Cov Ntsiab Lus Tseem Ceeb ntawm Geostatistics hauv Geophysics
Geostatistics yog ib ceg ntawm cov ntaub ntawv txheeb cais tshwj xeeb uas tsim los tshuaj xyuas cov ntaub ntawv cuam tshuam nrog qhov chaw, uas yog, cov ntaub ntawv uas cov nqi raug cuam tshuam los ntawm qhov chaw. Hauv geophysics, cov ntaub ntawv yuav luag ib txwm yog qhov chaw hauv qhov xwm txheej: lub ntiajteb txawj nqus, sib nqus, seismic, thiab kev ntsuas resistivity, nrog rau cov ntaub ntawv geochemical thiab cov cav ntoo, txhua yam khi rau cov kev sib koom ua ke tshwj xeeb. Yog li ntawd, geostatistics muab lub hauv paus tseem ceeb rau kev nkag siab txog cov qauv faib tawm ntawm cov txheej txheem hauv av, kwv yees cov nqi ntawm qhov chaw tsis ntsuas, thiab ntsuas qhov tsis paub meej ntawm kev txhais lus. Tsab xov xwm no tham txog cov ntsiab lus tseem ceeb ntawm geostatistics feem ntau siv hauv cov ntsiab lus geophysical.
Vim li cas Geostatistics thiaj tseem ceeb hauv Geophysics?
Kev tshawb fawb geophysical yeej ib txwm ntsib cov kev txwv ntawm kev kuaj. Nws tsis yooj yim sua kom ntsuas txhua qhov chaw ntawm qhov chaw lossis hauv av vim yog tus nqi, lub sijhawm, thiab kev nkag mus. Yog li ntawd, kev txhais lus geophysical xav tau kev sib xyaw thiab kev ua qauv. Kev sib xyaw yooj yim xws li kev ntsuas qhov deb rov qab (IDW) yooj yim, tab sis lawv feem ntau tsis quav ntsej txog cov qauv sib raug zoo ntawm qhov chaw thiab tsis muab kev ntsuas ntawm qhov tsis paub meej. Geostatistics hais txog ob qhov kev xav tau tseem ceeb: (1) siv cov qauv sib raug zoo ntawm qhov chaw ntawm cov ntaub ntawv rau kev kwv yees ntau dua, thiab (2) muab cov qauv ntsuas rau qhov tsis paub meej los qhia txog kev txiav txim siab tshawb nrhiav.
Hauv kev xyaum geophysical, geostatistics yog siv rau kev tsim cov ntawv qhia anomaly zoo dua thiab sib xws, qauv ntawm cov khoom pob zeb (porosity, permeability, nthwv dej velocity), kev koom ua ke ntawm ntau qhov chaw cov ntaub ntawv (piv txwv li seismic thiab qhov dej), thiab kev sim ntawm cov qauv hauv av rau cov xwm txheej kev pheej hmoo.
Cov Ntaub Ntawv Chaw thiab Lub Tswv Yim ntawm Random Fields
Lub ntsiab lus ntawm geostatistics yog saib cov xwm txheej geological lossis geophysical ua cov haujlwm random lossis cov teb random. Qhov no txhais tau tias cov nqi parameter xws li qhov ceev, magnetic susceptibility, lossis velocity P ntawm txhua qhov chaw raug suav hais tias yog kev paub txog cov txheej txheem random nrog cov qauv tshwj xeeb. Hauv txoj hauv kev no, peb lub hom phiaj tsis yog tsuas yog "kos daim ntawv qhia," tab sis es kwv yees qhov kev faib tawm ntawm cov nqi thiab kev sib raug zoo ntawm cov chaw.
Muaj ob qho tseem ceeb hauv tus qauv geostatistical: qhov sib txawv thiab qhov sib txawv hauv zos. Qhov sib txawv piav qhia txog kev hloov pauv loj (piv txwv li, kev nce ntawm qhov ceev ntawm sab qaum teb mus rau sab qab teb vim yog kev hloov pauv lithological hauv cheeb tsam). Qhov sib txawv hauv zos piav qhia txog kev hloov pauv me me uas feem ntau cuam tshuam nrog pob zeb heterogeneity, pob zeb tawg, lossis kev hloov pauv ntawm lub ntsej muag. Qhov sib txawv ntawm qhov sib txawv thiab qhov sib txawv pab peb xaiv txoj hauv kev tsim nyog: seb puas yuav xav tias tsuas yog nyob ruaj khov, lossis seb puas yuav suav nrog kev hloov pauv / sib txawv.
Kev Nyob Ruaj Khoov: Ib qho Kev Xav Yooj Yim Uas Siv Ntau Zaus
Ntau txoj kev geostatistical classical vam khom qhov kev xav ntawm stationarity, uas yog, cov khoom ntawm cov ntaub ntawv tseem tsis hloov pauv nrog kev hloov pauv ntawm qhov chaw. Daim ntawv feem ntau yog qhov thib ob-txheej txheem stationarity: qhov nruab nrab yog tas li, thiab cov kev sib txawv tsuas yog nyob ntawm qhov deb thiab kev coj ntawm kev sib cais (lag), tsis yog nyob ntawm qhov chaw tag nrho.
Hauv geophysics, qhov kev xav no tsis yog qhov tseeb tas li vim tias cov xwm txheej geological feem ntau hloov maj mam. Txawm li cas los xij, ntawm qee qhov ntsuas (piv txwv li, hauv ib qho lithological domain), qhov kev xav ntawm stationarity feem ntau yog qhov tsim nyog heev. Yog tias cov ntaub ntawv qhia txog qhov sib txawv muaj zog, detrending feem ntau yog ua lossis ib txoj kev hloov pauv, xws li universal kriging, yog siv uas haum rau qhov sib txawv.
Variogram: Lub Plawv ntawm Geostatistics
Lub tswv yim tseem ceeb tshaj plaws hauv geostatistics yog variogram (lossis semivariogram). Ib qho variogram qhia txog qhov zoo sib xws ntawm cov nqi ntawm cov ntaub ntawv hloov pauv li cas nrog qhov deb. Intuitively, ob lub ntsiab lus uas nyob ze ua ke feem ntau muaj cov nqi zoo sib xws, thaum cov ntsiab lus uas nyob deb sib nrug feem ntau muaj cov nqi sib txawv. Lub variogram ntsuas qhov tseem ceeb no.
Feem ntau, empirical semivariogram yog xam los ntawm:
\[
\gamma(h)=\frac{1}{2N(h)}\sum_{i=1}^{N(h)}[Z(x_i)-Z(x_i+h)]^2
\]
qhov twg \(h\) yog qhov lag (qhov deb thiab kev coj), \(N(h)\) yog tus lej ntawm cov khub ntaub ntawv ntawm qhov lag ntawd, thiab \(Z(x)\) yog tus nqi ntaub ntawv.
Peb qhov tseem ceeb ntawm cov variogram:
1. Nugget: tus nqi semivariogram ntawm qhov lag ze li xoom. Nuggets qhia txog qhov yuam kev ntsuas, suab nrov, lossis heterogeneity ntawm qhov ntsuas me dua qhov deb ntawm kev kuaj.
2. Sill: tus nqi semivariogram thaum nws mus txog qhov chaw tiaj tiaj. Qhov no muaj feem cuam tshuam rau tag nrho cov variance ntawm cov ntaub ntawv hauv thaj chaw ntawd.
3. Qhov ntau thiab tsawg: qhov deb uas qhov variogram mus txog lub sill. Hauv qab qhov ntau thiab tsawg, cov ntaub ntawv tseem muaj feem cuam tshuam; saum qhov ntau thiab tsawg, qhov kev sib raug zoo tsis muaj zog/ploj lawm.
Cov variograms kuj tseem tuaj yeem qhia anisotropy, uas yog kev sib raug zoo uas sib txawv nyob ntawm qhov kev taw qhia. Hauv geophysics, anisotropy feem ntau tshwm sim los ntawm cov qauv geological xws li bedding, faults, lossis sediment flow direction. Ib qho variogram directional pab txiav txim siab qhov kev taw qhia ntawm qhov loj tshaj plaws thiab tsawg tshaj plaws continuity, uas yog qhov tseem ceeb hauv kev ua qauv pas dej lossis kev txhais lus qauv.
Cov Qauv Variogram: Los ntawm Empirical mus rau Mathematical Functions
Cov qauv sib txawv ntawm empirical feem ntau muaj suab nrov thiab tsis tas li ua tau raws li qhov yuav tsum tau ua lej rau kev siv hauv kriging. Yog li ntawd, lawv yuav tsum tau teeb tsa nrog tus qauv theoretical xws li:
- Spherical
- Exponential
- Gaussian
– Matérn (yooj yim dua, tab sis nyuaj dua)
Kev xaiv qauv yog coj los ntawm cov duab ntawm cov variogram empirical thiab kev nkag siab txog geological. Piv txwv li, Gaussian qauv feem ntau tsim cov kev hloov pauv du heev ntawm qhov deb luv luv, tsim nyog rau cov kev ntsuas txuas ntxiv mus tas li. Exponential qauv yog rougher ntawm qhov deb luv luv, tsim nyog rau cov xwm txheej nrog kev hloov pauv sai.
Kriging: Kev Kwv Yees Zoo Tshaj Plaws Raws Li Variogram
Kriging yog ib txoj kev ntsuas geostatistical interpolation uas siv variogram los muab qhov kwv yees zoo tshaj plaws linear unbiased estimator (BLUE). Tsis zoo li cov txheej txheem ntsuas deterministic, kriging:
1. Xav txog qhov deb thiab qhov chaw sib raug zoo.
2. Tsim ib daim ntawv qhia kwv yees thiab daim ntawv qhia kev hloov pauv kriging (kev tsis paub meej).
Cov hom kriging uas siv ntau:
– Simple Kriging (SK): qhov nruab nrab yog paub thiab tsis hloov pauv.
– Ordinary Kriging (OK): qhov nruab nrab tsis paub tab sis xav tias yuav tsis hloov pauv hauv zej zog.
– Universal Kriging (UK): suav nrog qhov sib txawv/kev txav mus los (piv txwv li polynomial function nrog rau kev sib koom ua ke).
– Co-kriging: siv cov hloov pauv theem ob (piv txwv li kwv yees porosity nrog kev pab los ntawm seismic impedance).
– Qhov Ntsuas Kriging: rau cov ntaub ntawv categorical/events (piv txwv li, qhov muaj feem ntawm ib qho lithology tshwj xeeb).
Hauv kev siv geophysics, kev khawb kriging feem ntau yog qhov kev xaiv thawj zaug vim nws yooj ywm thiab tsis tas yuav xav txog qhov nruab nrab thoob ntiaj teb.
Kev Ua Qauv Geostatistical: Ntau Tshaj Li Daim Ntawv Qhia Xwb
Kev sib xyaw ua ke tsim tau ib qho qauv "zoo tshaj plaws", tab sis qhov chaw hauv qab av yeej tsis paub meej. Txhawm rau ntsuam xyuas kev pheej hmoo thiab tsim cov xwm txheej, kev sim ua geostatistical siv, xws li:
- Sequential Gaussian Simulation (SGS) rau cov hloov pauv tas mus li.
- Kev Ua Qauv Qhia Txog Qhov Sib Tshuam (SIS) rau cov kev hloov pauv categorical.
- Cov ntaub ntawv ntau lub ntsiab lus rau cov qauv geological nyuaj raws li cov duab cob qhia.
Cov kev sim ua qauv tsim ntau yam kev paub uas txhua yam sib xws nrog cov ntaub ntawv thiab variogram, tso cai rau peb xam cov lej sib txawv, quantiles, thiab probabilities. Hauv cov ntsiab lus geophysical, kev sim ua qauv yog qhov tseem ceeb rau kev npaj drilling, kev ntsuam xyuas volumetric uncertainty, thiab kev koom ua ke nrog flow modeling.
Kev Txheeb Xyuas Qauv: Kev Txheeb Xyuas Sib Txawv thiab Kev Tshawb Fawb
Kev siv geostatistics zoo tsis yog tsuas yog tsim cov variograms thiab kriging xwb. Yuav tsum tau ua kev ntsuam xyuas, piv txwv li:
- Kev lees paub ib qho xwb: txhua qhov taw tes raug kwv yees siv lwm cov ntsiab lus, tom qab ntawd piv rau tus nqi tiag tiag.
– Kev tshuaj xyuas cov khoom seem: seb cov khoom seem puas raug faib tawm yam tsis muaj kev sib cais, seb puas muaj kev ntxub ntxaug tsis tu ncua.
– Kriging variance check: seb qhov tsis paub meej puas tsim nyog (siab hauv thaj chaw uas muaj cov ntaub ntawv tsawg, qis hauv thaj chaw uas muaj cov ntaub ntawv ntau).
Kev lees paub pab txiav txim siab seb qhov variogram puas "du heev," qhov ntau thiab tsawg ntev/luv dhau, lossis muaj anisotropy uas tsis tau raug ntes.
Cov Teeb Meem Feem Ntau Hauv Cov Ntawv Thov Geophysical Geostatistical
Qee qhov teeb meem uas feem ntau tshwm sim:
1. Suab nrov thiab tsis yog Gaussian: Cov ntaub ntawv geophysical feem ntau muaj cov outliers thiab cov kev faib tawm tsis yog ib txwm muaj. Kev hloov pauv (piv txwv li, qhov qhab nia ib txwm muaj) qee zaum tsim nyog.
2. Kev kuaj tsis sib npaug: txoj kev ntsuas (trajectory) ua rau cov ntaub ntawv ntom ntom hauv ib qho kev taw qhia thiab tsis tshua muaj nyob rau lwm qhov kev taw qhia.
3. Tsis ruaj khov: kev hloov pauv hauv lithology lossis cov qauv hauv cheeb tsam ua rau muaj kev hloov pauv muaj zog.
4. Kev koom ua ke ntawm ntau qhov ntsuas: av qeeg yog qhov loj tab sis qhov kev daws teeb meem txawv ntawm cov ntaub ntawv qhia ntxaws ntxaws heev.
Kev kov yeej cov teeb meem no xav tau kev sib xyaw ua ke ntawm kev nkag siab txog lej thiab kev nkag siab txog geological/geophysical.
Kev kaw
Cov ntsiab lus tseem ceeb ntawm geostatistics—stationarity, variogram, kriging, thiab simulation—muab ib lub moj khaum muaj zog rau kev ua cov ntaub ntawv geophysical raws li qhov chaw. Nrog rau variogram, peb kos duab qhov sib raug zoo ntawm qhov chaw; nrog rau kriging, peb tau txais kev kwv yees zoo tshaj plaws thiab lawv qhov tsis paub meej; thiab nrog rau kev simulation, peb tsim ntau qhov xwm txheej uas qhia txog qhov tsis paub meej hauv qab av. Thaum kawg, geostatistics tsis yog tsuas yog ib txoj kev kos duab xwb, tab sis yog ib txoj hauv kev los ua kom muaj kev tshawb nrhiav geophysical thiab kev txiav txim siab txhais lus ntau dua.
Yog tias koj xav tau, kuv kuj tuaj yeem ntxiv cov piv txwv ntawm daim ntawv thov (piv txwv li, magnetic anomaly mapping lossis seismic velocity estimation), lossis suav nrog cov txheej txheem ua haujlwm los ntawm kev suav variogram mus rau kriging hauv ib qho software tshwj xeeb.
