文档介绍：IMAGE ESTIMATION BY EXAMPLE:
Geophysical soundings image construction
Multidimensional autoregression
Jon F. Claerbout
Cecil and Ida Green Professor of Geophysics
Stanford University
with
Sergey Fomel
Stanford University
c February 28, 2006
dedicated to the memory
of
Johannes “Jos” Claerbout
1974-1999
“What do we have to look forward to today?
There are a lot of things we have to look forward to today.”
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Contents
1 Basic operators and adjoints 1
FAMILIAR OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ADJOINT DEFINED: DOT-PRODUCT TEST . . . . . . . . . . . . . . . . 27
2 Model fitting by least squares 33
HOW TO DIVIDE NOISY SIGNALS . . . . . . . . . . . . . . . . . . . . . 33
MULTIVARIATE LEAST SQUARES . . . . . . . . . . . . . . . . . . . . . 39
KRYLOV SUBSPACE ITERATIVE METHODS . . . . . . . . . . . . . . . 45
INVERSE NMO STACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
VESUVIUS PHASE UNWRAPPING . . . . . . . . . . . . . . . . . . . . . 57
THE WORLD OF CONJUGATE GRADIENTS . . . . . . . . . . . . . . . . 66
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3 Empty bins and inverse interpolation 73
MISSING DATA IN ONE DIMENSION . . . . . . . . . . . . . . . . . . . . 74
WELLS NOT MATCHING THE SEISMIC MAP . . . . . . . . . . . . . . . 82
SEARCHING THE SEA OF GALILEE . . . . . . . . . . . . . . . . . . . . 87
INVERSE LINEAR INTERPOLATION . . . . . . . . . . . . . . . . . . . . 90
PREJUDICE, BULLHEADEDNESS, AND CROSS VALIDATION . . . . . 94
4 The helical coordinate 97
FILTERING ON A HELIX . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
FINITE DIFFERENCES ON A HELIX . . . . . . . . . . . . . . . . . . . . 107
CONTENTS
CAUSALITY AND SPECTAL FACTORIZATION . . . . . . . . . . . . . . 111
WILSON-BURG SPECTRAL FACTORIZATI