Wolfram Mathematica i le Geophysics

Faafetai i le tusitala o le blog Anton Ekimenko mo lana lipoti

Faatomuaga

O lenei tusi na tusia i le maea ai o le konafesi Wolfram Konafesi Tekonolosi Rusia ma o loo i ai se aotelega o le lipoti na ou tuuina atu. O le mea na tupu ia Iuni i St. Petersburg. Mafaufau i lo'u galue i se poloka mai le nofoaga o konafesi, sa le mafai ona ou taofia le auai i lenei mea na tupu. I le 2016 ma le 2017, sa ou faalogologo ai i lipoti o konafesi, ma o le tausaga lenei sa ou tuuina atu ai se folasaga. Muamua, o se mataupu manaia (e foliga mai ia te aʻu) ua aliali mai, lea o loʻo matou atinaʻeina Kirill Belov, ma lona lua, ina ua uma se suʻesuʻega umi o le tulafono a le Russian Federation e uiga i faiga faʻavae, i le atinaʻe lea ou te galue ai, e tusa ma le lua laisene na faʻaalia. Wolfram Mathematica.

Ae ou te lei agai i luma i le autu o lau lauga, ou te fia matauina le lelei o le faatulagaga o le faamoemoe. O le itulau asiasi a le konafesi e faʻaaogaina ai se ata o le Kazan Cathedral. O le falesa o se tasi o mataaga autu o St. Petersburg ma e matua manino lava le vaaia mai le hall lea na faia ai le konafesi.

Wolfram Mathematica i le Geophysics

I le ulufale atu i le Iunivesite o le Tamaoaiga a le Setete o St. Petersburg, na feiloai ai tagata auai e fesoasoani mai tamaiti aoga - latou te leʻi faatagaina i latou e leiloa. I le taimi o le resitalaina, na tuʻuina atu ai ni meaʻai laiti (se meataalo - o se faʻamaʻi moli, se peni, mea faʻapipiʻi ma faʻailoga Wolfram). Sa aofia ai foi le malologa o le aoauli ma le kofe i le faasologa o fonotaga. Ua uma ona ou matauina e uiga i kofe suamalie ma pai i luga o le puipui o le vaega - e lelei le au kuka. Faatasi ai ma lenei vaega folasaga, ou te fia faamamafa atu o le mea na tupu lava ia, lona faatulagaga ma le nofoaga ua uma ona aumaia ai lagona lelei.

O le lipoti na saunia e aʻu ma Kirill Belov e taʻua o le "Faʻaaogaina o Wolfram Mathematica e foia ai faʻafitauli i le geophysics faʻaoga. Su'esu'ega fa'apitoa o fa'amaumauga seismic po'o "mea na tafe ai vaitafe anamua." O le anotusi o le lipoti e aofia ai vaega e lua: muamua, o le faʻaogaina o algorithms o loʻo maua i totonu Wolfram Mathematica mo le suʻesuʻeina o faʻamatalaga faʻafanua, ma lona lua, o le auala lea e tuʻu ai faʻamatalaga faʻafanua i totonu o Wolfram Mathematica.

Su'esu'ega seismic

Muamua e tatau ona e faia se tafaoga puupuu i le geophysics. Geophysics o le saienisi lea e suʻesuʻeina uiga faaletino o maʻa. Ia, talu ai o maʻa e iai mea eseese: eletise, mageta, elastic, o loʻo i ai auala tutusa o le geophysics: suʻesuʻega eletise, suʻesuʻega faʻamaneta, suʻesuʻeina o seismic ... I le faʻamatalaga o lenei tusiga, o le a naʻo le faʻatalanoaina o le suʻega o le seismic i nisi auiliiliga. O le su'esu'eina o seismic o le auala autu lea e su'e ai le suauu ma le kesi. O le metotia e faʻavae i luga o le faʻamalosi o faʻamalosi faʻamalosi ma mulimuli ane faʻamaumauga o le tali mai maʻa o loʻo fatuina le nofoaga suʻesuʻe. E fa'aoso fa'atete'e i luga o le lau'ele'ele (fa'atasi ai ma le dynamite po'o mea e le pa'u e fa'aoso ai le tetete) po'o le sami (fa'atasi ai ma fana ea). E fa'asolo atu fa'atete'e fa'ama'i e ala i le ma'a papa, e fa'afo'i ma fa'aalia i tua'oi o fa'amafu ma mea 'ese'ese. O galu atagia e toe foʻi i luga ma faʻamauina e geophones i luga o le eleele (e masani lava o masini eletise e faʻavae i luga o le gaioiga o se maneta o loʻo taofia i totonu o se coil) poʻo le hydrophones i le sami (faʻavae i le piezoelectric effect). I le taimi e oʻo mai ai galu, e mafai e se tasi ona faʻamasino le loloto o faʻafanua faʻafanua.

Mea faigaluega toso vaa seismic
Wolfram Mathematica i le Geophysics

O le fana ea e fa'aosofia ai le tete'e
Wolfram Mathematica i le Geophysics

O galu e ui atu i le papa ma e faamaumauina i le hydrophones
Wolfram Mathematica i le Geophysics

Va'a su'esu'e su'esu'ega fa'apitonu'u "Ivan Gubkin" i le uafu latalata i le Alalaupapa Blagoveshchensky i St. Petersburg
Wolfram Mathematica i le Geophysics

Fa'ata'ita'iga fa'ailoga mafui'e

E eseese uiga faaletino o papa. Mo le su'esu'eina o le masi'i, e taua tele mea fa'amama - o le saoasaoa o le fa'asalalauina o tete ma le mamafa. Afai e lua laulau e tutusa pe tutusa meatotino, o le galu "o le a le matauina" le tuaoi i le va oi latou. Afai e ese le saosaoa o le galu i luga o laulau, ona tupu ai lea o le ata i le tuaoi o laulau. O le tele o le eseesega i meatotino, o le sili atu foi lea o le malosi o le ata. O lona malosi o le a fa'amoemoeina e le fa'atusa fa'atusa (rc):

Wolfram Mathematica i le Geophysics

o le ρ o le mamafa o papa, o le saosaoa o le galu, 1 ma le 2 o loʻo faʻaalia ai le pito i luga ma le pito i lalo.

O se tasi o fa'ata'ita'iga fa'ata'ita'iga sili ona faigofie ma masani ona fa'aaogaina o le fa'ata'ita'iga fa'asolosolo, pe a fa'atusaina le fa'amaumau fa'asologa o seismic o se fa'ai'uga o le fa'atupuina o se fa'asologa o fa'asologa o fa'ata'ita'iga fa'atasi ma se pulupulu su'esu'e:

Wolfram Mathematica i le Geophysics

o fea s(t) - seismic trace, i.e. mea uma na fa'amauina e se hydrophone po'o se geophone i se taimi fa'amaumau, w(t) - o le faailo na faia e le fana ea, n(t) - pisa fa'afuase'i.

Se'i tatou fa'atatauina se su'ega seismic synthetic e fai ma fa'ata'ita'iga. O le a matou faʻaogaina le Ricker pulse, faʻaaoga lautele i suʻesuʻega seismic, e fai ma faʻailoga muamua.

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]

Uluai lagona seismic
Wolfram Mathematica i le Geophysics

O le a matou setiina ni tuaoi se lua i le loloto o le 300 ms ma le 600 ms, ma o le faʻatusatusaga o ata o le a avea ma numera faʻafuaseʻi.

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]]

Fa'asologa o fa'asologa o mafaufauga
Wolfram Mathematica i le Geophysics

Sei o tatou fa'atatau ma fa'aali le fa'asologa o le mafui'e. Talu ai e eseese fa'ailoga o le fa'atusa, tatou te maua ai ni fa'ata'ita'iga se lua i luga o fa'asologa o le matete.

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]]

Ala fa'atusa
Wolfram Mathematica i le Geophysics

Mo lenei faʻataʻitaʻiga, e manaʻomia le faia o se faʻaagaga - o le mea moni, o le loloto o le laulau e faʻamoemoeina, ioe, i mita, ma o le faʻatusatusaina o le faʻasologa o le seismic e tupu mo le taimi. E sili atu ona sa'o le setiina o le loloto i mita ma fuafua taimi e taunu'u mai ai ma le iloa o le saosaoa i totonu o fa'afanua. I lenei tulaga, ou te setiina loa le laulau i luga o le taimi.

Afai tatou te talanoa e uiga i suʻesuʻega fanua, ona o se taunuuga o ia matauina o se numera tele o faasologa taimi tutusa (seismic traces) ua faamaumauina. Mo se faʻataʻitaʻiga, pe a suʻesuʻeina se 'upega tafaʻilagi 25 kilomita le umi ma 15 kilomita le lautele, lea, o se taunuuga o le galuega, o faʻailoga taʻitasi e faʻaalia ai se sela e fuaina 25x25 mita (o sea cell e taʻua o se talone), o le faʻamaumauga faʻamaumauga mulimuli o le a aofia ai le 600000 faʻailoga. Faʻatasi ai ma se taimi faʻataʻitaʻiga o le 1 ms ma se taimi puʻeina o le 5 sekone, o le faila faʻamaumauga mulimuli o le a sili atu i le 11 GB, ma o le voluma o le mea muamua "mata" e mafai ona selau o gigabytes.

Auala e galulue ai ma i latou Wolfram Mathematica?

Faʻapipiʻi GeologyIO

Na amata le atinaʻeina o le afifi lomiga i luga o le puipui VK o le vaega lagolago e tautala Rusia. Fa'afetai i tali a le nu'u, na vave maua ai se fofo. Ma o se taunuuga, na tupu aʻe i se atinaʻe ogaoga. E fetaui pou puipui a le Wolfram Community Na fa'ailogaina fo'i e fa'atonu. I le taimi nei, o loʻo lagolagoina e le afifi le galulue faʻatasi ma ituaiga faʻamaumauga o loʻo faʻaaogaina malosi i le alamanuia faʻafanua:

  1. fa'aulufale mai o fa'amaumauga o fa'afanua i fa'asologa o le ZMAP ma le IRAP
  2. fa'aulufaleina mai o fua i vaieli fa'atulagaina LAS
  3. fa'aulufalega ma fa'aulufaleina o faila faila SEGY

Ina ia faʻapipiʻi le afifi, e tatau ona e mulimuli i faʻatonuga i luga o le itulau download o le afifi faʻapipiʻi, i.e. fa'atino le code lea i so'o se Mathematica api:

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

A maeʻa lea o le a faʻapipiʻi le afifi i le faila le lelei, o le ala e mafai ona maua e pei ona taua i lalo:

FileNameJoin[{$UserBasePacletsDirectory, "Repository"}]

Mo se faʻataʻitaʻiga, o le a matou faʻaalia le gafatia autu o le afifi. O le valaau e faia masani mo afifi i le gagana Wolfram:

Get["GeologyIO`"]

Ua atia'e le afifi e fa'aaoga Wolfram Workbench. O lenei mea e mafai ai ona e faʻatasi ma le galuega autu o le afifi ma faʻamaumauga, lea e tusa ai ma le faʻatulagaina o faʻamatalaga e le ese mai le faʻamaumauga a Wolfram Mathematica lava ia, ma tuʻuina atu le afifi ma faila suʻega mo le tagata masani muamua.

Wolfram Mathematica i le Geophysics

Wolfram Mathematica i le Geophysics

O se faila, aemaise lava, o le faila "Marmousi.segy" - o se faʻataʻitaʻiga faʻataʻitaʻiga o se vaega faʻafanua, lea na atiaʻe e le French Petroleum Institute. I le faʻaaogaina o lenei faʻataʻitaʻiga, e faʻataʻitaʻiina e le au atinaʻe a latou lava algorithms mo le faʻataʻitaʻiina o galu, faʻasologa o faʻamaumauga, suiga o le seismic trace, ma isi. O le faʻataʻitaʻiga Marmousi lava ia o loʻo teuina i totonu o le fale teu oloa mai le mea na sii mai ai le afifi lava ia. Ina ia maua le faila, taʻavale le code lea:

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

Fa'aulufale i'uga - mea SEGYData
Wolfram Mathematica i le Geophysics

O le SEGY format e aofia ai le teuina o faʻamatalaga eseese e uiga i faʻamatalaga. Muamua, o fa'amatalaga tusitusia nei. E aofia ai faʻamatalaga e uiga i le nofoaga o le galuega, igoa o kamupani na faia fua, ma isi. I la matou tulaga, o lenei ulutala e valaʻau i se talosaga ma le TextHeader ki. O se ulutala fa'apuupuu o tusitusiga:

Short[marmousi["TextHeader"]]

"O le seti faʻamaumauga a Marmousi na gaosia i le Inisetiute ... o le saoasaoa o le 1500 m / s ma le maualuga o le 5500 m / s)"

E mafai ona e fa'aalia le fa'ata'ita'iga moni fa'afanua e ala i le fa'aogaina o fa'ailoga mafui'e e fa'aaoga ai le ki "traces" (o se tasi o fa'ailoga o le afifi o ki e le ma'ale'ale mata):

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

Fa'ata'ita'iga Marmousi
Wolfram Mathematica i le Geophysics

I le taimi nei, o le afifi foi e mafai ai ona e utaina faʻamatalaga i vaega mai faila tetele, e mafai ai ona faʻagasolo faila e mafai ona oʻo atu i le sefulu gigabytes le tele. O galuega a le afifi e aofia ai foi galuega mo le auina atu i fafo o faʻamatalaga i le .segy ma faʻapipiʻi vaega i le pito o le faila.

Tuʻueseese, e taua le matauina o le gaioiga o le afifi pe a galue ma le faʻalavelave faʻalavelave o faila .segy. Talu ai e faʻatagaina oe e le gata e maua faʻailoga taʻitasi ma ulutala e faʻaaoga ai ki ma faʻasino igoa, ae faʻapea foi ona suia ona tusi lea i se faila. O le tele o fa'amatalaga fa'apitoa o le fa'atinoga a GeologyIO e sili atu i le lautele o lenei tusiga ma e ono mana'omia se fa'amatalaga tu'ufa'atasi.

Fa'atatauga o su'esu'ega fa'ase'e ile su'esu'ega seismic

O le mafai ona fa'aulufale mai fa'amatalaga seismic i Wolfram Mathematica e mafai ai ona e fa'aogaina galuega fa'atino fa'ailoga mo fa'amatalaga fa'ata'ita'i. Talu ai o fa'asologa ta'itasi o seismic o lo'o fa'atusalia ai se faasologa o taimi, o se tasi o meafaigaluega autu mo le su'esu'eina o ia mea o le su'esu'ega fa'apitoa. Faatasi ai ma mea e manaʻomia muamua mo le suʻesuʻeina o le faʻasologa o faʻamaumauga o faʻamaumauga seismic, e mafai ona tatou taʻua, mo se faʻataʻitaʻiga, mea nei:

  1. O ituaiga galu eseese e fa'aalia i le fa'avasegaina o alavai. O lenei mea e mafai ai ona e faʻamaonia galu aoga ma taofiofia galu faʻalavelave.
  2. O mea papa e pei o le porosity ma le saturation e mafai ona afaina ai le faʻasologa o taimi. O le mea lea e mafai ai ona iloa maa e sili ona lelei.
  3. O lapisi e eseese mafiafia e mafua ai fa'aletonu i laina fa'avevesi eseese.

O le manatu lona tolu o le mea autu lea i le talaaga o lenei tusiga. O lo'o i lalo se vaega fa'ailoga mo le fa'atatauina o fa'ailoga mafui'e i le tulaga o se fa'amea ma le mafiafia eseese - o se fa'ata'ita'iga tina. O lenei fa'ata'ita'iga e masani ona su'esu'eina i su'esu'ega mafui'e e va'ili'ili ai fa'alavelave fa'alavelave pe a fa'apea galu o lo'o atagia mai i le tele o fa'apa'aga o lo'o fa'apipi'i le tasi i le isi.

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]]

Fa'ata'ita'iga o le fa'apipi'iina
Wolfram Mathematica i le Geophysics

O le saosaoa o le galu i totonu o le tina e 4500 m / s, i fafo atu o le tina 4000 m / s, ma o le mamafa e faʻapea e tumau 2200 g / cm³. Mo se fa'ata'ita'iga fa'apea, matou te fa'atatauina fa'atusatusaga o fa'ata'ita'iga ma fa'ailoga mafui'e.

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]

Su'ega seismic mo le fa'ata'ita'iga tina
Wolfram Mathematica i le Geophysics

O le fa'asologa o fa'asologa o mafui'e o lo'o fa'aalia i lenei fa'atusa e ta'ua o se vaega mafui'e. E pei ona mafai ona e vaʻaia, o lona faʻamatalaga e mafai foi ona faia i luga o se tulaga faʻapitoa, talu ai o le geometry o galu faʻaalia e fetaui lelei ma le faʻataʻitaʻiga na faʻamaonia muamua. Afai e te suʻesuʻeina faʻamatalaga i auiliiliga, o le ae matauina o faʻailoga mai le 1 i le tusa ma le 30 e le eseese - o le ata mai le taualuga o le faʻavae ma mai lalo e le faʻafefe le tasi i le isi. Amata mai le 31st trace, o mafaufauga e amata ona faʻalavelave. Ma, e ui lava i le faʻataʻitaʻiga, o le faʻataʻitaʻiga coefficients e le suia faʻalava - o le seismic traces e suia lo latou malosi pe a suia le mafiafia o le faʻavae.

Sei o tatou mafaufau i le tele o mafaufauga mai le pito i luga o le faʻatulagaga. Amata mai le 60th auala, o le malosi o le mafaufau e amata ona faateleina ma i le 70th auala e sili atu. O le auala lea e faʻaalia ai le faʻalavelaveina o galu mai le taualuga ma le pito i lalo o faʻamau, e taʻitaʻia ai i nisi tulaga i faʻalavelave taua i le faʻamaumauga o le 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]

Kalafi o le amplitude o le galu ua atagia mai le pito i luga o le tina
Wolfram Mathematica i le Geophysics

E talafeagai pe a maualalo le faailo, e amata ona aliali mai le faʻalavelave i mafiafia faʻavae tetele, ma i le tulaga o se faʻailoga maualuga, faʻalavelave e tupu i mafiafia laiti. O le snippet code o loʻo mulimuli mai e fatuina ai se faʻailoga ma ala o le 35 Hz, 55 Hz ma le 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]

Se seti o fa'ailo fa'apogai ma alaleo o 35 Hz, 55Hz, 85Hz
Wolfram Mathematica i le Geophysics

E ala i le fa'atatauina o fa'ailoga mafui'e ma le fa'avasegaina o kalafi o fa'ata'ita'iga o galu tetele, e mafai ona tatou va'ava'ai ai mo alaleo eseese o lo'o va'aia ai se fa'aletonu i mafiafia fa'avae eseese.

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]

Kalafi o le amplitudes o le galu atagia mai le pito i luga o le tina mo laina eseese
Wolfram Mathematica i le Geophysics

O le mafai ona faia ni faaiuga e uiga i le mafiafia o le faʻavaeina mai iʻuga o suʻesuʻega seismic e matua aoga lava, aua o se tasi o galuega autu i suʻesuʻega suauʻu o le iloiloina lea o mea sili ona lelei mo le tuʻuina o se vaieli (e pei o vaega o loʻo i ai le faʻavaeina. mafiafia). E le gata i lea, i totonu o le vaega faʻafanua atonu o loʻo i ai mea o loʻo mafua ai se suiga tele i le mafiafia o le faʻavae. O le mea lea e avea ai su'esu'ega fa'apitoa o se meafaigaluega aoga mo le su'esu'eina. I le isi vaega o le mataupu o le a tatou iloiloina atili ai ia mea faitino.

Fa'amatalaga fa'ata'ita'i. O fea na e maua mai ai ma mea e te suʻeina i totonu?

O mea na iloiloina i le tusiga na maua i Siberia i Sisifo. O le itulagi, e pei ona silafia e tagata uma e aunoa ma se tuusaunoaga, o le vaega autu o le gaosiga o suauu o lo tatou atunuu. O le atinaʻeina malosi o tupe teu na amata i le itulagi i le 60s o le seneturi talu ai. Ole auala autu ole su'esu'ega ole suau'u ole su'esu'ega seismic. E manaia le tilotilo i ata satelite o lenei teritori. I se laʻititi laʻititi, e mafai ona e matauina se numera tele o taufusi ma vaituloto; e ala i le faʻalauteleina o le faʻafanua, e mafai ona e vaʻaia nofoaga e viliina ai vaieli, ma e ala i le faʻalauteleina o le faʻafanua i le tapulaʻa, e mafai foi ona e iloa le faʻamamaina o faʻamatalaga faʻatasi ai ma seismic. sa fa'atinoina ni fa'amatalaga.

Ata Satelite o fa'afanua Yandex - Noyabrsk city area
Wolfram Mathematica i le Geophysics

Se feso'ota'iga o vaieli i se tasi o fanua
Wolfram Mathematica i le Geophysics

O maa o loʻo i ai le suauu o Western Siberia e tupu i le tele o loloto - mai le 1 km i le 5 km. O le tele o maa o loʻo i ai le suauu na fausia i le Jurassic ma Cretaceous taimi. O le vaitaimi o le Jurassic atonu e iloa e le toatele mai le ata o le igoa lava e tasi. Tau Jurassic sa matua ese lava mai le taimi nei. O le Encyclopedia Britannica o loʻo i ai se faasologa o paleomaps e faʻaalia ai vaitau taʻitasi.

Tuʻu faʻamalosi
Wolfram Mathematica i le Geophysics
vaitaimi Jurassic
Wolfram Mathematica i le Geophysics

Faamolemole ia matau i taimi o Jurassic, o le teritori o Siberia i Sisifo o se talafatai o le sami (fanua e sopoia e vaitafe ma se sami papaʻu). Talu ai sa lelei le tau, e mafai ona tatou manatu o se laufanua masani o lena taimi e pei o lenei:

Jurassic Siberia
Wolfram Mathematica i le Geophysics

I lenei ata, o le mea e taua ia i tatou e le o le tele o manu ma manulele, ae o le ata o le vaitafe i tua. O le vaitafe o le mea lava lea e tasi na matou tu ai muamua. O le mea moni o le gaioiga o vaitafe e mafai ai ona faʻaputu lelei maa oneone, lea o le a avea ma faatanoa mo le suauu. O nei faatanoa e mafai ona i ai se foliga uiga ese, lavelave (pei o se vaitafe) ma e fesuisuiaʻi le mafiafia - i tafatafa o auvai e laʻititi le mafiafia, ae latalata i le ogatotonu o le alavai poʻo i vaega o loʻo faʻateleina. O lea la, o vaitafe ua fausia i le Jurassic ua i ai nei i le loloto o le tusa ma le tolu kilomita ma o le autu o se sailiga mo faatanoa suauu.

Fa'amatalaga fa'ata'ita'i. Fa'atonuga ma fa'aaliga

Sei o tatou vave faia se faʻaagaga e uiga i mea faʻafefe o loʻo faʻaalia i totonu o le tusiga - ona o le mea moni o le aofaʻi o faʻamatalaga e faʻaaogaina mo le suʻesuʻega e taua tele - naʻo se vaega o le seti muamua o faʻasologa o seismic o loʻo aofia i totonu o le tusitusiga o le tusiga. O lenei mea e mafai ai e soʻo se tasi ona toe faia faʻatusatusaga o loʻo i luga.

Pe a galue ma faʻamatalaga seismic, e masani ona faʻaaogaina e le geophysicist polokalama faʻapitoa (e iai le tele o taʻitaʻi o pisinisi o loʻo faʻaaogaina ma le malosi, mo se faʻataʻitaʻiga Petrel poʻo Paradigm), lea e mafai ai ona e suʻesuʻeina ituaiga eseese o faʻamatalaga ma e iai se faʻaoga faʻataʻitaʻi talafeagai. E ui lava i mea faigofie uma, o nei ituaiga o polokalama e iai foi a latou faʻafitauli - mo se faʻataʻitaʻiga, o le faʻatinoina o algorithms faʻaonaponei i faʻamaumauga faʻamautu e manaʻomia le tele o le taimi, ma o avanoa mo le faʻaogaina o faʻatusatusaga e masani lava ona faʻatapulaʻaina. I se tulaga faapena, e matua faigofie lava le faʻaogaina o masini komepiuta komepiuta ma gagana maualuga polokalame, lea e faʻatagaina ai le faʻaogaina o le lautele algorithmic faavae ma, i le taimi lava e tasi, faia le tele o masani. O le mataupu faavae lea e faʻaaogaina e galue ai ma faʻamaumauga seismic i Wolfram Mathematica. E le talafeagai le tusiaina o le tele o galuega mo galuega faʻafesoʻotaʻi ma faʻamaumauga - e sili atu le taua o le faʻamautinoaina o le utaina mai se faʻasalalauga masani, faʻaogaina algorithms manaʻomia ia i latou ma toe faʻafoʻi atu i se faatulagaga fafo.

I le mulimuli ai i le polokalame fuafuaina, o le a matou utaina faʻamaumauga muamua o le seismic ma faʻaalia i totonu 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]

O faʻamaumauga na sii mai ma faʻaulufale mai i lenei auala o auala na faʻamaumau i luga o se eria e tusa ma le 10 i le 5 kilomita. Afai e maua faʻamatalaga e faʻaaoga ai le tolu-dimensional seismic suʻesuʻega (galu e le o faʻamauina i luga o faʻamatalaga geophysical taʻitoʻatasi, ae i luga o le eria atoa i le taimi e tasi), e mafai ona maua pusa faʻamaumauga seismic. O mea ia e tolu-dimensional, vaega tu'usa'o ma fa'alava e mafai ai se su'esu'ega auiliili o le si'osi'omaga fa'afanua. I le faʻataʻitaʻiga na iloiloina, o loʻo matou feagai ma faʻamatalaga tolu-dimensional. E mafai ona tatou maua nisi faʻamatalaga mai le ulutala tusitusiga, pei o lenei

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

C 1 O LE FAILA LENEI MO LE SU'ESU'EGA GEOLOGYIO PACKAGE
C 2
C 3
C 4
C 5 ASO IGOA FA'AASOGA: WOLFRAM USER
I 6 SU'ESU'EGA IGOA: I SE MEA I SIBERIA
C 7 ITU FAIGA FAI 3D SEISMIC VOLUME
C 8
C 9
C10 Z VAEGA: MUAMUA 2200M MULI 2400M

O lenei seti faʻamaumauga o le a lava mo i matou e faʻaalia ai vaega autu o le auiliiliga o faʻamaumauga. O fa'ailoga i le faila o lo'o fa'amauina fa'asolosolo ma e foliga ta'itasi e pei o le ata o lo'o i lalo - o le tufatufaina atu lea o le tele o galu fa'aalia i luga o le axis vertical (depth 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]

O se tasi o vaega o seismic fa'ailoga
Wolfram Mathematica i le Geophysics

O le iloaina o le tele o fa'ailoga o lo'o iai i itu ta'itasi o le nofoaga su'esu'e, e mafai ona e fa'atupuina se fa'asologa o fa'amaumauga e tolu-dimensional ma fa'aalia i le fa'aaogaina o le galuega Image3D[]

traces=seismic3DSEGY["traces"];
startIL=1050;EndIL=2000;stepIL=2; (*координата Х начала и конца съёмки и шаг трасс*)
startXL=1165;EndXL=1615;stepXL=2; (*координата Y начала и конца съёмки и шаг трасс*)
numIL=(EndIL-startIL)/stepIL+1;   (*количество трасс по оис Х*)
numXL=(EndXL-startXL)/stepIL+1;   (*количество трасс по оис Y*)
Image3D[ArrayReshape[Abs[traces/Max[Abs[traces[[All,1;;;;4]]]]],{numIL,numXL,101}],ViewPoint->{-1, 0, 0},Background->RGBColor[0,0,0]]

Ata 3D o se pusa fa'amaumauga o seismic. (Tu'u sa'o - loloto)
Wolfram Mathematica i le Geophysics

Afai o foliga fa'alenu'u o tului e fa'atupu ai ni fa'alavelave mata'utia mafui'e, ona fa'aogaina lea o meafaigaluega fa'aaliga ma manino. "E le taua" vaega o le pueina e mafai ona le vaaia, ae naʻo mea faʻaletonu e iloa. I Wolfram Mathematica e mafai ona faia lenei mea i le faʻaaogaina Opacity[] и 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]

Ata fa'amaufa'ailoga seismic fa'aogaina o le Opacity[] ma le Raster3D[] galuega Wolfram Mathematica i le Geophysics

E pei o le faʻataʻitaʻiga faʻapipiʻi, i luga o vaega o le uluaʻi pusa e mafai e se tasi ona iloa nisi o tuaoi faʻafanua (laupapa) faʻatasi ai ma suiga fesuisuiai.

O le meafaigaluega autu mo suʻesuʻega faʻapitoa o le Fourier transform. Faatasi ai ma lana fesoasoani, e mafai ona e suʻesuʻeina le amplitude-frequency spectrum o faʻasologa taʻitasi poʻo se vaega o faʻasologa. Ae ui i lea, a maeʻa ona tuʻuina atu faʻamatalaga i le faʻasologa o taimi, o faʻamatalaga e leiloa pe o a taimi (faitau i le loloto) o suiga ole taimi. Ina ia mafai ona vaʻaia suiga faʻailoga i luga o le taimi (loloto) axis, o le faʻaogaina o le Fourier faʻamalama ma le faʻaleagaina o le galu. O lenei tusiga e faʻaaogaina le faʻaleagaina o galu. O tekonolosi su'esu'ega Wavelet na amata fa'aaoga malosi i su'esu'ega seismic i le 90s. O le lelei i luga o le suiga o Fourier faʻamalama e manatu e sili atu le faʻatulagaina o taimi.

I le fa'aaogaina o le vaega o lo'o i lalo, e mafai ona e fa'avasegaina se tasi o fa'ailoga mafui'e i vaega ta'itasi:

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]

Fa'avasegaina o se fa'asologa i vaega
Wolfram Mathematica i le Geophysics

Ina ia su'esu'e pe fa'afefea ona tufatufa atu le malosi o le mafaufau i taimi eseese e taunu'u mai ai galu, e fa'aaogaina scalograms (fa'atusa ma se spectrogram). I le avea ai o se tulafono, i le faʻatinoga e le manaʻomia le suʻeina o vaega uma. E masani lava, e filifilia vaega maualalo, ogatotonu ma maualuga.

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. I'uga o galuega WaveletScalogram[]
Wolfram Mathematica i le Geophysics

Ole Gagana Wolfram e fa'aogaina le galuega mo le suiga ole galu Fa'aliliuga Fa'aauau[]. Ma o le faʻaaogaina o lenei galuega i le seti atoa o faʻasologa o le a faʻatinoina e faʻaaoga ai le galuega laulau[]. O iinei e taua le matauina o se tasi o le malosi o Wolfram Mathematica - o le mafai ona faʻaoga tutusa Laulau Fa'atusa[]. I le faʻataʻitaʻiga o loʻo i luga, e leai se manaʻoga mo le tutusa - o le tele o faʻamaumauga e le tele, ae pe a galue ma faʻataʻitaʻiga faʻamaumauga o loʻo i ai le fiaselau afe o faʻailoga, o se mea e manaʻomia.

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

A maeʻa ona faʻaogaina le galuega Fa'aliliuga Fa'aauau[] O fa'amaumauga fou e aliali mai e fetaui ma alaleo filifilia. I le faʻataʻitaʻiga o loʻo i luga, o nei alalaupapa e: 38Hz, 33Hz, 27Hz. O le filifiliga o alalaupapa e masani ona faia i luga o le faʻavae o suʻega - latou te maua faʻafanua aoga mo faʻasalalauga faʻasalalau eseese ma filifili le mea e sili ona faʻamatalaga mai le manatu o se geologist.

Afai e te manaʻomia le faʻasoaina o taunuʻuga ma au uo pe tuʻuina atu i le tagata faʻatau, e mafai ona e faʻaogaina le SEGYExport [] galuega a le GeologyIO package

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];

Faatasi ai ma le tolu o nei pusa (maualalo, ogatotonu, ma vaega maualuga), o le faʻafefiloi o le RGB e masani ona faʻaaogaina e vaʻaia faʻatasi ai faʻamatalaga. O vaega taʻitasi e tuʻuina atu lona lava lanu - mumu, lanumeamata, lanumoana. I Wolfram Mathematica e mafai ona faia lenei mea e faʻaaoga ai le galuega ColorCombine[].

O le taunuuga o ata ia e mafai ona faia ai fa'amatalaga fa'afanua. O meanders o loʻo faʻamauina i luga o le vaega e mafai ai ona faʻamalamalamaina paleochannels, lea e sili atu ona avea ma faatanoa ma o loʻo i ai faʻaagaga suauu. O le suʻesuʻeina ma le auʻiliʻiliga o analogues faʻaonaponei o sea vaitafe e mafai ai ona tatou fuafuaina vaega sili ona manuia o meanders. O alāvai lava ia e fa'ailoaina i papa mafiafia o ma'a oneone fa'avasega lelei ma ose faatanoa lelei mo le suau'u. O vaega i fafo atu o le "lace" anomalies e talitutusa lava ma le teuina o lologa i aso nei. Ole fa'aputuga ole lologa o lo'o fa'atusalia ma'a ele ma e le aoga le viliina i totonu o sone nei.

vaega RGB ole pusa fa'amaumauga. I le ogatotonu (i le itu agavale o le ogatotonu) e mafai ona e suʻeina le vaitafe feʻaveaʻi.
Wolfram Mathematica i le Geophysics
vaega RGB ole pusa fa'amaumauga. I le itu tauagavale e mafai ona e suʻeina le vaitafe feʻaveaʻi.
Wolfram Mathematica i le Geophysics

I nisi tulaga, o le tulaga lelei o fa'amaumauga seismic e mafai ai ona maua ata sili atu ona manino. E fa'alagolago lea i le faiga o galuega i le fanua, o meafaigaluega e fa'aogaina e le fa'aitiitiga o le pisa algorithm. I ia tulaga, e le gata o vaevaega o vaitafe o loʻo vaaia, ae faʻapea foʻi ma lologa uma lautele.

RGB fa'afefiloi o vaega e tolu o se pusa fa'amaumauga mase'i (vaega fa'asaga). Le loloto e tusa ma le 2 km.
Wolfram Mathematica i le Geophysics
Ata satelite o le Vaitafe Volga latalata Saratov
Wolfram Mathematica i le Geophysics

iʻuga

O Wolfram Mathematica e mafai ai ona e suʻesuʻeina faʻamaumauga o le seismic ma foia faʻafitauli faʻatatau e fesoʻotaʻi ma suʻesuʻega minerale, ma o le GeologyIO package e faʻafaigofie ai lenei faiga. O le faʻatulagaina o faʻamaumauga o seismic e pei o le faʻaaogaina o auala faʻapipiʻi e faʻavave ai faʻatusatusaga (Laulau Fa'atusa[], Fa'ata'ita'i[],…) e matua'i lelei ma fa'atagaina oe e fa'agasolo le tele o fa'amaumauga. I se tulaga tele, o loʻo faʻafaigofieina e faʻamaumauga faʻamaumauga o le GeologyIO package. I le auala, e mafai ona faʻaaogaina le afifi e le gata i le faʻaogaina o suʻesuʻega seismic. Toeitiiti lava tutusa ituaiga o faʻamatalaga o loʻo faʻaaogaina i le eleele penetrating radar ma seismology. Afai e iai ni au fautuaga ile faʻaleleia o le taunuuga, o faʻamatalaga faʻamaonia algorithms mai le Wolfram Mathematica arsenal e faʻaoga i ia faʻamatalaga, pe afai e i ai ni au faʻamatalaga faitio, faʻamolemole tuu se faamatalaga.

puna: www.habr.com

Faaopoopo i ai se faamatalaga