Subsurface mapping by ambient noise tomography: Difference between revisions

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'''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.<ref>{{cite web |last1=Sleeman |first1=Reinoud |title=Ambient Earth noise and instrumental noise |url=https://www.knmi.nl/kennis-en-datacentrum/achtergrond/ambient-earth-noise-and-instrumental-noise#:~:text=Ambient%20Earth%20noise%2C%20or%20background |access-date=2023-11-01}}</ref> 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.<ref name="tonyking2">{{cite journal |last1=Nishida |first1=Kiwamu |title=Ambient seismic wave field |journal=Proceedings of the Japan Academy, Series B |date=2017-08-02 |volume=93 |issue=7 |pages=423–448 |doi=10.2183/pjab.93.026 |pmid=28769015 |pmc=5713174 |bibcode=2017PJAB...93..423N |url=https://doi.org/10.2183/pjab.93.026}}</ref> We can utilize the ambient noise data collected by [[seismometers]] (or geophones) 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 (or seismometers) to find the [[velocities]] of seismic wavefields.<ref>{{cite journal |last1=Benson |first1=G. D. |last2=Ritzwoller |first2=M. H. |last3=Barmin |first3=M. P. |last4=Levshin |first4=A. L. |last5=Lin |first5=F. |last6=Moschetti |first6=M. P. |last7=Shapiro |first7=N. M. |last8=Yang |first8=Y. |title=Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements |journal=Geophysical Journal International |date=2007-06-01 |volume=169 |issue=3 |pages=1239–1260 |doi=10.1111/j.1365-246X.2007.03374.x |doi-access=free |arxiv=2007.03374 |bibcode=2007GeoJI.169.1239B |s2cid=229068738 }}</ref> A 2-dimensional or 3-dimensional velocity map, showing the spatial velocity difference of the subsurface, can thus be created for observing the [[geological structure]]s. Subsurface mapping by ambient noise [[tomography]] can be applied in different fields, such as detecting the underground void space,<ref>{{cite journal |last1=Wang |first1=Yao |last2=Khorrami |first2=Mohammad |last3=Tran |first3=Khiem T. |last4=Horhota |first4=David |title=Application of ambient noise tomography for deep void detection |journal=Journal of Applied Geophysics |date=2023 |volume=209 |doi=10.1016/j.jappgeo.2022.104922 |bibcode=2023JAG...20904922W |s2cid=255338249 |url=https://doi.org/10.1016/j.jappgeo.2022.104922|url-access=subscription }}</ref> monitoring [[landslides]],<ref>{{cite journal |last1=Le Breton |first1=Mathieu |last2=Bontemps |first2=Noelie |last3=Guillemot |first3=Antoine |last4=Baillet |first4=Laurent |last5=Larose |first5=Eric |title=Landslide monitoring using seismic ambient noise correlation: challenges and applications |journal=Earth-Science Reviews |date=2021-01-28 |volume=216 |pages=1–26 |doi=10.1016/j.earscirev.2021.103518 |bibcode=2021ESRv..21603518L |s2cid=234037825 |url=https://doi.org/10.1016/j.earscirev.2021.103518}}</ref> and mapping the crustal and upper [[Mantle (geology)|mantle]] structure.<ref>{{cite journal |last1=Yao |first1=Huajian |last2=Beghein |first2=Caroline |last3=Hilst |first3=Robert D. Van Der |title=Surface wave array tomography in SE Tibet from ambient seismic noise and two-station analysis - II. Crustal and upper-mantle structure |journal=Geophysical Journal International |date=2008-04-01 |volume=173 |issue=1 |pages=205–219 |doi=10.1111/j.1365-246X.2007.03696.x |bibcode=2008GeoJI.173..205Y |s2cid=29548841 |doi-access=free }}</ref>

= Subsurface Mapping by Ambient Noise Tomography =

(Brief Introduction) 150-200 words

Importance of Subsurface mapping

1. Understanding subsurface (lithology, structure...): important in several discipline: geotechnical engineering, volcanology, geomorphology, civil engineering, economic geology...

2. Drilling borehole: traditional method, but invasive

3. Geophysical survey: non-invasive method to image the subsurface

== Characteristics of ambient noise ==

Ambient noise as alternative geophysical survey method

Characteristic of ambient noise refers to several quantities that can distinguish different ambient noise, including origin, [[frequency]], property, and temporal variation.

4. Example of geophysical survey technique: electrical resistivity, gravity anomaly, seismic

5. Geophysical survey is more convenient in seismic active region: more active seismic source for correlation

6. For less seismic region: Use of ambient noise: raising usage and thus attention

=== ImportanceNature of Subsurfaceambient mappingnoise ===

Ambient noise, as the rising star of the seismic source for seismic research other than [[earthquake]], accounts for the naturally and anthropogenically produced seismic vibration of the background.<ref>{{cite journal |last1=Oakley |first1=David O. S. |last2=Forsythe |first2=Brandon |last3=Gu |first3=Xin |last4=Nyblade |first4=Andrew A. |last5=Brantley |first5=Susan L. |title=Seismic Ambient Noise Analyses Reveal Changing Temperature and Water Signals to 10s of Meters Depth in the Critical Zone |journal=Journal of Geophysical Research: Earth Surface |date=2021-01-13 |volume=126 |issue=2 |doi=10.1029/2020JF005823 |bibcode=2021JGRF..12605823O |s2cid=234198739 |doi-access=free }}</ref> This is different from the active seismic source created solely for seismic research or large seismic source from [[earthquake]]. [[Ocean]] is the most dominant natural origin of the ambient noise field.<ref name="tonyking4">{{cite journal |last1=Igel |first1=Jonas K. H. |last2=Bowden |first2=Daniel C. |last3=Fichtner |first3=Andreas |title=SANS: Publicly Available Daily Multi-Scale Seismic Ambient Noise Source Maps |journal=Journal of Geophysical Research: Solid Earth |date=2023 |volume=128 |issue=1 |doi=10.1029/2022JB025114 |bibcode=2023JGRB..12825114I |s2cid=255123230 |doi-access=free |hdl=20.500.11850/591152 |hdl-access=free }}</ref>

Draft 2

Most of the geological maps only show the superficial deposits and outcrops, which allows the public to discover the geological structures that are above the sea surface. For most of the geology related disciplines, such as geotechnical engineering, volcanology, geomorphology, civil engineering, exploration geology, however, understanding on the subsurface structures and to a small extent, lithology, is as important as those on surface. One of traditional method would be borehole drilling but it is invasive to the ground surface. Instead, geophysical survey is a non-invasive alternative for subsurface exploration and thus subsurface mapping.

Any seismic source is transmitted as either [[Body wave (seismology)|body wave]]s or [[surface waves]], where ambient noise is no exception. Summary of their properties are shown below.

=== Ambient noise as alternative geophysical survey method ===

Major geophysical survey techniques include electrical resistivity, gravity anomaly and seismic. Seismic survey is particularly reliable on the detection of subsurface rock structures and even hydrocarbons. Seismologists attempt to correlate the velocity anomaly with the geological structure after the collection and further analysis of the seismic signals. The collection of seismic signals is easier for regions with frequent earthquakes. For some seismic inactive regions like Korea Peninsula, however, the seismic signal analysis is more difficult<ref>{{cite journal |last1=Kil |first1=Dongwoo |last2=Hong |first2=Tae-Kyung |last3=Chung |first3=Dongchan |last4=Kim |first4=Byeongwoo |last5=Lee |first5=Junhyung |last6=Park |first6=Seongjun |title=Ambient Noise Tomography of Upper Crustal Structures and Quaternary Faults in the Seoul Metropolitan Area and Its Geological Implications |journal=Earth and Space Science |date=06 November 2021 |volume=8 |issue=11 |page=1 |pages=27 |doi=https://doi.org/10.1029/2021EA001983}}</ref>. Instead of the correlation from strong seismic sources like earthquake, the potential of ambient noise on subsurface structure mapping is discovered in recent years, which will be introduced below.

{| class="wikitable"

== Source of Ambient Noise ==

|+ Seismic Wave

Part 1: Source of Ambient Noise 700-800 words

|-

1. Brief description of seismic source

! Wave Type !! Body/Surface !! Description

1.1 1st stage of seismic research: seismic noise collection

|-

1.2 seismic noise primary classification

| [[P-wave]] || Body || 1. Can pass through solid and liquid.

1.2.1 active: airgun, hammer, can generate apparent seismic pulse; large source like explosion, similar magnitude as earthquake

2. Particle movement parallel to wave movement.

1.2.2 passive: background noise, either natural or humane

|-

1.3 Increasing application of passive seismic noise on seismic research

| [[S-wave]] || Body || 1. Can pass through solid only.

2. Nature of Ambient Noise

2. Particle movement perpendicular to wave movement.

2.1 Anthropogenic

|-

2.1.1 Commerical shipping

| [[Rayleigh wave]] || Surface || 1. Include both longitudinal & transverse motions.

2.1.2 Seismic Exploration

2. Amplitude decreases exponentially with increasing distance from surface.

2.1.3 Urban traffic and other activities

|-

2.2 Natural Noise

| [[Love wave]] || Surface || 1. Wave speed lower than P-wave & S-wave, but higher than Rayleigh wave.

2.2.1 Earthquake

2. Horizonal particle movement perpendicular to wave propagation.

2.2.2 Ocean wave, wind

|}

2.2.3 Typhoon

[[File:Overview Seismic Waves.jpg|thumb|Overview Seismic Waves|upright=2.5]]

3. Variation of Ambient Noise

The dominance of seismic wave transmission of ambient noise depends on several factors, while the research technique would determine the major type of seismic wave collected for ambient noise. For example, seismologists would often use spatial auto-correlation (SPAC) method which involve the collection and analysis of [[surface wave]].<ref>{{cite journal |last1=Nthaba |first1=Bokani |last2=Ikeda |first2=Tatsunori |last3=Nimiya |first3=Hiro |last4=Tsuji |first4=Takeshi |last5=Lio |first5=Yoshihisa |title=Ambient noise tomography for a high-resolution 3D S-wave velocity model of the Kinki Region, Southwestern Japan, using dense seismic array data |journal=Earth, Planets and Space |date=2022-06-20 |volume=74 |issue=1 |page=96 |doi=10.1186/s40623-022-01654-x |bibcode=2022EP&S...74...96N |doi-access=free }}</ref>

3.1 Cause of variation

3.2 Examples

=== Brief descriptionFrequency of seismicambient sourcenoise ===

Draft 2

Data collection of ambient noise is the prior stage of subsurface mapping, which is important for further analysis and correlation. The seismic noise can be transmitted either body wave (P-wave, S-wave) or surface wave (Rayleigh wave, Love wave), so as the constructed velocity models. For some of the seismic research and exploration, active seismic sources would be created intentionally to record the velocity change of seismic waves. Some examples of tools creating active seismic source include hammer[note1], airgun, and even artificial explosion, which may create seismic waves with similar magnitude as large earthquakes. Other than the artificial seismic sources, passive ambient noise can also be recorded and analysed. Ambient noise refers to the background noise originated either from natural events or anthropogenic activities. The use of ambient noise on velocity structure modelling has received more attention, especially in seismically inactive regions.

Ambient noise is often known as [[microseism]], where ‘micro’ means very small,<ref>{{cite web |title=micro |url=https://dictionary.cambridge.org/dictionary/english/micro#google_vignette |website=Cambridge Dictionary |access-date=2023-11-08}}</ref> and ‘seism’ is an alternative name for earthquake.<ref>{{cite web |title=seism |url=https://www.merriam-webster.com/dictionary/seism |publisher=Merriam-Webster |access-date=2023-11-05}}</ref> It can be further classified based on their frequency ranges, namely hum, primary microseism and secondary microseism.<ref name="tonyking3">{{cite journal |last1=Tanimoto |first1=Toshiro |last2=Anderson |first2=Aaron |title=Seismic noise between 0.003 Hz and 1.0 Hz and its classification |journal=Progress in Earth and Planetary Science |date=2023-09-11 |volume=10 |issue=1 |page=56 |doi=10.1186/s40645-023-00587-7 |bibcode=2023PEPS...10...56T |doi-access=free }}</ref> The table below shows the comparison of frequency range between the microseisms, arranged from increasing order. Figure a also shows graph of the frequency range of microseisms.

=== Nature of Ambient Noise ===

From an extensive range of frequency, ambient noise can be further classified into several categories, which are based on their origins.

{| class="wikitable"

==== Anthropogenic ====

|+ Frequency Range of [[Microseisms]]

The anthropogenic ambient noise, excluded those artificial seismic sources produced intentionally for research, are originated from human activities. Considering the ocean ambient noise source as an example, there are noises that are created unintentionally by human activities, such as shipping and offshore engineering work[ref2]. The importance of shipping reflects on the well-developed trading and commercial industries. International immigration and emigration of products and goods can be done via shipping. The shipping activities are thus becoming frequent. During the shipping process, the mechanical waves can be driven up along water surface and propagate through the ocean. Other than shipping, offshore engineering work can also produce surface waves. Engineering works, which are usually done on the continent to usually fulfil the demand of urban development, include but not limited to borehole drilling, foundation construction and geophysical surveys. Extended from the continent, reclamation has been actively carried out by many countries to create more land for urban development. Those engineering works can thus also be carried out offshore. The processes of offshore drilling and exploration create continuous mechanical waves that can also propagate through ocean.

|-

! Microseisms !! Frequency Range (Hz)

|-

| Hum || 9×10⁻³ - 8×10⁻²

|-

| Primary microseism || 9×10⁻³ - 8×10⁻²

|-

| Secondary microseism || 3×10⁻² - 1

|}

=== Origin of ambient noise ===

Regarding the continental urban areas, there are more examples of human activities creating the background noise. Other than the engineering works, the urban traffic is the major component of urban ambient noise. Although the mechanical waves of the continent are not as visible than those from the ocean, they can still be transmitted via the soil and rock layers. Cars travelling on the road can produce repeatable vibration on the road which can then be transmitted through the soil layers.

Ambient noise can be further classified into two major categories based on the origins of the noise.

==== Natural NoiseAnthropogenic ====

Anthropogenic ambient noise originates from human activities. Considering the ocean ambient noise source as an example, there are noises that are created unintentionally by human activities, such as shipping and offshore engineering work.<ref name="tonyking">{{cite journal |last1=Hildebrand |first1=John A. |title=Anthropogenic and natural sources of ambient noise in the ocean |journal=Marine Ecology Progress Series |date=2023-12-03 |volume=395 |pages=5–20 |doi=10.3354/meps08353 |url=https://www.researchgate.net/publication/240809612|doi-access=free }}</ref> During the shipping activity, [[mechanical waves]] can be driven up along the water surface and propagate through the ocean. [[Offshore engineering]] work can also produce surface waves. Engineering works include but are not limited to [[borehole]] drilling, [[Foundation (engineering)|foundation]] [[construction]] and [[geophysical survey]]s.<ref name="tonyking" /> Shoreline [[Land reclamation|reclamation]] has been actively carried out by many countries to create more land for urban development. Those engineering works can thus also be carried out offshore. The processes of offshore drilling and exploration create continuous mechanical waves that can also propagate through the ocean.

Natural ambient noise refers to the background noise produced from the natural events. Our natural environment is not stationary but constantly changing every moment because the nature itself is continuously modified by the weather, tectonic movements and biogenic activities. They can also produce low frequency background noise that can be further analysed. Some of the most significant events are listed below.

In continental urban areas, there are more examples of human activities creating background noise. Other than engineering works, urban traffic is the major component of urban ambient noise.<ref name="tonyking" /> Although the mechanical waves of the continent are not as visible than those from the ocean, they can still be transmitted via the soil and rock layers. Cars travelling on the road can produce repeatable vibration on the road which can then be transmitted through the soil layers.

Earthquake, as mentioned before, is one of the most remarkable events that can produce the most significant background noise. Earthquakes can be caused by the movement along two faults or plates. Seismic waves are released and penetrate through the soil and rock layers, causing the continents to shake. There are numerous earthquakes happened every day with different scales around the world. By recording the seismic waves produced from the earthquake, we can further understand the interior structure of the Earth.

==== Natural noise ====

The ocean wave is another possible natural ambient noise source. As mentioned before, the ocean wave can be produced by anthropogenic activities, such as commercial shipping and offshore engineering work. Besides, natural wind and marine animals can also induce weak ocean wave propagating through the ocean, which can be recorded by seismometers.

Natural ambient noise refers to the background noise produced from the natural events. The natural environment is not stationary but constantly changing because nature itself is continuously modified by [[weather]], tectonic movements and biogenic activities.<ref name="tonyking" /> They can also produce low frequency background noise. Some of the most significant events are listed below.

[[Wind]] can induce weak ocean waves propagating through the ocean. The varying atmospheric [[pressure]] was hypothesized as the origin before but is inadequate to support the existence of all types of [[microseism]]s.<ref name="tonyking2" /> Instead, ocean waves are proposed as the alternative origin of natural ambient noise. For example, the ocean swells interact with the sea coast to induce hum and primary microseisms, and the interaction of sea waves with opposite direction can produce secondary microseisms.<ref name="tonyking3" />

Other than the natural ambient noise propagated through solid and liquid, ambient noise propagated via air can also be recorded if it is strong enough. One of the examples is typhoon. Typhoon is one of the natural hazards whose frequency and strength are magnified by global warming. The strong thermal current creates a low-pressure zone where the air can circulate around the centre. In such case, the vibration of the air is strong enough to be recorded by seismometers.

=== Variation of ambient noise ===

To evaluate whether the collected ambient noise source can be further analysed, we must carefully consider if there are any regular variations or patterns of certain ambient noise source.<ref name="tonyking" /> Referring to the urban noise source, it may experience a daily variation, where the human activities are conducted mostly in daytime and reduced in nighttime. The ambient noise should thus increase in the daytime while reducereducing inat nighttimenight. Apart from the temporal variation, the spatial variation can also matter. For example, the commercial shipping is usually concentrated on certain routes. The corresponding amplitude of ambient noise should also decrease when moving away from the shipping routes.<ref name="tonyking" /> Nevertheless, it is still difficult to distinguish the ambient noise sources.

== Seismic velocity structure modelling ==

Part 2: Seismic Velocity Structure Modelling 700-800 words

[[Seismic velocity structure]] modelling is the modelling technique showing the velocity difference of seismic waves across areas. The modelling process involves some steps, including [[cross-correlation]], [[Green's function]], and [[Seismic inversion|inversion]]. The usage of ambient noise as source of seismic velocity structure modelling rises from 2001 when seismologists tried to correlate the diffused ambient noise wave fields'<ref>{{cite journal |last1=Sager |first1=Korbinian |last2=Ermert |first2=Laura |last3=Boehm |first3=Christian |last4=Fichtner |first4=Andreas |title=Towards full waveform ambient noise inversion |journal=Geophysical Journal International |date=12 July 2021 |volume=212 |pages=566–590 |doi=10.1093/gji/ggx429|doi-access=free |hdl=20.500.11850/224948 |hdl-access=free }}</ref> Velocity structure modelling are complex and require multiple mathematical calculations.

1. Data collection method

1.1 Tools of collection

1.2 Available online source

2. Ambient noise correlation

2.1 cross correlation

2.2 green's function

2.3 Inversion

3. Subsurface structure correlation with velocity imaging

3.1 example of subsurface structure

3.2 linkage of structure with velocity zone

3.2.1 low-velocity zone

3.2.2 high-velocity zone

4. Limitation

4.1 Factors affecting quality of resolution

=== Pre-processing of ambient noise data ===

== Seismic Velocity Structure Modelling ==

The pre-processing of ambient noise data refers to the filtering of the raw data before proceeding to further analysis (cross-correlation, inversion). Raw seismic data can be collected by either [[geophone]]s, [[seismometers]], or from authorized official bodies. There are also public ambient noise source maps available in recent years.<ref name="tonyking4" /> Since the seismometers collect all ambient seismic signals from all directions, the produced seismic waveforms may not reflect the actual background seismic vibrations. Instead, they often contain some occasional seismic signals from earthquakes and other instruments, which is unnecessary in general and thus required to be removed.<ref>{{cite journal |last1=da Silva |first1=Cicero Costa |last2=Poveda |first2=Esteban |last3=Dantas |first3=Renato Ramos da Silva |last4=Julia |first4=Jordi |title=Ambient Noise Tomography with Short-Period Stations: Case Study in the Borborema Province |journal=Pure and Applied Geophysics |date=2021-04-22 |volume=178 |issue=5 |pages=1709–1730 |doi=10.1007/s00024-021-02718-x |bibcode=2021PApGe.178.1709D |s2cid=233330462 |url=https://doi.org/10.1007/s00024-021-02718-x|url-access=subscription }}</ref>

The collected ambient noise can be further analysed to produce velocity structure maps which are used to correlated with the possible subsurface structures. The processes involved are complex and require multiple mathematical calculations.

==== Cross-correlation of ambient noise ====

=== Data collection method ===

[[File:Simplest case of cross correlation.jpg|thumb|Figure 1: Simplest situation of ambient noise cross correlation|upright=1.5]]

As mentioned before, the data collection of ambient noise is the primary step of any seismic research. The most common tool for seismic data collection is the seismometer. Other example could be the geophones. There are also seismic stations or observatories authorized by different official bodies. For example, Hong Kong Observatory has set up several seismic stations in different locations in Hong Kong. The seismic waves are recorded by the seismometers and shown as seismographs. Semimoist and geophysicists can then identify the arrival time of different body waves and surface waves. The seismic waves usually arrive in the order of P-wave, S-wave, Rayleigh wave, and Love wave. Nevertheless, the analysis of ambient noise is more difficult than simply identify the waves above.

[[File:Distribution of ambient noise source amended.jpg|thumb|Figure 2: Resulting Green's functions in different distribution of ambient noise sources|upright=1.5]]

Ambient noise [[cross correlation]] is the process of finding the receiving time lag of ambient noise sources between two nearby stations. Figure 1 illustrates the simplest case of ambient noise cross-correlation. For a pair of receivers (or seismometers or seismic stations) at different locations, the ambient noise signals would be received at a different time, assumed that they travel at the same velocity at the subsurface. The products of cross-correlation of those signals are new seismic waveforms, namely [[Green's function]]. Regarding the case with multiple ambient noise sources, the shape of the cross correlation function depends on whether the ambient noise sources are evenly distributed across a certain area. For the most ideal situation where the ambient noise signals are distributed evenly across all directions, the Green’s function would be highly symmetrical (see Figure 2).

==== Ambient Noise CorrelationInversion ====

Inversion is one of the techniques used in ambient noise tomography. Inversion of the Green’s function is used to retrieve the subsurface properties of the Earth, where seismic velocity is one of the important quantities. It is a crucial step in ambient noise tomography. Inversion in seismic analysis can be treated as finding the original factors of the subsurface that induce the current transmission of the ambient noise signals. Inversion of the Green’s function is conducted linearly in the early ambient noise tomography studies with the assumption that the velocity variation is small.<ref>{{cite journal |last1=Perez |first1=Ivan Cabrera |last2=D' Auria |first2=Luca |last3=Soubestre |first3=Jean |last4=Barrancos |first4=Jose |last5=Padilla |first5=German D. |last6=Perez |first6=Nemesio M. |title=A nonlinear multiscale inversion approach for ambient noise tomography |journal=Geophysical Journal International |date=2021 |volume=225 |issue=2 |pages=1158–1173 |doi=10.1093/gji/ggaa574 |doi-access=free }}</ref> [[Forward model]], as the essential process of inversion, is used to estimate the closest quantities of the earth subsurface properties. The cross-correlated seismic waves can be inverted either linearly or non-linearly.

Compared the seismographs of ambient noise with those recording active seismic sources, or simply reviewed any seismographs, you can discover the 'thickness' of the seismic waves. Despite the occasional increase in amplitude due to the active seismic source, the entire seismic waves are also in certain amplitudes, showing that there are certain activities that also produce weak seismic waves. The ambient noise seismographs are required to correlate together such that the velocity map can be produced.

=== Linkage of geological structure with velocity zone ===

==== Cross-correlation of ambient noise ====

Before interpreting the velocity zone, it is necessary to understand how the seismic velocity varies. In general, P and S wave travel faster in high density medium. Only P wave can travel through any medium while S wave can only travel through solids. Therefore, a low velocity zone can indicate some vacuum space in the subsurface layer, such as void space and faults. Conversely, a high velocity zone may refer to the [[lithology]] with closely packed rocks, such as igneous rock. To correlate the velocity zone with geological structure, it is necessary to consider the size and shape of the velocity zones, and more importantly, the resolution of the subsurface velocity image. The resolution of the image can affect the scale of the subsurface we can interpret. Sometimes, fieldwork is also needed in order to better correlate the velocity map.{{citation needed|date=November 2023}}

Cross-correlation is a widely used tool in several aspects. It is used to discover the time difference between two events and the factors behind. In seismology, cross correlation is also used in analysing the ambient noise. The basic idea of ambient noise cross correlation is to find the green's function of the two seismic ambient noise. Imagine if there are two seismic stations with one seismic source. The seismic wave will arrive both seismic stations at different time if their distances from the seismic sources are different. Seismologists try to find the travelling time lag between two stations. Expanding the sample into an area with multiple ambient noise sources, the seismic waves from the two stations can be cross-correlated if the source distribution is even across the whole sample area. Otherwise, the green's function will be uneven and difficult to correlate any relationship between two factors.

==== InversionExample of subsurface structure ====

Here are some examples of the subsurface structures and features, including but not limited to the following.

Inversion of a function involving finding the origin

* Void and hole space

* [[Fault (geology)|Fault]]

* [[Fold (geology)|Fold]]

* Oil and gas

* [[Joint]]

* [[Fracture]]

* [[Groundwater]]

== See also ==

*[[Seismology]]

*[[Seismic Interferometry]]

*[[Seismic inversion|Inversion]]

*[[Green's function]]

{{Clear}}

==References==

{{Reflist}}

[[Category:Geophysical imaging]]

Part 3: Application of Subsurface Mapping 700-800 words

1. Exploration of underground mines

2. Volcano Monitoring

3. Landslide Monitoring