Relations between reflection and transmission responses of 3-D inhomogeneous media Kees Wapenaar Department of Applied Earth Sciences Centre for Technical.

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

State AState B 00

State AState B

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

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

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

State AState B

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

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

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

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

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

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

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

Acoustic daylight imaging

Poster presentation Draganov et al.

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

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

Multiple elimination (van Borselen et al., 1996)

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

Schuster, 2001, EAGE

Seismic interferometry

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

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

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

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

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

Monitoring the universe by an array of telescopes

Monitoring the subsurface by an array of geophones

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

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

Shared infrastructure (2)