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Relations between reflection and transmission responses of 3-D inhomogeneous media Kees Wapenaar Department of Applied Earth Sciences Centre for Technical Geoscience Delft University of Technology Dallas SEG 2003 October 29

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Claerbout, 1968 SEG, 2002 Acoustic daylight imaging Berkhout, 1982 Multiple elimination Imaging from below Schuster, 2001 Seismic interferometry Herman, 1992 Wapenaar, 1993 True amplitude imaging

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Claerbout, 1968 SEG, 2002 Acoustic daylight imaging Berkhout, 1982 Multiple elimination Imaging from below Schuster, 2001 Seismic interferometry Herman, 1992 Wapenaar, 1993 True amplitude imaging One-way reciprocity theorems

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State A State B A A B B Reciprocity interrelates states A and B

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State A State B A A B B Reciprocity interrelates states A and B

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State AState B Downgoing wavesand upgoing waves One-way reciprocity theorems

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State AState B Convolution-type propagation invariant: constant One-way reciprocity theorems

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State AState B Convolution-type reciprocity theorem: One-way reciprocity theorems

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State AState B Correlation-type propagation invariant: constant One-way reciprocity theorems

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State AState B Correlation-type reciprocity theorem: One-way reciprocity theorems

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface Convolution- or correlation-type reciprocity

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface Convolution- or correlation-type reciprocity Sources at upper or lower boundary

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State AState B States A and B without free surface Convolution-type reciprocity Sources at upper boundary One-way source-receiver reciprocity

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State AState B 00

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State AState B

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States A and B without free surface Convolution-type reciprocity Sources at lower boundary

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States A and B without free surface Convolution-type reciprocity Source A at lower and source B at upper boundary

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State AState B States A and B with free surface Convolution-type reciprocity Sources at upper boundary

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State AState B

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States A and B with free surface Convolution-type reciprocity Sources at lower boundary

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States A and B with free surface Convolution-type reciprocity Source A at lower and source B at upper boundary

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Summary of one-way source-receiver reciprocity Without free surface: With free surface:

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State AState B States A and B without free surface Correlation-type reciprocity Sources at upper boundary From reflection to transmission

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Herman, 1992 Wapenaar and Herrmann, 1993 Application in inverse wave field extrapolation

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State AState B States A and B with free surface Correlation-type reciprocity Sources at lower boundary From transmission to reflection

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1500 m/s 2000 m/s Acoustic daylight imaging Syncline model

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Acoustic daylight imaging

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Poster presentation Draganov et al.

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State AState B State A without and state B with free surface Convolution-type reciprocity Sources at upper boundary Multiple elimination

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Berkhout, 1982; Verschuur, Berkhout and Wapenaar, 1992 Fokkema and van den Berg, 1993, Van Borselen et al, 1996

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Multiple elimination (van Borselen et al., 1996)

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State AState B State A without and state B with free surface Correlation-type reciprocity Sources at upper boundary Seismic interferometry

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Schuster, 2001, EAGE

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Seismic interferometry

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State AState B States A and B without free surface Correlation-type reciprocity Source A at upper and source B at lower boundary Reflection from below

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface Convolution- or correlation-type reciprocity

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State AState B Derivation of relations between reflection and transmission responses States A and B with or without free surface Convolution- or correlation-type reciprocity Sources at upper or lower boundary

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Claerbout, 1968 SEG, 2002 Acoustic daylight imaging Berkhout, 1982 Multiple elimination Imaging from below Schuster, 2001 Seismic interferometry Herman, 1992 Wapenaar, 1993 True amplitude imaging One-way reciprocity theorems

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Monitoring the universe by an array of telescopes

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Monitoring the subsurface by an array of geophones

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Combined monitoring the universe and the subsurface: Different applications; shared infrastructure

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25% of antennas in central core High speed data transport Antenna cluster (Station) Central processor X Shared infrastructure (1)

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Shared infrastructure (2)

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