Seismic interferometry

Last updated

Interferometry examines the general interference phenomena between pairs of signals in order to gain useful information about the subsurface. [1] Seismic interferometry (SI) utilizes the crosscorrelation of signal pairs to reconstruct the impulse response of a given media. Papers by Keiiti Aki (1957), [2] Géza Kunetz, and Jon Claerbout (1968) [3] helped develop the technique for seismic applications and provided the framework upon which modern theory is based.

Contents

A signal at a location A can be crosscorrelated with a signal at a location B to reproduce a virtual source-receiver pair using seismic interferometry. Crosscorrelation is often considered the key mathematical operation in this approach, but it is also possible to use convolution to come up with a similar result. The crosscorrelation of passive noise measured at a free surface reproduces the subsurface response as if it was induced by an impulsive point source, which is, by definition, equal to Green's function. [4] As such, it is possible to obtain information about the subsurface with no need for an active seismic source. [5] This method, however, is not limited to passive sources, and can be extended for use with active sources and computer–generated waveforms. [1]

Image showing usefulness of seismic waves to investigate the subsurface Seismic wave prop mine.gif
Image showing usefulness of seismic waves to investigate the subsurface

As of 2006 the field of seismic interferometry was beginning to change the way geophysicists view seismic noise. Seismic interferometry uses this previously–ignored background wavefield to provide new information that can be used to construct models of the subsurface as an inverse problem. Potential applications range from the continent scale to much smaller-scale natural hazards, industrial, and environmental applications. [1]

History and development

Claerbout (1968) developed a workflow to apply existing interferometry techniques to investigating the shallow subsurface, although it was not proven until later that seismic interferometry could be applied to real world media. [1] [6] The long term average of random ultrasound waves can reconstruct the impulse response between two points on an aluminum block. However, they had assumed random diffuse noise, limiting interferometry in real world conditions. In a similar case, it was shown that the expressions for uncorrelated noise sources reduce to a single crosscorrelation of observations at two receivers. The interferometric impulse response of the subsurface can be reconstructed using only an extended record of background noise, initially only for the surface and direct wave arrivals. [7] [8]

Crosscorrelations of seismic signals from both active and passive sources at the surface or in the subsurface can be used to reconstruct a valid model of the subsurface. [9] Seismic interferometry can produce a result similar to traditional methods without limitations on the diffusivity of the wavefield or ambient sources. In a drilling application, it is possible to utilize a virtual source to image the subsurface adjacent to a downhole location. This application is increasingly utilized particularly for exploration in subsalt settings. [10]

Mathematical and Physical Explanation

Seismic interferometry provides for the possibility of reconstructing the subsurface reflection response using the crosscorrelations of two seismic traces. [1] [5] Recent work [11] has mathematically demonstrated applications of crosscorrelation for reconstructing Green's function using wave field reciprocity theorem in a lossless, 3D heterogeneous medium. Traces are most often extended records of passive background noise, but it is also possible to utilize active sources depending on the objective. Seismic interferometry essentially exploits the phase difference between adjacent receiver locations to image the subsurface.

The conditions for the method to be valid, meaning to retrieve the Green's function from correlated signals, are given as follows: [1] [12]

The last two conditions are hard to meet directly in nature. However, thanks to the wave scattering, the waves are converted, which satisfies the equipartition condition. The equal distribution of sources is met thanks to the fact, that the waves are scattered in every direction. [12]

Seismic interferometry consists of simple crosscorrelation and stacking of actual receiver responses to approximate the impulse response as if a virtual source was placed at the location of the applicable receiver. [1] Crosscorrelation of continuous functions in the time domain is presented as Equation 1.

Equation 1

Where the functions are integrated as a function of time at different lag values. In fact, crosscorrelation can be understood conceptually as the traveltime lag associated with waveforms in two discrete receiver locations. Crosscorrelation is similar to convolution where the second function is folded relative to the first. [13]

Seismic interferometry is fundamentally similar to the optical interferogram produced by the interference of a direct and reflected wave passing through a glass lens where intensity is primarily dependent upon the phase component.

Principle of convolution. Similar to cross-correlation Convolution of spiky function with box.gif
Principle of convolution. Similar to cross-correlation

Equation 2

I = 1+2R2 cos[ω(λAr+λrB)]+R^4

Where: Intensity is related to the magnitude of the reflection coefficient (R) and the phase component ω(λAr+λrB). [5] [11] An estimate of the reflectivity distributions can be obtained through the crosscorrelation of the direct wave at a location A with the reflection recorded at a location B where A represents the reference trace. [9] The multiplication of the conjugate of the trace spectrum at A and the trace spectrum at B gives:

Equation 3

ФAB =Re^iω(λAr+λrB) + o.t.

Where: ФAB = product spectrum o.t. = additional terms, e.g. correlations of direct-direct,[ clarification needed ] etc. As in the previous case, the product spectrum is a function of phase.

Key: Changes in reflector geometry lead to changes in the correlation result and the reflector geometry can be recovered through the application of a migration kernel. [1] [9] Interpretation of raw interferograms is not normally attempted; crosscorrelated results are generally processed using some form of migration. [9]

In the simplest case, consider a rotating drill bit at depth radiating energy that is recorded by geophones on the surface. It is possible to assume that the phase of the source wavelet at a given position is random and utilize the crosscorrelation of the direct wave at a location A with a ghost reflection at a location B to image a subsurface reflector without any knowledge regarding the source location. [9] The crosscorrelation of traces A and B in the frequency domain simplifies as:

Equation 4

Ф(A, B) = −(Wiω)^2 Re^iω(λArλrB)+o.t.

Where: Wi(ω) = frequency domain source wavelet (ith wavelet)

The crosscorrelation of the direct wave at a location A with a ghost reflection at a location B removes the unknown source term where:

Equation 5

Ф(A,B)≈Re^iω(λArλrB)

This form is equivalent to a virtual source configuration at a location A imaging hypothetical reflections at a location B. Migration of these correlation positions removes the phase term and yields a final migration image at position x where:

m(x) = Σø(A,B,λAx+λxB)

Where: ø(A,B,t) = temporal correlation between locations A and B with lag time t

This model has been applied to simulate subsurface geometry in West Texas using simulated models including a traditional buried source and a synthetic (virtual) rotating drill bit source to produce similar results. [9] [14] A similar model demonstrated the reconstruction of a simulated subsurface geometry. [5] In this case, the reconstructed subsurface response correctly modeled the relative positions of primaries and multiples. Additional equations can be derived to reconstruct signal geometries in a wide variety of cases.

Applications

Seismic interferometry is currently utilized primarily in research and academic settings. In one example, passive listening and the crosscorrelation of long noise traces was used to approximate the impulse response for shallow subsurface velocity analysis in Southern California. Seismic interferometry provided a result comparable to that indicated using elaborate inversion techniques. Seismic interferometry is most often used for the examination of the near surface and is often utilized to reconstruct surface and direct waves only. As such, seismic interferometry is commonly used to estimate ground roll to aid in its removal. [1] Seismic interferometry simplifies estimates of shear wave velocity and attenuation in a standing building. [15] Seismic interferometry has been applied to image the seismic scattering [16] and velocity structure [17] of volcanoes.

Seismic display as recorded by geophones Seg-y picture.gif
Seismic display as recorded by geophones

Exploration and production

Increasingly, seismic interferometry is finding a place in exploration and production. [18] SI can image dipping sediments adjacent to salt domes. [19] Complex salt geometries are poorly resolved using traditional seismic reflection techniques. An alternative method calls for the use of downhole sources and receivers adjacent to subsurface salt features. It is often difficult to generate an ideal seismic signal in a downhole location. [18] [19] Seismic interferometry can virtually move a source into a downhole location to better illuminate and capture steeply dipping sediments on the flank of a salt dome. In this case, the SI result was very similar to that obtained using an actual downhole source. Seismic interferometry can locate the position of an unknown source and is often utilized in hydrofrac applications to map the extent of induced fractures. [9] It is possible that interferometric techniques can be applied to timelapse seismic monitoring of subtle changes in reservoir properties in the subsurface. [1]

Limitations

Seismic interferometry applications are currently limited by a number of factors. Real world media and noise represent limitations for current theoretical development. For example, for interferometry to work noise sources must be uncorrelated and completely surround the region of interest. In addition, attenuation and geometrical spreading are largely neglected and need to be incorporated into more robust models. [1] Other challenges are inherent to seismic interferometry. For example, the source term only drops out in the case of the crosscorrelation of a direct wave at a location A with a ghost reflection at a location B. The correlation of other waveforms can introduce multiples to the resulting interferogram. Velocity analysis and filtering can reduce but not eliminate the occurrence of multiples in a given dataset. [9]

Although there have been many advancements in seismic interferometry challenges still remain. One of the biggest remaining challenges is extending the theory to account for real world media and noise distributions in the subsurface. Natural sources typically do not comply with mathematical generalizations and may in fact display some degree of correlation. [1] Additional problems must be addressed before applications of seismic interferometry can become more widespread.

Notes

  1. 1 2 3 4 5 6 7 8 9 10 11 12 Curtis et al. 2006
  2. ↑ Aki, Keiiti (1957). "Space and time spectra of stationary stochastic waves, with special reference to microtremors". Bulletin of the Earthquake Research Institute. 35: 415–457. hdl:2261/11892.
  3. ↑ Claerbout, Jon F. (April 1968). "Synthesis of a Layered Medium from ITS Acoustic Transmission Response". Geophysics. 33 (2): 264–269. Bibcode:1968Geop...33..264C. doi:10.1190/1.1439927.
  4. ↑ Snieder, Roel; Wapenaar, Kees (2010-09-01). "Imaging with ambient noise". Physics Today. 63 (9): 44–49. Bibcode:2010PhT....63i..44S. doi:10.1063/1.3490500. ISSN   0031-9228.
  5. 1 2 3 4 Draganov, Wapenaar & Thorbecke 2006
  6. ↑ Weaver & Lobkis 2001
  7. ↑ Wapenaar 2004
  8. ↑ Campillo & Paul 2003
  9. 1 2 3 4 5 6 7 8 Schuster et al. 2004
  10. ↑ Bakulin & Calvert 2004
  11. 1 2 Wapenaar & Fokkema 2006
  12. 1 2 Larose, Eric; Carrière, Simon; Voisin, Christophe; Bottelin, Pierre; Baillet, Laurent; Guéguen, Philippe; Walter, Fabian; Jongmans, Denis; Guillier, Bertrand; Garambois, Stéphane; Gimbert, Florent (2015-05-01). "Environmental seismology: What can we learn on earth surface processes with ambient noise?". Journal of Applied Geophysics. 116: 62–74. Bibcode:2015JAG...116...62L. doi:10.1016/j.jappgeo.2015.02.001. ISSN   0926-9851.
  13. ↑ Animation
  14. ↑ Yu, Followill & Schuster 2003
  15. ↑ Snieder & Safak 2006
  16. ↑ Chaput et al., 2012
  17. ↑ Brenguier et al. 2007
  18. 1 2 Hornby & Yu 2007
  19. 1 2 Lu et al. 2006

Related Research Articles

An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects.

Seismic tomography or seismotomography is a technique for imaging the subsurface of the Earth using seismic waves. The properties of seismic waves are modified by the material through which they travel. By comparing the differences in seismic waves recorded at different locations, it is possible to create a model of the subsurface structure. Most commonly, these seismic waves are generated by earthquakes or man-made sources such as explosions. Different types of waves, including P, S, Rayleigh, and Love waves can be used for tomographic images, though each comes with their own benefits and downsides and are used depending on the geologic setting, seismometer coverage, distance from nearby earthquakes, and required resolution. The model created by tomographic imaging is almost always a seismic velocity model, and features within this model may be interpreted as structural, thermal, or compositional variations. Geoscientists apply seismic tomography to a wide variety of settings in which the subsurface structure is of interest, ranging in scale from whole-Earth structure to the upper few meters below the surface.

Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio.

<span class="mw-page-title-main">Reflection seismology</span> Explore subsurface properties with seismology

Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator. Reflection seismology is similar to sonar and echolocation.

<span class="mw-page-title-main">Array processing</span> Area of research in signal processing

Array processing is a wide area of research in the field of signal processing that extends from the simplest form of 1 dimensional line arrays to 2 and 3 dimensional array geometries. Array structure can be defined as a set of sensors that are spatially separated, e.g. radio antenna and seismic arrays. The sensors used for a specific problem may vary widely, for example microphones, accelerometers and telescopes. However, many similarities exist, the most fundamental of which may be an assumption of wave propagation. Wave propagation means there is a systemic relationship between the signal received on spatially separated sensors. By creating a physical model of the wave propagation, or in machine learning applications a training data set, the relationships between the signals received on spatially separated sensors can be leveraged for many applications.

<span class="mw-page-title-main">Vertical seismic profile</span> Vibration measurement using boreholes

In geophysics, vertical seismic profile (VSP) is a technique of seismic measurements used for correlation with surface seismic data. The defining characteristic of a VSP is that either the energy source, or the detectors are in a borehole. In the most common type of VSP, hydrophones, or more often geophones or accelerometers, in the borehole record reflected seismic energy originating from a seismic source at the surface.

Exploration geophysics is an applied branch of geophysics and economic geology, which uses physical methods at the surface of the Earth, such as seismic, gravitational, magnetic, electrical and electromagnetic, to measure the physical properties of the subsurface, along with the anomalies in those properties. It is most often used to detect or infer the presence and position of economically useful geological deposits, such as ore minerals; fossil fuels and other hydrocarbons; geothermal reservoirs; and groundwater reservoirs. It can also be used to detect the presence of unexploded ordnance.

<span class="mw-page-title-main">Magnetotellurics</span> Electromagnetic geophysical technique

Magnetotellurics (MT) is an electromagnetic geophysical method for inferring the earth's subsurface electrical conductivity from measurements of natural geomagnetic and geoelectric field variation at the Earth's surface.

<span class="mw-page-title-main">Interferometric synthetic-aperture radar</span> Geodesy and remote sensing technique

Interferometric synthetic aperture radar, abbreviated InSAR, is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar (SAR) images to generate maps of surface deformation or digital elevation, using differences in the phase of the waves returning to the satellite or aircraft. The technique can potentially measure millimetre-scale changes in deformation over spans of days to years. It has applications for geophysical monitoring of natural hazards, for example earthquakes, volcanoes and landslides, and in structural engineering, in particular monitoring of subsidence and structural stability.

<span class="mw-page-title-main">Seismic source</span> Device that generates controlled seismic energy used for seismic surveys

A seismic source is a device that generates controlled seismic energy used to perform both reflection and refraction seismic surveys. A seismic source can be simple, such as dynamite, or it can use more sophisticated technology, such as a specialized air gun. Seismic sources can provide single pulses or continuous sweeps of energy, generating seismic waves, which travel through a medium such as water or layers of rocks. Some of the waves then reflect and refract and are recorded by receivers, such as geophones or hydrophones.

<span class="mw-page-title-main">Geophysical imaging</span>

Geophysical imaging is a minimally destructive geophysical technique that investigates the subsurface of a terrestrial planet. Geophysical imaging is a noninvasive imaging technique with a high parametrical and spatio-temporal resolution. It can be used to model a surface or object understudy in 2D or 3D as well as monitor changes.

Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity, which requires the signal to be sparse in some domain. The second one is incoherence, which is applied through the isometric property, which is sufficient for sparse signals. Compressed sensing has applications in, for example, magnetic resonance imaging (MRI) where the incoherence condition is typically satisfied.

Seismic migration is the process by which seismic events are geometrically re-located in either space or time to the location the event occurred in the subsurface rather than the location that it was recorded at the surface, thereby creating a more accurate image of the subsurface. This process is necessary to overcome the limitations of geophysical methods imposed by areas of complex geology, such as: faults, salt bodies, folding, etc.

The seismoelectrical method is based on the generation of electromagnetic fields in soils and rocks by seismic waves. This technique is still under development and in the future it may have applications like detecting and characterizing fluids in the underground by their electrical properties, among others, usually related to fluids.

In geophysics, geology, civil engineering, and related disciplines, seismic noise is a generic name for a relatively persistent vibration of the ground, due to a multitude of causes, that is often a non-interpretable or unwanted component of signals recorded by seismometers.

<span class="mw-page-title-main">Near-surface geophysics</span> Geophysics of first tens of meters below surface

Near-surface geophysics is the use of geophysical methods to investigate small-scale features in the shallow subsurface. It is closely related to applied geophysics or exploration geophysics. Methods used include seismic refraction and reflection, gravity, magnetic, electric, and electromagnetic methods. Many of these methods were developed for oil and mineral exploration but are now used for a great variety of applications, including archaeology, environmental science, forensic science, military intelligence, geotechnical investigation, treasure hunting, and hydrogeology. In addition to the practical applications, near-surface geophysics includes the study of biogeochemical cycles.

Multidimensional seismic data processing forms a major component of seismic profiling, a technique used in geophysical exploration. The technique itself has various applications, including mapping ocean floors, determining the structure of sediments, mapping subsurface currents and hydrocarbon exploration. Since geophysical data obtained in such techniques is a function of both space and time, multidimensional signal processing techniques may be better suited for processing such data.

Michel Campillo is a French seismologist and geophysicist who is currently a professor at Grenoble Alpes University.

<span class="mw-page-title-main">Seismic data acquisition</span> Stage of seismic exploration

Seismic data acquisition is the first of the three distinct stages of seismic exploration, the other two being seismic data processing and seismic interpretation. Seismic acquisition requires the use of a seismic source at specified locations for a seismic survey, and the energy that travels within the subsurface as seismic waves generated by the source gets recorded at specified locations on the surface by what are known as receivers.

Subsurface mapping by ambient noise tomography is the mapping underground geological structures under the assistance of seismic signals. Ambient noise, which is not associated with the earthquake, is the background seismic signals. Given that the ambient noises have low frequencies in general, the further classification of ambient noise include secondary microseisms, primary microseisms, and seismic hum, based on different range of frequencies. We can utilize the ambient noise data collected by seismometers to create images for the subsurface under the following processes. Since the ambient noise is considered as diffuse wavefield, we can correlate the filtered ambient noise data from a pair of seismic stations to find the velocities of seismic wavefields. A 2-dimensional or 3-dimensional velocity map, showing the spatial velocity difference of the subsurface, can thus be created for observing the geological structures. Subsurface mapping by ambient noise tomography can be applied in different fields, such as detecting the underground void space, monitoring landslides, and mapping the crustal and upper mantle structure.

References

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.