Wolfram Mathematica hauv Geophysics

Ua tsaug rau tus sau blog Anton Ekimenko rau nws daim ntawv qhia

Taw qhia

Daim ntawv no tau sau thaum lub rooj sib tham Wolfram Lavxias teb sab Technology Conference thiab muaj cov ntsiab lus ntawm daim ntawv qhia kuv tau muab. Qhov kev tshwm sim tau tshwm sim thaum Lub Rau Hli hauv St. Xav tias kuv ua haujlwm ib ntu ntawm qhov chaw sib tham, kuv pab tsis tau tab sis tuaj koom qhov kev tshwm sim no. Xyoo 2016 thiab 2017, kuv tau mloog cov lus tshaj tawm hauv lub rooj sib tham, thiab xyoo no kuv tau nthuav tawm. Ua ntej, qhov nthuav (zoo li kuv) lub ntsiab lus tau tshwm sim, uas peb tab tom txhim kho nrog Kirill Belov, thiab thib ob, tom qab kev kawm ntev ntawm txoj cai lij choj ntawm Lavxias Federation hais txog kev rau txim rau txoj cai, ntawm lub tuam txhab uas kuv ua haujlwm, ntau li ob daim ntawv tso cai tshwm sim. Wolfram Mathematica.

Ua ntej yuav mus rau lub ntsiab lus ntawm kuv cov lus, kuv xav kom nco ntsoov lub koom haum zoo ntawm qhov kev tshwm sim. Lub rooj sib tham nplooj ntawv mus xyuas siv cov duab ntawm Kazan Cathedral. Lub tsev teev ntuj yog ib qho ntawm lub ntsiab attractions ntawm St. Petersburg thiab pom meej heev los ntawm lub tsev uas lub rooj sib tham tau tshwm sim.

Wolfram Mathematica hauv Geophysics

Ntawm qhov nkag mus rau St. Petersburg State Economic University, cov neeg tuaj koom tau ntsib los ntawm cov pab cuam los ntawm cov tub ntxhais kawm - lawv tsis pub lawv poob. Thaum lub sijhawm sau npe, cov khoom plig me me tau muab tawm (ib qho khoom ua si - lub ntsej muag ci ntsa iab, cwj mem, ntawv nplaum nrog cov cim Wolfram). Noj su thiab so kas fes kuj suav nrog hauv lub rooj sib tham. Kuv twb tau sau tseg txog cov kas fes qab thiab cov ncuav qab zib ntawm pawg phab ntsa - cov kws ua zaub mov zoo heev. Nrog rau qhov kev taw qhia no, kuv xav hais ntxiv tias qhov kev tshwm sim nws tus kheej, nws cov hom ntawv thiab qhov chaw twb tau coj tus cwj pwm zoo.

Daim ntawv tshaj tawm uas tau npaj los ntawm kuv thiab Kirill Belov yog hu ua "Siv Wolfram Mathematica los daws cov teeb meem hauv kev siv geophysics. Spectral tsom xam ntawm seismic cov ntaub ntawv los yog "qhov twg ancient dej ntws." Cov ntsiab lus ntawm tsab ntawv ceeb toom npog ob ntu: ua ntej, kev siv cov algorithms muaj nyob rau hauv Wolfram Mathematica rau kev txheeb xyuas cov ntaub ntawv geophysical, thiab qhov thib ob, qhov no yog yuav ua li cas muab cov ntaub ntawv geophysical rau hauv Wolfram Mathematica.

Kev tshawb nrhiav seismic

Ua ntej koj yuav tsum ua kom luv luv mus rau hauv geophysics. Geophysics yog science uas kawm txog lub cev lub cev ntawm pob zeb. Zoo, txij li thaum pob zeb muaj cov khoom sib txawv: hluav taws xob, sib nqus, elastic, muaj cov txheej txheem ntawm geophysics: hluav taws xob prospecting, magnetic prospecting, seismic prospecting... Kev tshawb nrhiav seismic yog txoj hauv kev tseem ceeb ntawm kev tshawb nrhiav roj thiab roj. Cov txheej txheem yog ua raws li qhov excitation ntawm elastic vibrations thiab cov ntaub ntawv tom ntej ntawm cov lus teb los ntawm cov pob zeb ua rau thaj chaw kawm. Kev vibrations zoo siab rau hauv av (nrog dynamite lossis tsis tawg qhov chaw ntawm elastic vibrations) lossis hauv hiav txwv (nrog phom cua). Elastic vibrations propagate los ntawm cov pob zeb loj, raug refracted thiab xav txog ntawm cov ciam teb ntawm cov khaubncaws sab nraud povtseg nrog cov khoom sib txawv. Reflected nthwv dej rov qab los rau saum npoo thiab raug kaw los ntawm geophones ntawm thaj av (feem ntau yog cov khoom siv hluav taws xob electrodynamic raws li kev txav ntawm cov hlau nplaum tshem tawm hauv lub kauj) lossis hydrophones hauv hiav txwv (raws li cov nyhuv piezoelectric). Thaum lub sijhawm tuaj txog ntawm nthwv dej, ib tus tuaj yeem txiav txim siab qhov tob ntawm geological txheej.

Seismic nkoj towing khoom
Wolfram Mathematica hauv Geophysics

Cov phom cua excites elastic vibrations
Wolfram Mathematica hauv Geophysics

Cov nthwv dej dhau los ntawm pob zeb loj thiab raug kaw los ntawm hydrophones
Wolfram Mathematica hauv Geophysics

Geophysical tshawb fawb nkoj "Ivan Gubkin" ntawm lub pier ze ntawm Blagoveshchensky Choj nyob rau hauv St.
Wolfram Mathematica hauv Geophysics

Seismic teeb liab qauv

Pob zeb muaj qhov sib txawv ntawm lub cev. Rau kev tshawb nrhiav seismic, elastic zog yog qhov tseem ceeb - qhov ceev ntawm kev nthuav tawm ntawm elastic vibrations thiab ntom. Yog tias ob txheej txheej muaj tib yam lossis zoo sib xws, ces yoj "yuav tsis pom" ciam teb ntawm lawv. Yog hais tias lub yoj speeds nyob rau hauv cov khaubncaws sab nraud povtseg txawv, ces reflection yuav tshwm sim nyob rau hauv ciam teb ntawm cov khaubncaws sab nraud povtseg. Qhov ntau dua qhov sib txawv ntawm cov khoom, qhov kev xav tau ntau dua. Nws qhov kev siv zog yuav raug txiav txim los ntawm qhov kev cuam tshuam coefficient (rc):

Wolfram Mathematica hauv Geophysics

qhov twg ρ yog lub pob zeb ceev, ν yog qhov nrawm nrawm, 1 thiab 2 qhia cov txheej sab saud thiab qis.

Ib qho ntawm cov qauv yooj yim tshaj plaws thiab feem ntau siv seismic teeb liab qauv yog cov qauv convolution, thaum cov ntaub ntawv kaw seismic kab yog sawv cev raws li qhov tshwm sim ntawm convolution ntawm ib theem ntawm kev xav coefficients nrog kev soj ntsuam pulse:

Wolfram Mathematica hauv Geophysics

qhov twg s(t) - seismic taug qab, i.e. txhua yam uas tau kaw los ntawm hydrophone lossis geophone thaum lub sijhawm kaw cia, w(t) - lub teeb liab tsim los ntawm rab phom cua, n(t) - random suab nrov.

Cia peb suav cov khoom siv hluav taws xob seismic ua piv txwv. Peb yuav siv Ricker mem tes, dav siv hauv kev tshawb nrhiav seismic, raws li qhov pib teeb liab.

length=0.050; (*Signal lenght*)
dt=0.001;(*Sample rate of signal*)
t=Range[-length/2,(length)/2,dt];(*Signal time*)
f=35;(*Central frequency*)
wavelet=(1.0-2.0*(Pi^2)*(f^2)*(t^2))*Exp[-(Pi^2)*(f^2)*(t^2)];
ListLinePlot[wavelet, Frame->True,PlotRange->Full,Filling->Axis,PlotStyle->Black,
PlotLabel->Style["Initial wavelet",Black,20],
LabelStyle->Directive[Black,Italic],
FillingStyle->{White,Black},ImageSize->Large,InterpolationOrder->2]

Initial seismic impulse
Wolfram Mathematica hauv Geophysics

Peb yuav teeb tsa ob thaj tsam ntawm qhov tob ntawm 300 ms thiab 600 ms, thiab cov coefficients reflection yuav yog tus lej random

rcExample=ConstantArray[0,1000];
rcExample[[300]]=RandomReal[{-1,0}];
rcExample[[600]]=RandomReal[{0,1}];
ListPlot[rcExample,Filling->0,Frame->True,Axes->False,PlotStyle->Black,
PlotLabel->Style["Reflection Coefficients",Black,20],
LabelStyle->Directive[Black,Italic]]

Qhov sib txawv ntawm qhov sib txawv coefficient
Wolfram Mathematica hauv Geophysics

Cia peb suav thiab tso saib cov kab seismic. Txij li cov coefficients reflection muaj cov cim sib txawv, peb tau txais ob qhov kev hloov pauv ntawm cov kab seismic.

traceExamle=ListConvolve[wavelet[[1;;;;1]],rcExample];
ListPlot[traceExamle,
PlotStyle->Black,Filling->0,Frame->True,Axes->False,
PlotLabel->Style["Seismic trace",Black,20],
LabelStyle->Directive[Black,Italic]]

Simulated khiav
Wolfram Mathematica hauv Geophysics

Rau qhov piv txwv no, nws yog ib qho tsim nyog yuav tau txais kev tshwj tseg - qhov tseeb, qhov tob ntawm cov khaubncaws sab nraud povtseg yog txiav txim siab, ntawm chav kawm, nyob rau hauv meters, thiab kev suav ntawm seismic kab tshwm sim rau lub sijhawm sau. Nws yuav yog qhov tseeb dua los teeb tsa qhov tob hauv metres thiab suav lub sijhawm tuaj txog paub txog qhov nrawm hauv cov txheej. Nyob rau hauv cov ntaub ntawv no, kuv tam sim ntawd teem cov khaubncaws sab nraud povtseg ntawm lub sij hawm axis.

Yog tias peb tham txog kev tshawb fawb hauv cheeb tsam, tom qab ntawd los ntawm cov kev soj ntsuam zoo li no, ntau lub sijhawm zoo sib xws (seismic traces) raug kaw. Piv txwv li, thaum kawm ib qhov chaw 25 km ntev thiab 15 km dav, qhov twg, raws li ib tug tshwm sim ntawm kev ua hauj lwm, txhua kab cim characterizes ib tug cell ntsuas 25x25 meters (xws li lub xovtooj hu ua ib tug nyob rau hauv), cov ntaub ntawv zaum kawg array yuav muaj 600000 kab. Nrog rau lub sijhawm ua piv txwv ntawm 1 ms thiab lub sijhawm kaw ntawm 5 vib nas this, cov ntaub ntawv kawg yuav muaj ntau dua 11 GB, thiab qhov ntim ntawm cov khoom qub "raw" tuaj yeem yog ntau pua gigabytes.

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Pob GeologyIO

Kev txhim kho ntawm pob pib qhov teeb meem nyob rau ntawm phab ntsa VK ntawm pab pawg neeg hais lus Lavxias. Ua tsaug rau zej zog cov lus teb, kev daws teeb meem tau pom sai heev. Thiab yog li ntawd, nws tau loj hlob mus rau hauv kev loj hlob loj. Sib raug Wolfram Community phab ntsa ncej Nws tau txawm cim los ntawm cov neeg saib xyuas. Tam sim no, lub pob txhawb kev ua haujlwm nrog cov ntaub ntawv hauv qab no uas nquag siv hauv kev lag luam geological:

  1. ntshuam daim ntawv qhia cov ntaub ntawv hauv ZMAP thiab IRAP hom
  2. ntshuam kev ntsuas hauv LAS hom qhov dej
  3. input thiab output ntawm seismic ntaub ntawv hom SEGY

Txhawm rau txhim kho lub pob, koj yuav tsum ua raws li cov lus qhia ntawm nplooj ntawv rub tawm ntawm pob sib dhos, i.e. ua cov cai hauv qab no hauv ib qho twg Phau ntawv Mathematica:

If[PacletInformation["GeologyIO"] === {}, PacletInstall[URLDownload[
    "https://wolfr.am/FiQ5oFih", 
    FileNameJoin[{CreateDirectory[], "GeologyIO-0.2.2.paclet"}]
]]]

Tom qab ntawd lub pob yuav raug ntsia rau hauv lub neej ntawd nplaub tshev, txoj hauv kev uas tuaj yeem tau txais raws li hauv qab no:

FileNameJoin[{$UserBasePacletsDirectory, "Repository"}]

Ua piv txwv, peb yuav ua kom pom lub peev xwm tseem ceeb ntawm pob. Kev hu yog ua ib txwm ua rau pob khoom hauv Wolfram Lus:

Get["GeologyIO`"]

Lub pob yog tsim los siv Wolfram Workbench. Qhov no tso cai rau koj mus nrog lub luag haujlwm tseem ceeb ntawm lub pob nrog cov ntaub ntawv, uas nyob rau hauv cov nqe lus ntawm kev nthuav qhia hom tsis txawv ntawm cov ntaub ntawv ntawm Wolfram Mathematica nws tus kheej, thiab muab lub pob nrog cov ntaub ntawv xeem rau thawj tus neeg paub.

Wolfram Mathematica hauv Geophysics

Wolfram Mathematica hauv Geophysics

Xws li cov ntaub ntawv, tshwj xeeb tshaj yog, yog cov ntaub ntawv "Marmousi.segy" - qhov no yog cov qauv hluavtaws ntawm seem geological, uas tau tsim los ntawm Fabkis Petroleum Institute. Siv cov qauv no, cov neeg tsim khoom sim lawv tus kheej algorithms rau yoj teb qauv, ua cov ntaub ntawv, seismic trace inversion, thiab lwm yam. Tus qauv Marmousi nws tus kheej yog khaws cia rau hauv lub repository los ntawm qhov twg lub pob nws tus kheej tau rub tawm. Txhawm rau kom tau txais cov ntaub ntawv, khiav cov cai hauv qab no:

If[Not[FileExistsQ["Marmousi.segy"]], 
URLDownload["https://wolfr.am/FiQGh7rk", "Marmousi.segy"];]
marmousi = SEGYImport["Marmousi.segy"]

Import result - SEGYData object
Wolfram Mathematica hauv Geophysics

SEGY hom ntawv suav nrog khaws ntau cov ntaub ntawv hais txog kev soj ntsuam. Ua ntej, cov no yog cov lus hais. Qhov no suav nrog cov ntaub ntawv hais txog qhov chaw ua haujlwm, cov npe ntawm cov tuam txhab uas tau ua qhov kev ntsuas, thiab lwm yam. Hauv peb qhov xwm txheej, lub taub hau no raug hu los ntawm kev thov nrog tus yuam sij TextHeader. Ntawm no yog ib qho shortened text header:

Short[marmousi["TextHeader"]]

"Cov ntaub ntawv Marmousi tau tsim los ntawm Lub Tsev Haujlwm ...nimum tshaj tawm ntawm 1500 m / s thiab qhov siab tshaj plaws ntawm 5500 m / s)"

Koj tuaj yeem tso saib cov qauv geological tiag tiag los ntawm kev nkag mus rau cov cim seismic siv qhov "txheej txheem" ​​tus yuam sij (ib qho ntawm cov yam ntxwv ntawm lub pob yog tias cov yuam sij yog qhov tsis txaus ntseeg):

ArrayPlot[Transpose[marmousi["traces"]], PlotTheme -> "Detailed"]

Qauv Marmousi
Wolfram Mathematica hauv Geophysics

Tam sim no, lub pob kuj tso cai rau koj thauj cov ntaub ntawv hauv qhov chaw los ntawm cov ntaub ntawv loj, ua rau nws muaj peev xwm ua cov ntaub ntawv uas nws loj tuaj yeem ncav cuag kaum tawm gigabytes. Lub pob lub zog kuj suav nrog kev ua haujlwm rau kev xa tawm cov ntaub ntawv mus rau .segy thiab ib feem ntxiv rau qhov kawg ntawm cov ntaub ntawv.

Cais, nws yog tsim nyog sau cia lub functionality ntawm lub pob thaum ua hauj lwm nrog cov complex qauv ntawm .segy ntaub ntawv. Txij li thaum nws tso cai rau koj tsis tsuas yog nkag mus rau ib tus neeg cov cim thiab cov headers siv cov yuam sij thiab cov ntsuas, tab sis kuj hloov lawv thiab sau lawv rau hauv cov ntaub ntawv. Ntau yam ntawm cov ntsiab lus ntawm GeologyIO qhov kev siv yog dhau ntawm qhov ntawm tsab xov xwm no thiab tej zaum tsim nyog tau txais cov lus piav qhia cais.

Qhov cuam tshuam ntawm spectral tsom xam hauv seismic tshawb nrhiav

Lub peev xwm los import seismic cov ntaub ntawv rau hauv Wolfram Mathematica tso cai rau koj siv cov teeb liab ua haujlwm ua haujlwm rau cov ntaub ntawv sim. Txij li txhua qhov seismic trace sawv cev rau lub sijhawm, ib qho ntawm cov cuab yeej tseem ceeb rau kev kawm lawv yog spectral tsom xam. Ntawm qhov yuav tsum tau ua ua ntej rau kev txheeb xyuas qhov zaus ntawm cov ntaub ntawv seismic, peb tuaj yeem sau npe, piv txwv li, hauv qab no:

  1. Ntau hom nthwv dej muaj qhov sib txawv ntawm qhov sib txawv ntawm qhov sib txawv. Qhov no tso cai rau koj kom pom cov nthwv dej muaj txiaj ntsig thiab txo qis kev cuam tshuam tsis zoo.
  2. Pob zeb cov khoom xws li porosity thiab saturation tuaj yeem cuam tshuam cov zaus muaj pes tsawg leeg. Qhov no ua rau nws muaj peev xwm txheeb xyuas cov pob zeb nrog cov khoom zoo tshaj plaws.
  3. Cov khaubncaws sab nraud povtseg nrog cov thicknesses sib txawv ua rau muaj qhov tsis sib xws hauv ntau zaus.

Lub ntsiab lus thib peb yog qhov tseem ceeb hauv cov ntsiab lus ntawm kab lus no. Hauv qab no yog ib qho code fragment rau xam seismic kab nyob rau hauv cov ntaub ntawv ntawm ib txheej nrog txawv thickness - ib tug wedge qauv. Cov qauv no yog ib txwm kawm hauv kev tshawb nrhiav seismic los txheeb xyuas qhov cuam tshuam cuam tshuam thaum nthwv dej tshwm sim los ntawm ntau txheej txheej yog superimposed rau ib leeg.

nx=200;(* Number of grid points in X direction*)
ny=200;(* Number of grid points in Y direction*)
T=2;(*Total propagation time*)
(*Velocity and density*)
modellv=Table[4000,{i,1,ny},{j,1,nx}];(* P-wave velocity in m/s*)
rho=Table[2200,{i,1,ny},{j,1,nx}];(* Density in g/cm^3, used constant density*)
Table[modellv[[150-Round[i*0.5];;,i]]=4500;,{i,1,200}];
Table[modellv[[;;70,i]]=4500;,{i,1,200}];
(*Plotting model*)
MatrixPlot[modellv,PlotLabel->Style["Model of layer",Black,20],
LabelStyle->Directive[Black,Italic]]

Model ntawm pinch-out formation
Wolfram Mathematica hauv Geophysics

Lub nthwv dej ceev hauv lub npoo yog 4500 m / s, sab nraum lub npoo 4000 m / s, thiab qhov ceev yog kwv yees li 2200 g / cmΒ³. Rau cov qauv zoo li no, peb suav cov coefficients reflection thiab seismic traces.

rc=Table[N[(modellv[[All,i]]-PadLeft[modellv[[All,i]],201,4000][[1;;200]])/(modellv[[All,i]]+PadLeft[modellv[[All,i]],201,4500][[1;;200]])],{i,1,200}];
traces=Table[ListConvolve[wavelet[[1;;;;1]],rc[[i]]],{i,1,200}];
starttrace=10;
endtrace=200;
steptrace=10;
trasenum=Range[starttrace,endtrace,steptrace];
traserenum=Range[Length@trasenum];
tracedist=0.5;
Rotate[Show[
Reverse[Table[
	ListLinePlot[traces[[trasenum[[i]]]]*50+trasenum[[i]]*tracedist,Filling->{1->{trasenum[[i]]*tracedist,{RGBColor[0.97,0.93,0.68],Black}}},PlotStyle->Directive[Gray,Thin],PlotRange->Full,InterpolationOrder->2,Axes->False,Background->RGBColor[0.97,0.93,0.68]],
		{i,1,Length@trasenum}]],ListLinePlot[Transpose[{ConstantArray[45,80],Range[80]}],PlotStyle->Red],PlotRange->All,Frame->True],270Degree]

Seismic traces rau lub wedge qauv
Wolfram Mathematica hauv Geophysics

Cov kab ke ntawm seismic kab nyob rau hauv daim duab no yog hu ua seismic seem. Raws li koj tuaj yeem pom, nws txoj kev txhais lus kuj tseem tuaj yeem ua tiav ntawm qib intuitive, txij li lub geometry ntawm cov nthwv dej uas pom tau meej meej sib haum rau cov qauv uas tau teev tseg ua ntej. Yog tias koj txheeb xyuas cov kab hauv kev nthuav dav ntxiv, koj yuav pom tias cov kab ntawm 1 mus rau kwv yees li 30 tsis txawv - qhov kev xav ntawm lub ru tsev ntawm kev tsim thiab hauv qab tsis sib tshooj. Pib los ntawm 31st kab, qhov kev xav tau pib cuam tshuam. Thiab, txawm hais tias nyob rau hauv tus qauv, lub reflection coefficients tsis hloov horizontally - cov seismic ib feem hloov lawv siv raws li lub thickness ntawm lub tsim hloov.

Cia peb xav txog qhov amplitude ntawm kev xav los ntawm tus ciam teb sab saud ntawm qhov tsim. Pib los ntawm txoj kev 60th, qhov kev siv ntawm qhov kev xav tau pib nce thiab ntawm txoj kev 70th nws ua siab tshaj plaws. Qhov no yog li cas kev cuam tshuam ntawm nthwv dej ntawm lub ru tsev thiab hauv qab ntawm cov khaubncaws sab nraud povtseg tshwm sim nws tus kheej, ua rau qee qhov kev tsis txaus ntseeg tseem ceeb hauv cov ntaub ntawv seismic.

ListLinePlot[GaussianFilter[Abs[traces[[All,46]]],3][[;;;;2]],
InterpolationOrder->2,Frame->True,PlotStyle->Black,
PlotLabel->Style["Amplitude of reflection",Black,20],
LabelStyle->Directive[Black,Italic],
PlotRange->All]

Graph ntawm lub amplitude ntawm lub reflected nthwv dej ntawm lub sab sauv ntug ntawm lub wedge
Wolfram Mathematica hauv Geophysics

Nws yog qhov laj thawj uas thaum lub teeb liab qis dua, kev cuam tshuam pib tshwm sim ntawm qhov loj tsim thicknesses, thiab nyob rau hauv cov ntaub ntawv ntawm ib tug high-frequency teeb liab, cuam tshuam tshwm sim ntawm me thicknesses. Cov kab lus hauv qab no tsim cov teeb liab nrog zaus ntawm 35 Hz, 55 Hz thiab 85 Hz.

waveletSet=Table[(1.0-2.0*(Pi^2)*(f^2)*(t^2))*Exp[-(Pi^2)*(f^2)*(t^2)],
{f,{35,55,85}}];
ListLinePlot[waveletSet,PlotRange->Full,PlotStyle->Black,Frame->True,
PlotLabel->Style["Set of wavelets",Black,20],
LabelStyle->Directive[Black,Italic],
ImageSize->Large,InterpolationOrder->2]

Ib txheej ntawm qhov chaw teeb liab nrog zaus ntawm 35 Hz, 55 Hz, 85 Hz
Wolfram Mathematica hauv Geophysics

Los ntawm kev xam seismic traces thiab plotting graphs ntawm reflected nthwv dej amplitudes, peb yuav pom tau hais tias rau txawv frequencies ib tug anomaly raug soj ntsuam ntawm txawv formation thicknesses.

tracesSet=Table[ListConvolve[waveletSet[[j]][[1;;;;1]],rc[[i]]],{j,1,3},{i,1,200}];

lowFreq=ListLinePlot[GaussianFilter[Abs[tracesSet[[1]][[All,46]]],3][[;;;;2]],InterpolationOrder->2,PlotStyle->Black,PlotRange->All];
medFreq=ListLinePlot[GaussianFilter[Abs[tracesSet[[2]][[All,46]]],3][[;;;;2]],InterpolationOrder->2,PlotStyle->Black,PlotRange->All];
highFreq=ListLinePlot[GaussianFilter[Abs[tracesSet[[3]][[All,46]]],3][[;;;;2]],InterpolationOrder->2,PlotStyle->Black,PlotRange->All];

Show[lowFreq,medFreq,highFreq,PlotRange->{{0,100},All},
PlotLabel->Style["Amplitudes of reflection",Black,20],
LabelStyle->Directive[Black,Italic],
Frame->True]

Graphs ntawm lub amplitudes ntawm lub reflected nthwv dej los ntawm sab sauv ntug ntawm lub wedge rau txawv frequencies
Wolfram Mathematica hauv Geophysics

Lub peev xwm los txiav txim siab txog qhov tuab ntawm qhov tsim los ntawm cov txiaj ntsig ntawm kev soj ntsuam seismic yog qhov tseem ceeb heev, vim tias ib qho ntawm cov haujlwm tseem ceeb hauv kev tshawb nrhiav roj yog los ntsuas cov ntsiab lus tseem ceeb tshaj plaws rau kev tso dej (piv txwv li, cov cheeb tsam uas tsim muaj. tuab). Tsis tas li ntawd, nyob rau hauv seem geological tej zaum yuav muaj cov khoom uas nws genesis ua rau ib tug ntse hloov nyob rau hauv lub thickness ntawm tsim. Qhov no ua rau kev tsom xam spectral yog ib qho cuab yeej zoo rau kev kawm lawv. Nyob rau hauv tshooj tom ntej ntawm tsab xov xwm peb yuav xav txog xws li cov khoom geological nyob rau hauv kom meej ntxiv.

Cov ntaub ntawv sim. Koj tau txais lawv qhov twg thiab nrhiav dab tsi hauv lawv?

Cov ntaub ntawv txheeb xyuas hauv tsab xov xwm tau txais hauv Western Siberia. Lub cheeb tsam, raws li txhua tus neeg tsis muaj kev zam tej zaum yuav paub, yog thaj chaw tsim cov roj tseem ceeb ntawm peb lub tebchaws. Active kev loj hlob ntawm deposits pib nyob rau hauv lub cheeb tsam nyob rau hauv lub 60s ntawm lub xeem caug xyoo. Txoj hauv kev tseem ceeb ntawm kev tshawb nrhiav cov roj deposits yog kev tshawb nrhiav seismic. Nws yog qhov nthuav kom saib cov duab satellite ntawm thaj chaw no. Ntawm qhov me me, koj tuaj yeem nco txog ntau qhov chaw swamps thiab pas dej; los ntawm kev nthuav dav daim ntawv qhia, koj tuaj yeem pom cov chaw zoo drilling, thiab los ntawm kev nthuav daim ntawv qhia txog qhov txwv, koj tuaj yeem paub qhov txawv ntawm qhov profile nrog seismic. kev soj ntsuam tau ua tiav.

Satellite duab ntawm Yandex maps - Noyabrsk nroog cheeb tsam
Wolfram Mathematica hauv Geophysics

Ib lub network ntawm cov ntaub qhwv dej ntawm ib qho ntawm cov teb
Wolfram Mathematica hauv Geophysics

Cov pob zeb muaj roj ntawm Western Siberia tshwm sim nyob rau hauv ntau qhov tob - los ntawm 1 km txog 5 km. Lub ntsiab ntim ntawm pob zeb uas muaj roj tau tsim nyob rau hauv Jurassic thiab Cretaceous lub sij hawm. Lub sijhawm Jurassic yog tej zaum paub rau ntau tus los ntawm cov yeeb yaj kiab ntawm tib lub npe. Jurassic kev nyab xeeb tau txawv txawv ntawm cov niaj hnub no. Phau ntawv Encyclopedia Britannica muaj ntau cov paleomaps uas qhia txog txhua lub sijhawm helogical.

Tam sim no tense
Wolfram Mathematica hauv Geophysics
Lub sijhawm Jurassic
Wolfram Mathematica hauv Geophysics

Thov nco ntsoov tias nyob rau hauv Jurassic lub sij hawm, thaj tsam ntawm Western Siberia yog ib tug hiav txwv ntug dej hiav txwv (dej hla los ntawm cov dej thiab ib tug ntiav dej hiav txwv). Txij li qhov kev nyab xeeb tau zoo, peb tuaj yeem xav tias thaj chaw zoo li lub sijhawm ntawd zoo li no:

Jurassic Siberia
Wolfram Mathematica hauv Geophysics

Hauv daim duab no, qhov tseem ceeb rau peb tsis yog tsiaj thiab noog, tab sis cov duab ntawm tus dej hauv keeb kwm yav dhau. Tus dej yog tib yam khoom geological uas peb nres thaum ntxov. Qhov tseeb yog tias kev ua haujlwm ntawm cov dej ntws tso cai rau cov xuab zeb zoo sib sau ua ke, uas tom qab ntawd yuav dhau los ua cov dej rau cov roj. Cov reservoirs tuaj yeem muaj qhov txawv txav, qhov nyuaj (zoo li lub txaj dej) thiab lawv muaj qhov sib txawv ntawm cov tuab - nyob ze ntawm ntug dej lub thickness yog me me, tab sis ze rau qhov nruab nrab ntawm cov channel los yog hauv cov cheeb tsam me me nws nce. Yog li, cov dej ntws hauv Jurassic tam sim no nyob rau hauv qhov tob ntawm peb kilometers thiab yog cov khoom ntawm kev tshawb nrhiav cov roj reservoirs.

Cov ntaub ntawv sim. Kev ua thiab kev pom

Cia peb tam sim ua qhov tshwj xeeb txog cov ntaub ntawv seismic uas tau qhia hauv tsab xov xwm - vim qhov tseeb tias cov ntaub ntawv siv rau kev tsom xam yog qhov tseem ceeb - tsuas yog ib feem ntawm cov thawj txheej ntawm seismic kab nyob rau hauv cov ntawv nyeem. Qhov no yuav tso cai rau leej twg los tsim cov kev suav sau saum toj no.

Thaum ua hauj lwm nrog seismic cov ntaub ntawv, ib tug geophysicist feem ntau siv tshwj xeeb software (muaj ob peb lub lag luam cov thawj coj uas nws cov kev loj hlob nquag siv, piv txwv li Petrel los yog Paradigm), uas tso cai rau koj los soj ntsuam ntau hom ntaub ntawv thiab muaj ib tug yooj yim graphical interface. Txawm hais tias txhua yam yooj yim, cov software no kuj muaj lawv qhov tsis zoo - piv txwv li, kev siv cov algorithms niaj hnub nyob rau hauv cov qauv ruaj khov yuav siv sij hawm ntau heev, thiab qhov muaj peev xwm rau kev suav automation feem ntau yog txwv. Nyob rau hauv cov xwm txheej zoo li no, nws yooj yim heev los siv cov tshuab computer lej thiab cov lus programming qib siab, uas tso cai rau kev siv ntau lub hauv paus algorithmic thiab, tib lub sijhawm, ua haujlwm ntau. Qhov no yog lub hauv paus ntsiab lus siv los ua haujlwm nrog cov ntaub ntawv seismic hauv Wolfram Mathematica. Nws yog qhov tsis tsim nyog los sau cov kev ua haujlwm nplua nuj rau kev sib tham ua haujlwm nrog cov ntaub ntawv - nws yog qhov tseem ceeb dua kom ntseeg tau tias kev thauj khoom los ntawm cov ntawv lees paub feem ntau, siv cov kev xav tau rau lawv thiab xa lawv rov qab mus rau lwm hom ntawv.

Ua raws li cov tswv yim npaj, peb yuav thauj cov ntaub ntawv seismic qub thiab tso rau hauv Wolfram Mathematica:

Get["GeologyIO`"]
seismic3DZipPath = "seismic3D.zip";
seismic3DSEGYPath = "seismic3D.sgy";
If[FileExistsQ[seismic3DZipPath], DeleteFile[seismic3DZipPath]];
If[FileExistsQ[seismic3DSEGYPath], DeleteFile[seismic3DSEGYPath]];
URLDownload["https://wolfr.am/FiQIuZuH", seismic3DZipPath];
ExtractArchive[seismic3DZipPath];
seismic3DSEGY = SEGYImport[seismic3DSEGYPath]

Cov ntaub ntawv rub tawm thiab xa tawm hauv txoj kev no yog txoj hauv kev sau tseg ntawm thaj chaw ntsuas 10 los ntawm 5 km. Yog tias cov ntaub ntawv tau txais los ntawm kev siv peb-dimensional seismic daim ntawv ntsuam xyuas txoj kev (nthwv dej tsis yog nyob rau hauv ib tug neeg geophysical profiles, tab sis nyob rau hauv tag nrho cov cheeb tsam ib txhij), nws yuav ua tau kom tau seismic cov ntaub ntawv cubes. Cov no yog cov khoom peb-dimensional, ntsug thiab kab rov tav seem uas tso cai rau cov ncauj lus kom ntxaws txog thaj chaw geological. Hauv qhov piv txwv tau txiav txim siab, peb tab tom soj ntsuam cov ntaub ntawv peb sab. Peb tuaj yeem tau txais qee cov ntaub ntawv los ntawm cov ntawv sau npe, zoo li qhov no

StringPartition[seismic3DSEGY["textheader"], 80] // TableForm

C 1 NO YOG DEMO FILE FOR GEOLOGYIO PACKAGE Test
C 2
C 3
C 4
C 5 HNUB neeg siv lub npe: WOLFRAM USER
C 6 SURVEY NAME: QHOV CHAW NYOB SIBERIA
C 7 COV NTAUB NTAWV HOM 3D SEISMIC VOLUME
C 8
C 9
C10 Z RANGE: Thawj 2200M kawg 2400M

Cov ntaub ntawv no yuav txaus rau peb los ua kom pom cov theem tseem ceeb ntawm kev txheeb xyuas cov ntaub ntawv. Cov kab nyob rau hauv cov ntaub ntawv tau sau tseg ua ntu zus thiab txhua tus ntawm lawv zoo ib yam li cov duab hauv qab no - qhov no yog qhov kev faib tawm ntawm cov amplitudes ntawm reflected nthwv dej raws li ntsug axis (qhov tob axis).

ListLinePlot[seismic3DSEGY["traces"][[100]], InterpolationOrder -> 2, 
 PlotStyle -> Black, PlotLabel -> Style["Seismic trace", Black, 20],
 LabelStyle -> Directive[Black, Italic], PlotRange -> All, 
 Frame -> True, ImageSize -> 1200, AspectRatio -> 1/5]

Ib qho ntawm cov seismic seem taug qab
Wolfram Mathematica hauv Geophysics

Paub tias muaj pes tsawg kab nyob rau hauv txhua qhov kev taw qhia ntawm thaj chaw kawm, koj tuaj yeem tsim cov ntaub ntawv peb-dimensional array thiab tso saib nws siv Image3D[] muaj nuj nqi

traces=seismic3DSEGY["traces"];
startIL=1050;EndIL=2000;stepIL=2; (*ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚Π° Π₯ Π½Π°Ρ‡Π°Π»Π° ΠΈ ΠΊΠΎΠ½Ρ†Π° ΡΡŠΡ‘ΠΌΠΊΠΈ ΠΈ шаг трасс*)
startXL=1165;EndXL=1615;stepXL=2; (*ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚Π° Y Π½Π°Ρ‡Π°Π»Π° ΠΈ ΠΊΠΎΠ½Ρ†Π° ΡΡŠΡ‘ΠΌΠΊΠΈ ΠΈ шаг трасс*)
numIL=(EndIL-startIL)/stepIL+1;   (*количСство трасс ΠΏΠΎ оис Π₯*)
numXL=(EndXL-startXL)/stepIL+1;   (*количСство трасс ΠΏΠΎ оис Y*)
Image3D[ArrayReshape[Abs[traces/Max[Abs[traces[[All,1;;;;4]]]]],{numIL,numXL,101}],ViewPoint->{-1, 0, 0},Background->RGBColor[0,0,0]]

XNUMXD duab ntawm cov ntaub ntawv seismic lub voos xwmfab. (Vertical axis - qhov tob)
Wolfram Mathematica hauv Geophysics

Yog hais tias lub geological nta ntawm kev txaus siab tsim khaus seismic anomalies, ces visualization cov cuab yeej nrog transparency yuav siv tau. "Tsis tseem ceeb" thaj chaw ntawm cov ntaubntawv povthawj siv tuaj yeem ua rau pom tsis pom, tsuas yog pom qhov tsis txaus ntseeg. Hauv Wolfram Mathematica qhov no tuaj yeem ua tiav siv Opacity[] ΠΈ Raster3D[].

data = ArrayReshape[Abs[traces/Max[Abs[traces[[All,1;;;;4]]]]],{numIL,numXL,101}];
Graphics3D[{Opacity[0.1], Raster3D[data, ColorFunction->"RainbowOpacity"]}, 
Boxed->False, SphericalRegion->True, ImageSize->840, Background->None]

Seismic data cube duab siv Opacity[] thiab Raster3D[] ua haujlwm Wolfram Mathematica hauv Geophysics

Raws li nyob rau hauv cov piv txwv hluavtaws, ntawm cov seem ntawm lub qhov cub qub tuaj yeem txheeb xyuas qee thaj tsam ntawm thaj chaw (txheej txheem) nrog kev hloov pauv hloov.

Cov cuab yeej tseem ceeb rau kev tsom xam spectral yog Fourier hloov. Nrog nws cov kev pab, koj tuaj yeem ntsuas qhov amplitude-frequency spectrum ntawm txhua kab los yog pawg kab. Txawm li cas los xij, tom qab xa cov ntaub ntawv mus rau qhov chaw zaus, cov ntaub ntawv ploj ntawm lub sijhawm twg (nyeem ntawm qhov tob) qhov zaus hloov pauv. Txhawm rau kom muaj peev xwm txheeb xyuas cov teeb liab hloov pauv ntawm lub sijhawm (qhov tob) axis, lub qhov rais Fourier hloov pauv thiab wavelet decomposition yog siv. Kab lus no siv wavelet decomposition. Wavelet tsom xam tshuab tau pib nquag siv hauv kev tshawb nrhiav seismic hauv 90s. Qhov zoo dua ntawm qhov rais Fourier hloov pauv yog suav tias yog lub sijhawm daws teeb meem zoo dua.

Siv cov kab lus hauv qab no, koj tuaj yeem decompose ib qho ntawm cov seismic traces rau hauv ib tus neeg cov khoom:

cwd=ContinuousWaveletTransform[seismicSection["traces"][[100]]]
Show[
ListLinePlot[Re[cwd[[1]]],PlotRange->All],
ListLinePlot[seismicSection["traces"][[100]],
PlotStyle->Black,PlotRange->All],ImageSize->{1500,500},AspectRatio->Full,
PlotLabel->Style["Wavelet decomposition",Black,32],
LabelStyle->Directive[Black,Italic],
PlotRange->All,
Frame->True]

Decomposition ntawm ib tug kab nyob rau hauv cov khoom
Wolfram Mathematica hauv Geophysics

Txhawm rau ntsuas seb lub zog xav tau npaum li cas faib rau lub sijhawm sib txawv nthwv dej tuaj txog, scalograms (analogous rau ib spectrogram) yog siv. Raws li txoj cai, hauv kev xyaum tsis tas yuav tshuaj xyuas tag nrho cov khoom. Feem ntau, cov khoom siv qis, nruab nrab thiab siab zaus raug xaiv.

freq=(500/(#*contWD["Wavelet"]["FourierFactor"]))&/@(Thread[{Range[contWD["Octaves"]],1}]/.contWD["Scales"])//Round;
ticks=Transpose[{Range[Length[freq]],freq}];
WaveletScalogram[contWD,Frame->True,FrameTicks->{{ticks,Automatic},Automatic},FrameTicksStyle->Directive[Orange,12],
FrameLabel->{"Time","Frequency(Hz)"},LabelStyle->Directive[Black,Bold,14],
ColorFunction->"RustTones",ImageSize->Large]

Scalogram. Kev ua haujlwm tshwm sim WaveletScalogram[]
Wolfram Mathematica hauv Geophysics

Wolfram Language siv lub luag haujlwm rau kev hloov pauv wavelet ContinuousWaveletTransform[]. Thiab daim ntawv thov ntawm qhov kev ua haujlwm no rau tag nrho cov kab ke yuav raug coj los siv cov haujlwm Rooj []. Ntawm no nws tsim nyog sau cia ib qho ntawm qhov muaj zog ntawm Wolfram Mathematica - muaj peev xwm siv kev sib luag ParallelTable[]. Hauv qhov piv txwv saum toj no, tsis tas yuav tsum muaj kev sib luag - qhov ntim ntawm cov ntaub ntawv tsis loj, tab sis thaum ua haujlwm nrog cov ntaub ntawv sim cov txheej txheem uas muaj ntau pua txhiab tus kab, qhov no yog qhov tsim nyog.

tracesCWD=Table[Map[Hilbert[#,0]&,Re[ContinuousWaveletTransform[traces[[i]]][[1]]][[{13,15,18}]]],{i,1,Length@traces}]; 

Tom qab siv lub luag haujlwm ContinuousWaveletTransform[] Cov ntaub ntawv tshiab tshwm sim sib xws rau cov zaus xaiv. Hauv qhov piv txwv saum toj no, cov zaus no yog: 38Hz, 33Hz, 27Hz. Kev xaiv ntawm zaus feem ntau yog ua los ntawm kev sim - lawv tau txais daim ntawv qhia zoo rau kev sib txawv zaus ua ke thiab xaiv cov ntaub ntawv tshaj tawm los ntawm qhov pom ntawm ib tus kws tshawb fawb geologist.

Yog tias koj xav tau qhia cov txiaj ntsig nrog cov npoj yaig lossis muab rau cov neeg siv khoom, koj tuaj yeem siv SEGYExport[] ua haujlwm ntawm GeologyIO pob

outputdata=seismic3DSEGY;
outputdata["traces",1;;-1]=tracesCWD[[All,3]];
outputdata["textheader"]="Wavelet Decomposition Result";
outputdata["binaryheader","NumberDataTraces"]=Length[tracesCWD[[All,3]]];
SEGYExport["D:result.segy",outputdata];

Nrog peb ntawm cov ntsuas no (tsawg zaus, nruab nrab zaus, thiab cov khoom siv siab zaus), RGB blending feem ntau yog siv los pom cov ntaub ntawv ua ke. Txhua yam khoom yog muab nws cov xim - liab, ntsuab, xiav. Hauv Wolfram Mathematica qhov no tuaj yeem ua tiav siv cov haujlwm ColorCombine[].

Qhov tshwm sim yog cov duab los ntawm kev txhais geological tuaj yeem ua tau. Cov kab lus uas tau sau tseg rau ntawm ntu ua rau nws muaj peev xwm delineate paleochannels, uas muaj feem ntau yuav yog cov reservoir thiab muaj roj reserves. Kev tshawb nrhiav thiab kev tshuaj xyuas ntawm cov niaj hnub analogues ntawm cov dej ntws zoo li no tso cai rau peb los txiav txim siab qhov feem ntau pheej hmoo ntawm kev sib tw. Cov channel lawv tus kheej yog cov yam ntxwv los ntawm cov txheej tuab ntawm cov xuab zeb zoo sib xyaw thiab yog cov dej zoo rau cov roj. Cov cheeb tsam sab nraud ntawm "lace" anomalies zoo ib yam li cov dej nyab niaj hnub. Cov dej nyab hauv av feem ntau sawv cev los ntawm cov pob zeb clayey thiab kev khawb rau hauv cov cheeb tsam no yuav tsis muaj txiaj ntsig.

RGB hlais ntawm cov ntaub ntawv lub voos xwmfab. Hauv nruab nrab (me ntsis mus rau sab laug ntawm qhov chaw) koj tuaj yeem taug qab tus dej ntws.
Wolfram Mathematica hauv Geophysics
RGB hlais ntawm cov ntaub ntawv lub voos xwmfab. Ntawm sab laug koj tuaj yeem taug qab tus dej ntws.
Wolfram Mathematica hauv Geophysics

Qee zaum, qhov zoo ntawm cov ntaub ntawv seismic tso cai rau cov duab pom tseeb dua. Qhov no nyob ntawm cov txheej txheem kev ua haujlwm hauv teb, cov cuab yeej siv los ntawm kev txo suab nrov algorithm. Nyob rau hauv cov ntaub ntawv no, tsis tsuas yog cov fragment ntawm dej systems yog pom, tab sis kuj tag nrho txuas ntxiv paleo-dej.

RGB sib xyaw ntawm peb yam ntawm cov ntaub ntawv seismic lub voos xwmfab (kab rov tav hlais). Qhov tob yog kwv yees li 2 km.
Wolfram Mathematica hauv Geophysics
Satellite duab ntawm tus dej Volga ze Saratov
Wolfram Mathematica hauv Geophysics

xaus

Wolfram Mathematica tso cai rau koj los txheeb xyuas cov ntaub ntawv seismic thiab daws cov teeb meem cuam tshuam txog kev tshawb nrhiav pob zeb, thiab pob GeologyIO ua rau cov txheej txheem no yooj yim dua. Cov qauv ntawm cov ntaub ntawv seismic yog xws li siv cov txheej txheem ua kom nrawm rau kev suav (ParallelTable[], ParallelDo[],…) ua tau zoo heev thiab tso cai rau koj los ua cov ntaub ntawv loj. Rau qhov loj, qhov no tau yooj yim los ntawm cov ntaub ntawv khaws cia nta ntawm GeologyIO pob. Los ntawm txoj kev, lub pob tuaj yeem siv tsis tau tsuas yog hauv thaj chaw ntawm kev tshawb nrhiav seismic. Yuav luag tib hom ntaub ntawv yog siv rau hauv av nkag mus radar thiab seismology.Yog tias koj muaj lus qhia txog yuav ua li cas los txhim kho qhov tshwm sim, cov teeb liab tsom xam algorithms los ntawm Wolfram Mathematica arsenal muaj feem xyuam rau cov ntaub ntawv no, lossis yog tias koj muaj lus pom zoo, thov tawm lus.

Tau qhov twg los: www.hab.com

Ntxiv ib saib