# Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

## Abstract

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

- 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 National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1376284

- Report Number(s):
- SAND-2017-8848

656347

- 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.
```*Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.*. United States: N. p., 2017.
Web. doi:10.2172/1376284.

```
Preston, Leiph.
```*Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.*. United States. doi:10.2172/1376284.

```
Preston, Leiph. Tue .
"Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.". United States. doi:10.2172/1376284. https://www.osti.gov/servlets/purl/1376284.
```

```
@article{osti_1376284,
```

title = {Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.},

author = {Preston, Leiph},

abstractNote = {Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.},

doi = {10.2172/1376284},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Aug 01 00:00:00 EDT 2017},

month = {Tue Aug 01 00:00:00 EDT 2017}

}