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# Accession Number:

## ADA210707

# Title:

## Iterative Network Magnitude Estimation and Uncertainty Assessment with Noisy and Clipped Data

# Descriptive Note:

## Final rept. Jun 1987-Jun 1989

# Corporate Author:

## TELEDYNE GEOTECH ALEXANDRIA VA ALEXANDRIA LABS

# Report Date:

## 1989-06-01

# Pagination or Media Count:

##
64.0

# Abstract:

## This document discusses the similarities and differences between two iterative estimators that are suitable for the network m sub b estimation problem, namely a modification of the Iterative Least-Squares method ILS due to Scheme and Hahn 1979 and the Maximum-Liklihood Estimator MLE. Both methods reduce to the usual Least Square Multiple Factors LSMF method when the censored data are deleted from the network observational data. For the censored case, the standard deviation sigma of the obscuring noise must be solved through iteration along with the event magnitudes and the station corrections. An extra constraint on sigma is necessary to determine which optimal estimation scheme is of interest. The final value of sigma for each iterative scheme can be used as a good approximation to the unbiased estimate of the standard deviation of the perturbing noise. By scaling this sigma value by the square root of the number of observations associated with each unknown parameter, the uncertainty in each estimated parameter can be approximated efficiently. These error estimates seem to differ from the unbiased standard errors only by a common multiplying constant across all stations and all event m sub bs. The bootstrap method is reviewed and adapted to the case of multivariate estimation with doubly censored data.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#