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Model misspecification and bias in the least-squares algorithm; implications for linearized isotropic AVO

Henning Hoeber
Model misspecification and bias in the least-squares algorithm; implications for linearized isotropic AVO (in Rock physics, Agnibha Das (editor) and Madhumita Sengupta (editor))
Leading Edge (Tulsa, OK) (September 2021) 40 (9): 646-654

Abstract

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the chi -angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.


ISSN: 1070-485X
EISSN: 1938-3789
Serial Title: Leading Edge (Tulsa, OK)
Serial Volume: 40
Serial Issue: 9
Title: Model misspecification and bias in the least-squares algorithm; implications for linearized isotropic AVO
Title: Rock physics
Author(s): Hoeber, Henning
Author(s): Das, Agnibhaeditor
Author(s): Sengupta, Madhumitaeditor
Affiliation: CGG, Crawley, United Kingdom
Affiliation: Amazon Web Services, Houston, TX, United States
Pages: 646-654
Published: 202109
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 25
Accession Number: 2021-057825
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2021, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 2021
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