Ka'idoji na Asali na Tsarin Kasa a fannin Kimiyyar Kasa
Geostatistics wani reshe ne na kididdiga da aka tsara musamman don nazarin bayanan da suka shafi sararin samaniya, wato, bayanan da ƙimarsu ke tasiri ga wurin da ake amfani da su. A cikin ilimin kimiyyar ƙasa, bayanai kusan koyaushe suna da yanayi na sarari: ma'aunin nauyi, maganadisu, girgizar ƙasa, da juriya, da kuma bayanan binciken ƙasa da rijiyoyi, duk suna da alaƙa da takamaiman daidaitawa. Saboda haka, ilimin ƙasa yana ba da tushe mai mahimmanci don fahimtar tsarin rarraba sigogi na ƙarƙashin ƙasa, kimanta ƙima a wurare marasa aunawa, da kuma tantance rashin tabbas na fassarori. Wannan labarin ya tattauna mahimman ra'ayoyin ilimin ƙasa da aka fi amfani da su a cikin mahallin ilimin ƙasa.
Me yasa ilimin Geostatistics yake da mahimmanci a fannin Geophysics?
Binciken ƙasa yana fuskantar ƙuntatawa na samfura akai-akai. Ba zai yiwu a auna kowane wuri a saman ko ƙasa ba saboda farashi, lokaci, da ƙuntatawa na shiga. Saboda haka, fassarar ƙasa tana buƙatar haɗawa da ƙira. Sauƙaƙan haɗa abubuwa kamar auna nesa ta baya (IDW) suna da sauƙi, amma galibi suna yin watsi da tsarin haɗin sarari kuma ba sa ba da ma'aunin rashin tabbas. Geostatistics yana magance manyan buƙatu guda biyu: (1) amfani da tsarin haɗin sararin samaniya na bayanai don ƙarin kimantawa na gaske, da (2) samar da tsarin adadi don rashin tabbas don ba da damar yanke shawara kan bincike.
A cikin aikin ilimin ƙasa, ana amfani da ilimin ƙasa don ƙirƙirar taswirorin da suka fi kyau kuma masu daidaito, yin samfurin halayen duwatsu (porosity, permeability, speed of wave), haɗa bayanai masu tushe da yawa (misali girgizar ƙasa da rijiyoyi), da kuma kwaikwayon samfuran ƙasa don yanayin haɗari.
Bayanan Sarari da Tsarin Filayen Bazuwar
Ma'anar ilimin kididdigar ƙasa shine kallon abubuwan da suka faru a fannin ƙasa ko ƙasa a matsayin ayyukan bazuwar ko filayen bazuwar. Wannan yana nufin cewa ana ɗaukar ƙimar sigogi kamar yawa, saurin maganadisu, ko saurin P a kowane wuri a matsayin aiwatar da wani tsari na bazuwar tare da takamaiman tsari. A wannan hanyar, burinmu ba wai kawai shine "zana taswira ba," amma a maimakon haka mu kimanta rarrabawar dabi'u da alaƙar da ke tsakanin wurare.
Akwai muhimman abubuwa guda biyu a cikin tsarin kididdigar ƙasa: yanayin yanayi da bambancin yanayi na gida. Yanayin yanayi yana bayyana manyan canje-canje (misali, ƙaruwar yawan jama'a daga arewa zuwa kudu saboda canje-canjen ilimin halittar yanki). Bambancin yanayi na gida yana bayyana ƙananan canje-canjen yanayi waɗanda galibi ke da alaƙa da bambancin duwatsu, karyewar yanayi, ko canje-canjen yanayi. Bambancin da ke tsakanin yanayin yanayi da bambancin yanayi yana taimaka mana mu zaɓi hanyar da ta dace: ko kawai mu ɗauki yanayi mara tsayawa, ko kuma mu haɗa da yanayin yanayi a sarari.
Tsarin Tsaftacewa: Zato na Asali da Aka Fi Amfani da Shi
Yawancin hanyoyin ilimin kididdiga na gargajiya sun dogara ne akan zato na stationarity, wato, halayen kididdiga na bayanan ba sa canzawa tare da canje-canje a wurin. Siffar da aka fi sani ita ce stationarity na tsari na biyu: matsakaicin yana da daidaito, kuma bambancin ya dogara ne kawai akan nisan da alkiblar rabuwa (lag), ba akan cikakken matsayi ba.
A fannin ilimin ƙasa, wannan zato ba koyaushe yake daidai ba saboda yanayin ƙasa sau da yawa yana canzawa a hankali. Duk da haka, a wasu ma'auni (misali, a cikin yanki ɗaya na ilimin ƙasa), zato na tsayayye sau da yawa yana da ma'ana. Idan bayanan sun nuna wani yanayi mai ƙarfi, yawanci ana yin detrending ko kuma ana amfani da wani nau'in hanya, kamar kriging na duniya, wanda ya dace da yanayin.
Variogram: Zuciyar Geostatistics
Mafi shaharar ra'ayi a fannin ilimin geostatistics shine variogram (ko semivariogram). Variogram yana nuna yadda kamanceceniyar ƙimar bayanai ke canzawa tare da nisa. A zahiri, maki biyu da ke kusa da juna galibi suna da ƙima iri ɗaya, yayin da maki da ke da nisa suna da ƙima daban-daban. Variogram yana ƙididdige wannan ƙa'ida.
Ana ƙididdige semivariogram na gwaji ta hanyar:
\[
\gamma(h)=\frac{1}{2N(h)}\sum_{i=1}^{N(h)}[Z(x_i)-Z(x_i+h)]^2
\]
inda \(h\) shine lag (nisa da alkibla), \(N(h)\) shine adadin nau'ikan bayanai a wannan lag ɗin, kuma \(Z(x)\) shine ƙimar bayanai.
Muhimman sigogin variogram guda uku:
1. Nugget: ƙimar semivariogram a lokacin da ya kusa kusantowa sifili. Nuggets suna nuna kuskuren aunawa, hayaniya, ko bambancin a sikelin da ya fi ƙasa da nisan samfurin.
2. Sill: ƙimar semivariogram lokacin da ya kai wani matsayi. Wannan yana da alaƙa da jimlar bambancin bayanai a cikin wannan yanki.
3. Nisa: nisan da variogram ke kusantar sill. A ƙasa da kewayon, bayanai har yanzu suna da alaƙa; sama da kewayon, haɗin yana da rauni/ɓacewa.
Variograms kuma na iya nuna anisotropy, wanda shine alaƙar da ke bambanta dangane da alkibla. A cikin ilimin kimiyyar ƙasa, anisotropy yakan taso ne daga tsarin ƙasa kamar kayan gado, lahani, ko alkiblar kwararar laka. Variogram na alkibla yana taimakawa wajen tantance alkiblar mafi girma da mafi ƙarancin ci gaba, wanda yake da mahimmanci a cikin ƙirar tafki ko fassarar tsarin.
Tsarin Variogram: Daga Ayyukan Lissafi zuwa Ayyukan Lissafi
Sau da yawa ana samun hayaniya a cikin na'urorin gwaji kuma ba koyaushe suke cika buƙatun lissafi don amfani a cikin kriging ba. Saboda haka, ana buƙatar a haɗa su da samfurin nazari kamar:
- Siffa mai siffar ƙwallo
- Exponential
– Gaussian
– Matérn (mafi sassauƙa, amma mafi rikitarwa)
Zaɓar samfuri yana gudana ne ta hanyar siffar variogram na gwaji da fahimtar yanayin ƙasa. Misali, samfuran Gaussian galibi suna samar da sauye-sauye masu santsi a kan ɗan gajeren nisa, waɗanda suka dace da sigogi masu ci gaba sosai. Samfuran Exponential sun fi tsauri a kan ɗan gajeren nisa, waɗanda suka dace da abubuwan da ke faruwa tare da canje-canje masu sauri.
Kriging: Kimantawa Mafi Kyau Dangane da Variogram
Kriging wata hanya ce ta haɗa bayanai tsakanin ƙasa da ƙasa wadda ke amfani da variogram don samar da mafi kyawun kimantawa mai layi ɗaya (BLUE). Ba kamar hanyoyin haɗa bayanai tsakanin deterministic ba, kriging:
1. Yi la'akari da nisa da alaƙar sarari.
2. Yana samar da taswirar kimantawa da kuma taswirar bambancin kriging (rashin tabbas).
Nau'ikan kriging da aka fi sani:
– Simple Kriging (SK): matsakaicin sananne ne kuma mai dorewa.
– Ordinary Kriging (OK): matsakaicin ba a san shi ba amma ana tsammanin yana dawwama a cikin unguwannin yankin.
– Universal Kriging (Birtaniya): ya haɗa da yanayin/zubar da kaya (misali aikin polynomial dangane da daidaitawa).
- Haɗin gwiwa: ta amfani da masu canji na biyu (misali kimanta porosity tare da taimakon ƙarfin girgizar ƙasa).
– Alamar Kriging: don bayanan rarrabuwa/taron (misali yuwuwar wani takamaiman ilimin lissafi).
A fannin ilimin ƙasa da aka yi amfani da shi, kriging na yau da kullun galibi zaɓi ne mai ƙarfi na farko saboda yana da sassauƙa kuma baya buƙatar ɗaukar matsakaicin duniya da aka sani.
Kwaikwayon Geostatistical: Fiye da Taswira Kawai
Interpolation yana samar da samfurin "mafi kyau" guda ɗaya, amma ƙarƙashin ƙasa ba ya taɓa tabbata. Don tantance haɗari da ƙirƙirar yanayi, ana amfani da kwaikwayon yanayin ƙasa, kamar:
– Tsarin Gaussian Mai Sauƙi (SGS) don masu canzawa masu ci gaba.
– Kwaikwayon Mai Nuna Jerin Abubuwa (SIS) don masu canji na rukuni.
- Ƙididdiga masu maki da yawa don tsarin ƙasa mai rikitarwa dangane da hotunan horo.
Kwaikwayo suna samar da abubuwa da yawa da suka dace da bayanai da bambance-bambancen bayanai, wanda ke ba mu damar ƙididdige kewayon yuwuwar, adadi, da yuwuwar. A cikin mahallin ilimin ƙasa, kwaikwayo suna da mahimmanci don tsara haƙa rami, kimanta rashin tabbas na girma, da haɗawa da ƙirar kwarara.
Tabbatar da Samfuri: Tabbatarwa da Bincike
Kyakkyawan kididdigar ƙasa ba ta tsaya ga ƙirƙirar variograms da kriging ba. Ya kamata a gudanar da kimantawa, misali:
– Tabbatar da daidaiton rabe-raben rabe-raben rabe-rabe: kowane maki ana hasashensa ta amfani da wasu maki, sannan a kwatanta shi da ainihin ƙimar.
– Binciken da ya rage: ko an rarraba ragowar bazuwar, ko akwai son zuciya ta tsari.
– Binciken bambancin Kriging: ko rashin tabbas ɗin ya dace (yana da yawa a yankunan da bayanai ba su da yawa, ƙasa a yankunan da bayanai ke da yawa).
Tabbatarwa yana taimakawa wajen tantance ko variogram ɗin yana da "santsi," kewayon yana da tsayi/gajere sosai, ko kuma akwai anisotropy wanda ba a kama shi ba.
Kalubalen da Aka Fi Sani a Aikace-aikacen Geophysics Geostatistical
Wasu ƙalubale da kan taso:
1. Hayaniya da ba ta Gaussian ba: Bayanan ilimin ƙasa galibi suna ɗauke da abubuwan da ba su dace ba da kuma rarrabawar da ba ta dace ba. Sauye-sauye (misali, maki na yau da kullun) wani lokacin suna da mahimmanci.
2. Samfurin da bai daidaita ba: hanyar aunawa (hanyar hanya) tana sa bayanai su yi yawa a hanya ɗaya kuma su yi ƙaranci a ɗayan hanyar.
3. Rashin tsayawa: canje-canje a cikin ilimin halittar jiki ko tsarin yanki suna haifar da yanayi mai ƙarfi.
4. Haɗin kai mai girma dabam-dabam: girgizar ƙasa babban abu ne amma ƙudurin ya bambanta da cikakkun bayanai na rijiyoyin.
Cin nasara kan waɗannan ƙalubalen yana buƙatar haɗin fahimtar ƙididdiga da fahimtar yanayin ƙasa/geophysics.
Penutup
Manyan ra'ayoyin ilimin kididdigar ƙasa - stationarity, variogram, kriging, da kuma kwaikwayo - suna samar da tsari mai ƙarfi don sarrafa bayanan ilimin ƙasa bisa ga wuri. Tare da variogram, muna tsara tsarin haɗin sararin samaniya; tare da kriging, muna samun kimantawa mafi kyau da rashin tabbas ɗinsu; kuma tare da kwaikwayo, muna gina yanayi da yawa waɗanda ke nuna rashin tabbas na ƙasa a zahiri. A ƙarshe, ilimin ƙasa ba wai kawai dabarar taswira ba ce, amma hanya ce ta adadi don yin ƙarin bayani game da bincike da yanke shawara kan ilimin ƙasa da fassara.
Idan kuna so, zan iya ƙara misalan aikace-aikacen (misali taswirar rashin daidaituwar maganadisu ko kimanta saurin girgizar ƙasa), ko kuma haɗa da aikin aiki mai amfani daga lissafin variogram zuwa kriging a cikin takamaiman software.
