Basic Earth Imaging

Basic Earth Imaging - Basic Earth Imaging Jon F. Claerbout...

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Unformatted text preview: Basic Earth Imaging Jon F. Claerbout c November 17, 2010 Contents 1 Field recording geometry 1 1.1 RECORDING GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Fast ship versus slow ship . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 TEXTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Texture of horizontal bedding, marine data . . . . . . . . . . . . . . 7 1.2.2 Texture of land data: near-surface problems . . . . . . . . . . . . . . 8 2 Adjoint operators 11 2.1 FAMILIAR OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 Adjoint derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Zero padding is the transpose of truncation . . . . . . . . . . . . . . 15 2.1.3 Adjoints of products are reverse-ordered products of adjoints . . . . 16 2.1.4 Nearest-neighbor coordinates . . . . . . . . . . . . . . . . . . . . . . 17 2.1.5 Data-push binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.6 Linear interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.7 Causal integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 ADJOINTS AND INVERSES . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1 Dot product test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Waves in strata 23 3.1 TRAVEL-TIME DEPTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Vertical exaggeration . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 HORIZONTALLY MOVING WAVES . . . . . . . . . . . . . . . . . . . . . 24 3.2.1 Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.2 LMO by nearest-neighbor interpolation . . . . . . . . . . . . . . . . 28 CONTENTS 3.2.3 Muting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 DIPPING WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Rays and fronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Rays and fronts ....
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Basic Earth Imaging - Basic Earth Imaging Jon F. Claerbout...

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