# Identifying arbitrary parameter zonation using multiple level set functions

## Abstract

In this paper, we extended the analytical level set method [1, 2] for identifying a piece-wisely heterogeneous (zonation) binary system to the case with an arbitrary number of materials with unknown material properties. In the developed level set approach, starting from an initial guess, the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables (hydraulic head) is minimized. We derived an expression for the propagation velocity of the interface between any two materials, which is related to the permeability contrast between the materials on two sides of the interface, the sensitivity of the head to permeability, and the head residual. We also formulated an expression for updating the permeability of all materials, which is consistent with the steepest descent of the objective function. The developed approach has been demonstrated through many examples, ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the Los Alamos National Laboratory. These examples indicate that the level set method can successfully identify zonation structures, even if the number of materials in the model domain is not exactly known in advance. Although the evolution of the materialmore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Florida State Univ., Tallahassee, FL (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Environmental Management (EM)

- OSTI Identifier:
- 1430001

- Report Number(s):
- LA-UR-17-26150

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 364; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Earth Sciences; Mathematics; Level set method; parameter identification; inverse model

### Citation Formats

```
Lu, Zhiming, Vesselinov, Velimir Valentinov, and Lei, Hongzhuan.
```*Identifying arbitrary parameter zonation using multiple level set functions*. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.03.016.

```
Lu, Zhiming, Vesselinov, Velimir Valentinov, & Lei, Hongzhuan.
```*Identifying arbitrary parameter zonation using multiple level set functions*. United States. doi:10.1016/j.jcp.2018.03.016.

```
Lu, Zhiming, Vesselinov, Velimir Valentinov, and Lei, Hongzhuan. Wed .
"Identifying arbitrary parameter zonation using multiple level set functions". United States.
doi:10.1016/j.jcp.2018.03.016.
```

```
@article{osti_1430001,
```

title = {Identifying arbitrary parameter zonation using multiple level set functions},

author = {Lu, Zhiming and Vesselinov, Velimir Valentinov and Lei, Hongzhuan},

abstractNote = {In this paper, we extended the analytical level set method [1, 2] for identifying a piece-wisely heterogeneous (zonation) binary system to the case with an arbitrary number of materials with unknown material properties. In the developed level set approach, starting from an initial guess, the material interfaces are propagated through iterations such that the residuals between the simulated and observed state variables (hydraulic head) is minimized. We derived an expression for the propagation velocity of the interface between any two materials, which is related to the permeability contrast between the materials on two sides of the interface, the sensitivity of the head to permeability, and the head residual. We also formulated an expression for updating the permeability of all materials, which is consistent with the steepest descent of the objective function. The developed approach has been demonstrated through many examples, ranging from totally synthetic cases to a case where the flow conditions are representative of a groundwater contaminant site at the Los Alamos National Laboratory. These examples indicate that the level set method can successfully identify zonation structures, even if the number of materials in the model domain is not exactly known in advance. Although the evolution of the material zonation depends on the initial guess field, inverse modeling runs starting with different initial guesses fields may converge to the similar final zonation structure. These examples also suggest that identifying interfaces of spatially distributed heterogeneities is more important than estimating their permeability values.},

doi = {10.1016/j.jcp.2018.03.016},

journal = {Journal of Computational Physics},

number = C,

volume = 364,

place = {United States},

year = {Wed Mar 14 00:00:00 EDT 2018},

month = {Wed Mar 14 00:00:00 EDT 2018}

}