### Abstract

A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady state water level data is presented. The method involves solving a family of generalized nonlinear regression problems and then selecting one particular solution from this family by means of a comparative analysis of residuals. A linearized error analysis of the solution is included. This analysis allows one to estimate the convariance of the transmissivity estimates as well as the square error of the estimates of hydraulic head. An efficient explicit numerical scheme for solving the inverse problem in an approximate manner when errors in water level data are sufficiently small is also described.

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

Pages (from-to) | 845-860 |

Number of pages | 16 |

Journal | Water Resources Research |

Volume | 15 |

Issue number | 4 |

State | Published - Aug 1979 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Water Resources Research*,

*15*(4), 845-860.

**STATISTICAL APPROACH TO THE INVERSE PROBLEM OF AQUIFER HYDROLOGY - 1. THEORY.** / Neuman, Shlomo P; Yakowitz, Sidney.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 15, no. 4, pp. 845-860.

}

TY - JOUR

T1 - STATISTICAL APPROACH TO THE INVERSE PROBLEM OF AQUIFER HYDROLOGY - 1. THEORY.

AU - Neuman, Shlomo P

AU - Yakowitz, Sidney

PY - 1979/8

Y1 - 1979/8

N2 - A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady state water level data is presented. The method involves solving a family of generalized nonlinear regression problems and then selecting one particular solution from this family by means of a comparative analysis of residuals. A linearized error analysis of the solution is included. This analysis allows one to estimate the convariance of the transmissivity estimates as well as the square error of the estimates of hydraulic head. An efficient explicit numerical scheme for solving the inverse problem in an approximate manner when errors in water level data are sufficiently small is also described.

AB - A new statistically based approach to the problem of estimating spatially varying aquifer transmissivities on the basis of steady state water level data is presented. The method involves solving a family of generalized nonlinear regression problems and then selecting one particular solution from this family by means of a comparative analysis of residuals. A linearized error analysis of the solution is included. This analysis allows one to estimate the convariance of the transmissivity estimates as well as the square error of the estimates of hydraulic head. An efficient explicit numerical scheme for solving the inverse problem in an approximate manner when errors in water level data are sufficiently small is also described.

UR - http://www.scopus.com/inward/record.url?scp=0018651209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0018651209&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0018651209

VL - 15

SP - 845

EP - 860

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 4

ER -