drawn, and their simulation to be performed; this is a computationally expensive procedure. We investigate the concept of sample extensions as a means to improve efficiency when solving fully nonlinear inverse problems. A sample's extension is defined as the set of models or parameter values whose forward function values are directly accessible from a sample for which the forward function has already been evaluated, obviating the need for additional forward function evaluations. In a specific case of first-arrival travel time calculations used in seismic travel time tomography, we apply sample extensions to obtain a continuous region with non-zero hypervolume within parameter space, across all of which the forward function values are known given only a single forward simulation. We devise a deterministic sampling technique that identifies the most informative extensions by solving an optimisation problem. In an illustrative tomographic example that involves a single travel time datum, we find 51 optimal samples, and use them to construct an analytic approximation to the Bayesian posterior pdf. Additionally, we propose an extensions-based algorithm for real-world tomography scenarios and apply it to a synthetic 2D example. This study highlights two fundamental problems that make the method inefficient: (1) limited hypervolumes of extensions and (2) neglecting parameter correlations to simplify analytic calculations. Finding solutions to these problems defines possible directions for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Semi-analytic but Biased Uncertainty Assessment Method using Sample Extensions, Analysed for Nonlinear Travel Time Tomography Zhao, Xuebin Curtis, Andrew Geophysics Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior probability distribution functions (pdf's). To obtain robust inference results often requires millions of model parameter value samples to be drawn, and their simulation to be performed; this is a computationally expensive procedure. We investigate the concept of sample extensions as a means to improve efficiency when solving fully nonlinear inverse problems. A sample's extension is defined as the set of models or parameter values whose forward function values are directly accessible from a sample for which the forward function has already been evaluated, obviating the need for additional forward function evaluations. In a specific case of first-arrival travel time calculations used in seismic travel time tomography, we apply sample extensions to obtain a continuous region with non-zero hypervolume within parameter space, across all of which the forward function values are known given only a single forward simulation. We devise a deterministic sampling technique that identifies the most informative extensions by solving an optimisation problem. In an illustrative tomographic example that involves a single travel time datum, we find 51 optimal samples, and use them to construct an analytic approximation to the Bayesian posterior pdf. Additionally, we propose an extensions-based algorithm for real-world tomography scenarios and apply it to a synthetic 2D example. This study highlights two fundamental problems that make the method inefficient: (1) limited hypervolumes of extensions and (2) neglecting parameter correlations to simplify analytic calculations. Finding solutions to these problems defines possible directions for future research. |
| title | A Semi-analytic but Biased Uncertainty Assessment Method using Sample Extensions, Analysed for Nonlinear Travel Time Tomography |
| topic | Geophysics |
| url | https://arxiv.org/abs/2507.16353 |