# Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.

## Abstract

Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fraction of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1395209

- Report Number(s):
- SAND2017-10143

657088

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Preston, Leiph.
```*Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.*. United States: N. p., 2017.
Web. doi:10.2172/1395209.

```
Preston, Leiph.
```*Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.*. United States. doi:10.2172/1395209.

```
Preston, Leiph. Fri .
"Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.". United States. doi:10.2172/1395209. https://www.osti.gov/servlets/purl/1395209.
```

```
@article{osti_1395209,
```

title = {Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.},

author = {Preston, Leiph},

abstractNote = {Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fraction of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.},

doi = {10.2172/1395209},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2017},

month = {9}

}