### Abstract

A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady water level and flux data. The new method is based on a variational theory developed by G. Chavent which is extended to the case of generalized nonlinear least squares. The method is implemented numerically by a finite element scheme. The inverse problem is posed in terms of log transmissivities instead of transmissivities and is solved by a Fletcher-Reeves conjugate gradient algorithm in conjunction with Newton's method for determining the step size to be taken at each iteration. Two theoretical examples are included to demonstrate the ability of the new method to deal with artificial noise of a relatively large amplitude, derived from a given stochastic model.

Original language | English (US) |
---|---|

Pages (from-to) | 331-346 |

Number of pages | 16 |

Journal | Water Resources Research |

Volume | 16 |

Issue number | 2 |

State | Published - Apr 1980 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Aquatic Science
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology

### Cite this

**STATISTICAL APPROACH TO THE INVERSE PROBLEM OF AQUIFER HYDROLOGY - 3. IMPROVED SOLUTION METHOD AND ADDED PERSPECTIVE.** / Neuman, Shlomo P.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 16, no. 2, pp. 331-346.

}

TY - JOUR

T1 - STATISTICAL APPROACH TO THE INVERSE PROBLEM OF AQUIFER HYDROLOGY - 3. IMPROVED SOLUTION METHOD AND ADDED PERSPECTIVE.

AU - Neuman, Shlomo P

PY - 1980/4

Y1 - 1980/4

N2 - A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady water level and flux data. The new method is based on a variational theory developed by G. Chavent which is extended to the case of generalized nonlinear least squares. The method is implemented numerically by a finite element scheme. The inverse problem is posed in terms of log transmissivities instead of transmissivities and is solved by a Fletcher-Reeves conjugate gradient algorithm in conjunction with Newton's method for determining the step size to be taken at each iteration. Two theoretical examples are included to demonstrate the ability of the new method to deal with artificial noise of a relatively large amplitude, derived from a given stochastic model.

AB - A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady water level and flux data. The new method is based on a variational theory developed by G. Chavent which is extended to the case of generalized nonlinear least squares. The method is implemented numerically by a finite element scheme. The inverse problem is posed in terms of log transmissivities instead of transmissivities and is solved by a Fletcher-Reeves conjugate gradient algorithm in conjunction with Newton's method for determining the step size to be taken at each iteration. Two theoretical examples are included to demonstrate the ability of the new method to deal with artificial noise of a relatively large amplitude, derived from a given stochastic model.

UR - http://www.scopus.com/inward/record.url?scp=0019227492&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019227492&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0019227492

VL - 16

SP - 331

EP - 346

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 2

ER -