Editing Reflection seismology (section)

==Summary of the method==

[[Seismic wave]]s are mechanical perturbations that travel in the Earth at a speed governed by the [[acoustic impedance]] of the medium in which they are travelling.  The acoustic (or seismic) impedance, ''Z'', is defined by the equation:

:<math>Z=v\rho \ </math>,

where ''v'' is the seismic [[Phase velocity|wave velocity]] and ''&rho;'' ([[Greek alphabet|Greek]] ''[[rho (letter)|rho]]'') is the [[density]] of the rock.

When a seismic wave travelling through the Earth encounters an interface between two materials with different acoustic impedances, some of the wave energy will [[Reflection (physics)|reflect]] off the interface and some will [[refraction|refract]] through the interface.  At its most basic, the seismic reflection technique consists of generating seismic waves and measuring the time taken for the waves to travel from the source, reflect off an interface and be detected by an array of receivers (as [[geophone]]s or [[hydrophone]]s) at the surface.<ref name="SheriffGeldart">Sheriff, R. E., Geldart, L. P., (1995), 2nd Edition. Exploration Seismology. Cambridge University Press.</ref>  Knowing the travel times from the source to various receivers, and the velocity of the seismic waves, a geophysicist then attempts to reconstruct the pathways of the waves in order to build up an image of the subsurface.

In common with other geophysical methods, reflection seismology may be seen as a type of [[inverse problem]].  That is, given a set of data collected by [[experiment]]ation and the physical laws that apply to the experiment, the experimenter wishes to develop an [[model (abstract)|abstract model]] of the physical system being studied.  In the case of reflection seismology, the experimental data are recorded seismograms, and the desired result is a model of the structure and physical properties of the Earth's crust.  In common with other types of inverse problems, the results obtained from reflection seismology are usually not unique (more than one model adequately fits the data) and may be sensitive to relatively small errors in data collection, processing, or analysis.<ref>{{Cite journal|last1=Bube|first1=Kenneth P.|last2=Burridge|first2=Robert|date=1983-10-01|title=The One-Dimensional Inverse Problem of Reflection Seismology|url=https://epubs.siam.org/doi/10.1137/1025122|journal=SIAM Review|volume=25|issue=4|pages=497–559|doi=10.1137/1025122|issn=0036-1445|url-access=subscription}}</ref>  For these reasons, great care must be taken when interpreting the results of a reflection seismic survey.

===The reflection experiment===
The general principle of seismic reflection is to send [[elastic waves]] (using an energy source such as [[dynamite]] [[explosion]] or [[Vibroseis]]) into the Earth, where each layer within the Earth reflects a portion of the wave's energy back and allows the rest to refract through. These reflected energy waves are recorded over a predetermined time period (called the record length) by receivers that detect the motion of the ground in which they are placed.  On land, the typical receiver used is a small, portable instrument known as a [[geophone]], which converts [[ground motion]] into an [[analog signal|analogue]] electrical signal. In water, [[hydrophone]]s are used, which convert pressure changes into electrical signals.  Each receiver's response to a single shot is known as a “trace” and is recorded onto a [[data storage device]], then the shot location is moved along and the process is repeated.  Typically, the recorded signals are subjected to significant amounts of [[signal processing]].<ref name=rs/>{{rp|2-3,21}}

===Reflection and transmission at normal incidence===
[[File:Normal reflection at an interface.png|thumb|P-wave reflects off an interface at normal incidence]]
When a seismic P-wave encounters a boundary between two materials with different acoustic impedances, some of the energy in the wave will be reflected at the boundary, while some of the energy will be transmitted through the boundary.  The [[amplitude]] of the reflected wave is predicted by multiplying the amplitude of the incident wave by the seismic ''[[reflection coefficient]]'' <math>R</math>, determined by the [[Acoustic impedance|impedance]] contrast between the two materials.<ref name=rs>{{cite book |last1=Sheriff |first1=R. E. |last2=Geldart |first2=L. P. |title=Exploration seismology, Volume 1, History, theory, and data acquisition |date=1982 |publisher=Cambridge University Press |location=Cambridge |isbn=0521243734 |pages=67}}</ref>

For a wave that hits a boundary at [[surface normal|normal]] incidence (head-on), the expression for the reflection coefficient is simply

:<math>R=\frac{Z_2 - Z_1}{Z_2 + Z_1}</math>,

where <math>Z_1</math> and <math>Z_2</math> are the impedance of the first and second medium, respectively.<ref name=rs/>

Similarly, the amplitude of the incident wave is multiplied by the ''[[transmission coefficient]]'' <math>T</math> to predict the amplitude of the wave transmitted through the boundary.  The formula for the normal-incidence transmission coefficient is

:<math>T=1+R=\frac{2 Z_2}{(Z_2 + Z_1)}</math>.<ref name=rs/>

As the sum of the energies of the reflected and transmitted wave has to be equal to the energy of the incident wave, it is easy to show that

:<math>\frac{R^2}{Z_1}+\frac{T^2}{Z_2}=\frac{Z_2(Z_2 - Z_1)^2+4Z_1Z_2^2}{Z_1Z_2(Z_1+Z_2)^2}=\frac{1}{Z_1}</math>.

By observing changes in the strength of reflections, seismologists can infer changes in the seismic impedances. In turn, they use this information to infer changes in the properties of the rocks at the interface, such as [[density]] and [[Phase velocity|wave velocity]],<ref name=rs/> by means of [[seismic inversion]].

===Reflection and transmission at non-normal incidence===
[[File:Reflection at an interface.png|thumb|Diagram showing the mode conversions that occur when a P-wave reflects off an interface at non-normal incidence]]

The situation becomes much more complicated in the case of non-normal incidence, due to mode conversion between [[P-waves]] and [[S-waves]], and is described by the [[Zoeppritz equations]].  In 1919, Karl Zoeppritz derived 4 equations that determine the amplitudes of [[Reflection (physics)|reflected]] and [[refraction|refracted]] waves at a planar interface for an incident P-wave as a function of the angle of incidence and six independent elastic parameters.<ref name="SheriffGeldart" />  These equations have 4 unknowns and can be solved but they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved.<ref>{{Cite journal | doi=10.1190/1.1441936| title=A simplification of the Zoeppritz equations| journal=Geophysics| volume=50| issue=4| pages=609–614| year=1985| last1=Shuey| first1=R. T.| bibcode=1985Geop...50..609S}}</ref>

The reflection and transmission coefficients, which govern the amplitude of each reflection, vary with angle of incidence and can be used to obtain information about (among many other things) the fluid content of the rock.  Practical use of non-normal incidence phenomena, known as AVO (see [[amplitude versus offset]]) has been facilitated by theoretical work to derive workable approximations to the [[Zoeppritz equations]] and by advances in computer processing capacity.  AVO studies attempt with some success to predict the fluid content (oil, gas, or water) of potential reservoirs, to lower the risk of drilling unproductive wells and to identify new petroleum reservoirs.  The 3-term simplification of the Zoeppritz equations that is most commonly used was developed in 1985 and is known as the "Shuey equation".  A further 2-term simplification is known as the "Shuey approximation", is valid for angles of incidence less than 30 degrees (usually the case in seismic surveys) and is given below:<ref name="Avseth">Avseth, P, T Mukerji and [[Gary M. Mavko|G Mavko]] (2005). Quantitative seismic interpretation. Cambridge University Press, Cambridge, p. 183</ref>

:<math>R(\theta ) = R(0) + G \sin^2 \theta </math>

where <math>R(0)</math> = reflection coefficient at zero-offset (normal incidence); <math>G</math> = AVO gradient, describing reflection behaviour at intermediate offsets and <math>(\theta)</math> = angle of incidence.  This equation reduces to that of normal incidence at <math>(\theta)</math>=0.

===Interpretation of reflections===
The time it takes for a reflection from a particular boundary to arrive at the geophone is called the ''travel time''.  If the seismic wave velocity in the rock is known, then the travel time may be used to estimate the depth to the reflector.  For a simple vertically traveling wave, the travel time <math>t</math> from the surface to the reflector and back is called the Two-Way Time (TWT) and is given by the formula

:<math>t = 2\frac{d}{V}</math>,
where <math>d</math> is the depth of the reflector and <math>V</math> is the wave velocity in the rock.<ref name=rs/>{{rp|81}}

A series of apparently related reflections on several seismograms is often referred to as a ''reflection event''.  By correlating reflection events, a seismologist can create an estimated cross-section of the [[geology|geologic]] structure that generated the reflections.<ref name=rs/>{{rp|196-199}}

===Sources of noise===
[[File:Types of noise on a seismic record.png|thumb|Sources of noise on a seismic record. Top-left: air wave; top-right: head wave; bottom-left: surface wave; bottom-right: multiple.]]
In addition to reflections off interfaces within the subsurface, there are a number of other seismic responses detected by receivers and are either unwanted or unneeded:

====Air wave====
The airwave travels directly from the source to the receiver and is an example of [[coherent noise]].  It is easily recognizable because it travels at a speed of 330&nbsp;m/s, the [[speed of sound]] in air.

====Ground roll / Rayleigh wave / Scholte wave / Surface wave====
A [[Rayleigh wave]] typically propagates along a free surface of a solid, but the elastic constants and [[density]] of air are very low compared to those of rocks so the surface of the Earth is approximately a [[free surface]]. Low velocity, low frequency and high amplitude Rayleigh waves are frequently present on a seismic record and can obscure signal, degrading overall data quality.  They are known within the industry as ‘Ground Roll’ and are an example of coherent noise that can be attenuated with a carefully designed seismic survey.<ref>{{cite web | website = [[Schlumberger]] Oilfield Glossary | title = Ground Roll | url = http://www.glossary.oilfield.slb.com/Display.cfm?Term=ground%20roll | access-date = 8 September 2013 | archive-date = 31 May 2012 | archive-url = https://web.archive.org/web/20120531161347/http://www.glossary.oilfield.slb.com/Display.cfm?Term=ground%20roll | url-status = dead }}</ref>  The [[Scholte wave]] is similar to
ground roll but occurs at the sea-floor (fluid/solid interface) and it can possibly obscure and mask deep reflections in marine seismic records.<ref>{{cite arXiv|eprint=1306.4383|last1=Zheng|first1=Yingcai|title=Scholte waves generated by seafloor topography|last2=Fang|first2=Xinding|last3=Liu|first3=Jing|last4=Fehler|first4=Michael C.|year=2013|class=physics.geo-ph}}</ref> 
The velocity of these waves varies with wavelength, so they are said to be dispersive and the shape of the wavetrain varies with distance.<ref>Dobrin, M. B., 1951, Dispersion in seismic surface waves, Geophysics, 16, 63–80.</ref>

====Refraction / Head wave / Conical wave====
A head wave refracts at an interface, travelling along it, within the lower medium and produces oscillatory motion parallel to the interface.  This motion causes a disturbance in the upper medium that is detected on the surface.<ref name="SheriffGeldart" />  The same phenomenon is utilised in [[seismic refraction]].

====Multiple reflection====
An event on the seismic record that has incurred more than one reflection is called a ''multiple''.  Multiples can be either short-path (peg-leg) or long-path, depending upon whether they interfere with primary reflections or not.<ref>{{cite web | website = [[Schlumberger]] Oifield Glossary | title = Multiples Reflection | url = http://www.glossary.oilfield.slb.com/Display.cfm?Term=multiple%20reflection | access-date = 8 September 2013 | archive-date = 2 June 2012 | archive-url = https://web.archive.org/web/20120602102742/http://www.glossary.oilfield.slb.com/Display.cfm?Term=multiple%20reflection | url-status = dead }}</ref><ref>{{cite journal | last = Pendrel | first = J. | title = Seismic Inversion—A Critical Tool in Reservoir Characterization | journal = Scandinavian Oil-Gas Magazine | issue= 5/6 | year = 2006 | pages = 19–22}}</ref>

Multiples from the bottom of a body of water and the air-water interface are common in marine seismic data, and are suppressed by [[seismic processing]].

====Cultural noise====
Cultural noise includes noise from weather effects, planes, helicopters, electrical pylons, and ships (in the case of marine surveys), all of which can be detected by the receivers.

====Electromagnetic noise====
Particularly important in urban environments (i.e. power lines), it is hardly removable. Some particular sensor as microelectromechanical systems (MEMs) are used to decrease these interference when in such environments.<ref>{{Cite journal|last1=Malehmir|first1=Alireza|last2=Zhang|first2=Fengjiao|last3=Dehghannejad|first3=Mahdieh|last4=Lundberg|first4=Emil|last5=Döse|first5=Christin|last6=Friberg|first6=Olof|last7=Brodic|first7=Bojan|last8=Place|first8=Joachim|last9=Svensson|first9=Mats|last10=Möller|first10=Henrik|date=2015-11-01|title=Planning of urban underground infrastructure using a broadband seismic landstreamer — Tomography results and uncertainty quantifications from a case study in southwestern Sweden|url=https://library.seg.org/doi/10.1190/geo2015-0052.1|journal=Geophysics|volume=80|issue=6|pages=B177–B192|doi=10.1190/geo2015-0052.1|bibcode=2015Geop...80B.177M|issn=0016-8033|url-access=subscription}}</ref>

===2D versus 3D===
The original seismic reflection method involved acquisition along a two-dimensional vertical profile through the crust, now referred to as 2D data. This approach worked well with areas of relatively simple geological structure where dips are low. However, in areas of more complex structure, the 2D technique failed to properly image the subsurface due to out of plane reflections and other artefacts. Spatial aliasing is also an issue with 2D data due to the lack of resolution between the lines. Beginning with initial experiments in the 1960s, the seismic technique explored the possibility of full three-dimensional acquisition and processing. In the late 1970s the first large 3D datasets were acquired and by the 1980s and 1990s this method became widely used.<ref name="CSEG_2001">{{Cite journal |last=Galbraith |first=M. |date=2001 |title=3D Seismic Surveys – Past, Present and Future |journal=CSEG Recorder |publisher=Canadian Society of Exploration Geophysicists |volume=26 |issue=6}}</ref><ref name="Cartwright_&_Huuse_2005">{{Cite journal |last1=Cartwright |first1=J. |last2=Huuse |first2=M. |year=2005 |title=3D seismic technology: the geological 'Hubble' |journal=Basin Research |volume=17 |issue=1 |pages=1–20 |doi=10.1111/j.1365-2117.2005.00252.x|bibcode=2005BasR...17....1C |s2cid=129218651 }}</ref>