scholarly journals Green’s function retrieval with Marchenko and inter-source seismic interferometry method for drill-bit seismic while drilling

2018 ◽  
Vol 15 (5) ◽  
pp. 2047-2059
Author(s):  
Liwen Xu ◽  
Hao Chen ◽  
Xiumei Zhang ◽  
Xiuming Wang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Drill Bit ◽  
Interferometry Method

scholarly journals Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A211-75A227 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob ◽  
Roel Snieder ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Bending Waves ◽  
Complex Source ◽  
Recent Developments ◽  
Diffusion Phenomena ◽  
Quantum Mechanical Scattering ◽  
Moving Media

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over differ-ent sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

scholarly journals Drill bit noise imaging without pilot trace, a near surface interferometry example

2019 ◽  
Author(s):  
Mehdi Asgharzadeh ◽  
Ashley Grant ◽  
Andrej Bona ◽  
Milovan Urosevic
Keyword(s):  
Source Function ◽  
Acoustic Energy ◽  
Seismic Interferometry ◽  
Drill Bit ◽  
Interferometric Imaging ◽  
Near Surface ◽  
Pilot Signal ◽  
Shallow Subsurface ◽  
Noise Data ◽  
Interferometry Method

Abstract. Acoustic energy emitted by drill bit can be recorded by geophones on the surface and processed for an image of the subsurface using seismic interferometry methods. Pilot sensors record bit signal on the drill rig and play an important role in processing geophone traces for the image. When pilot traces are not available, traces of the nearest geophone to the rig may be used in deconvolution and crosscorrelation of data but extra signal processing efforts are required to reduce the effect of source signature on crosscorrelation results. In this study, we use seismic interferometry method to image the shallow subsurface beneath a 2D geophone array by converting geophones to virtual sources. As there is no pilot signal available for this survey, we use nearest geophone trace for pilot crosscorrelation and pilot deconvolution. We modify the spectrum of pilot crosscorrelation and deconvolution results so that the effect of source function on virtual data is minimized. We then migrate the virtual shots and compare the results of interferometric imaging with the available image from 3D (active source) survey and assess the efficiency of our approach. We show that drill bit noise data can be used to generate a reasonably accurate image of the subsurface even in the absence of pilot recordings but the results should be checked for appearance of virtual multiples and depth inconsistencies that are caused by errors in the migration velocity.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

scholarly journals Marchenko imaging

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA39-WA57 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut ◽  
Filippo Broggini ◽  
Evert Slob ◽  
...  
Keyword(s):  
Green’S Function ◽  
Inverse Scattering ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Target Zone ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Marchenko Equation ◽  
Internal Multiples

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

scholarly journals Suppressing nonphysical reflections in Green’s function estimates using source-receiver interferometry

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. Q15-Q25 ◽  
Author(s):  
Simon King ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Seismic Interferometry ◽  
Elastic Model ◽  
Internal Multiples ◽  
Velocity Spectra ◽  
Interval Velocities ◽  
Streamer Data

Seismic interferometry retrieves the Green’s function propagating between two receiver locations using their recordings from an enclosing boundary of sources. Theory requires that sources completely surround the two receivers, but constraints in exploration seismology restrict sources to locations near the surface of the earth. Seismic interferometry by crosscorrelation then introduces usually undesirable nonphysical reflections (spurious multiples) in the Green’s function estimates. We found that the dominant nonphysical reflections can be converted into physical reflections via convolution using source-receiver interferometry. The resultant Green’s functions display fewer nonphysical reflections and show significantly better agreement with the true Green’s functions than those obtained using crosscorrelational interferometry. Nonphysical reflections can be further suppressed by iterating the convolution step. By comparing the velocity spectra of the Green’s functions retrieved by crosscorrelational and source-receiver interferometry, we can retrospectively identify the dominant nonphysical reflections introduced by crosscorrelational interferometry. We found that the nonphysical reflections are particularly important for constructing the primary reflections and internal multiples in source-receiver interferometry. This is because the primary reflections and internal multiples cannot be created via the convolution of physical reflections. Instead, the primary reflections and internal multiples are retrieved by the appropriate convolution between a nonphysical and physical reflection. We compared crosscorrelational interferometry and source-receiver interferometry using synthetic towed streamer data for a 1D acoustic and 2.5D elastic model, respectively. We also found that the nonphysical reflections obtained using crosscorrelational interferometry allow for the direct estimation of interval velocities and layer thicknesses without the need to use Dix inversion in the 1D example.

scholarly journals On the relation between seismic interferometry and the migration resolution function

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. T61-T66 ◽  
Author(s):  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Seismic Interferometry ◽  
Resolution Function ◽  
Migration Literature ◽  
Double Focusing ◽  
Wavefield Extrapolation ◽  
Backward Propagation

Seismic interferometry refers to the process of retrieving new seismic responses by crosscorrelating seismic observations at different receiver locations. Seismic migration is the process of forming an image of the subsurface by wavefield extrapolation. Comparing the expressions for backward propagation known from migration literature with the Green’s function representations for seismic interferometry reveals that these seemingly distinct concepts are mathematically equivalent. The frequency-domain representation for the resolution function of migration is identical to that for the Green’s function retrieved by seismic interferometry (or its square, in the case of double focusing). In practice, they differ because the involved Green’s functions in seismic interferometry are all defined in the actual medium, whereas in migration one of the Green’s functions is defined in a background medium.

scholarly journals Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A195-75A209 ◽  
Author(s):  
Kees Wapenaar ◽  
Deyan Draganov ◽  
Roel Snieder ◽  
Xander Campman ◽  
Arie Verdel
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Source Function ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Direct Wave ◽  
Reflected Wave

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the [Formula: see text]-axis, the crosscorrelation of the responses at two receivers along the [Formula: see text]-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transient (as in exploration seismology) or a noise signal (as in passive seismology), then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is theretrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surface-wave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

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