# Some numerical approaches to solving one-dimensional inverse problems

## Abstract

A class of one-dimensional inverse scattering problems are studied with the goal of reconstructing (say) propagation speed to moderate accuracy as inexpensively as possible. Three alternatives are discussed; all starting from a change to the travel-time variable and converting the problem to integral equation form. The approaches are compared as to their economy of use and the problems for which they are effective. Several numerical examples illustrate these comparisons.

- Authors:

- Publication Date:

- Research Org.:
- Denver Univ., CO (USA). Dept. of Mathematics

- OSTI Identifier:
- 6437888

- Report Number(s):
- DOE/ER/10769-2

TRN: 81-009983

- DOE Contract Number:
- AC02-80ER10769

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INVERSE SCATTERING PROBLEM; ONE-DIMENSIONAL CALCULATIONS; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; VELOCITY; WKB APPROXIMATION; EQUATIONS; MATHEMATICS; 645500* - High Energy Physics- Scattering Theory- (-1987); 658000 - Mathematical Physics- (-1987)

### Citation Formats

```
Hagin, F.
```*Some numerical approaches to solving one-dimensional inverse problems*. United States: N. p., 1980.
Web. doi:10.2172/6437888.

```
Hagin, F.
```*Some numerical approaches to solving one-dimensional inverse problems*. United States. https://doi.org/10.2172/6437888

```
Hagin, F. Tue .
"Some numerical approaches to solving one-dimensional inverse problems". United States. https://doi.org/10.2172/6437888. https://www.osti.gov/servlets/purl/6437888.
```

```
@article{osti_6437888,
```

title = {Some numerical approaches to solving one-dimensional inverse problems},

author = {Hagin, F.},

abstractNote = {A class of one-dimensional inverse scattering problems are studied with the goal of reconstructing (say) propagation speed to moderate accuracy as inexpensively as possible. Three alternatives are discussed; all starting from a change to the travel-time variable and converting the problem to integral equation form. The approaches are compared as to their economy of use and the problems for which they are effective. Several numerical examples illustrate these comparisons.},

doi = {10.2172/6437888},

url = {https://www.osti.gov/biblio/6437888},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1980},

month = {1}

}

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