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Scientific Investigations Report 2010-5168

Approaches to Highly Parameterized Inversion: Pilot-Point Theory Guidelines, and Research Directions

By John E. Doherty, Michael N. Fienen, and Randall J. Hunt

Thumbnail of and link to report PDF (900 KB)ABSTRACT

Pilot points have been used in geophysics and hydrogeology for at least 30 years as a means to bridge the gap between estimating a parameter value in every cell of a model and subdividing models into a small number of homogeneous zones. Pilot points serve as surrogate parameters at which values are estimated in the inverse-modeling process, and their values are interpolated onto the modeling domain in such a way that heterogeneity can be represented at a much lower computational cost than trying to estimate parameters in every cell of a model. Although the use of pilot points is increasingly common, there are few works documenting the mathematical implications of their use and even fewer sources of guidelines for their implementation in hydrogeologic modeling studies. This report describes the mathematics of pilot-point use, provides guidelines for their use in the parameter-estimation software suite (PEST), and outlines several research directions. Two key attributes for pilot-point definitions are highlighted. First, the difference between the information contained in the every-cell parameter field and the surrogate parameter field created using pilot points should be in the realm of parameters which are not informed by the observed data (the null space). Second, the interpolation scheme for projecting pilot-point values onto model cells ideally should be orthogonal. These attributes are informed by the mathematics and have important ramifications for both the guidelines and suggestions for future research.

First posted January 13, 2011

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Suggested citation:

Doherty, J.E., Fienen, M.N., and Hunt, R.J., 2010, Approaches to highly parameterized inversion: Pilot-point theory, guidelines, and research directions: U.S. Geological Survey Scientific Investigations Report 2010–5168, 36 p.



Contents

Abstract

Introduction

Theory

Background and Issues Regarding Use of Pilot Points

Current Research Topics

Summary

References Cited

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