ʻO Wolfram Mathematica ma Geophysics

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Hōʻike

Ua kākau ʻia kēia memo ma hope o ka ʻaha kūkā ʻO Wolfram Russian Technology Conference a aia kahi hōʻuluʻulu o ka hōʻike aʻu i hāʻawi ai. Ua mālama ʻia ka hanana i Iune ma St. Petersburg. Ke noʻonoʻo nei e hana wau i kahi poloka mai ka kahua hālāwai kūkā, ʻaʻole hiki iaʻu ke ʻae i ka hele ʻana i kēia hanana. Ma 2016 a me 2017, ua hoʻolohe au i nā hōʻike o ka hālāwai kūkā, a i kēia makahiki ua hāʻawi wau i kahi hōʻike. ʻO ka mea mua, ua ʻike ʻia kahi kumuhana hoihoi (me he mea lā iaʻu), a mākou e hoʻomohala nei Kirill Belov, a ʻo ka lua, ma hope o ka noiʻi lōʻihi ʻana i ke kānāwai o ka Russian Federation e pili ana i nā kulekele hoʻopaʻi, ma ka ʻoihana kahi aʻu e hana ai, ʻoi aku ka nui o nā laikini ʻelua. ʻO Wolfram Mathematica.

Ma mua o ka neʻe ʻana i ke kumuhana o kaʻu haʻiʻōlelo, makemake wau e ʻike i ka hoʻonohonoho maikaʻi ʻana o ka hanana. Hoʻohana ka ʻaoʻao kipa o ka ʻaha kūkā i kahi kiʻi o ka Kazan Cathedral. ʻO ka halepule kekahi o nā hiʻohiʻona nui o St.

ʻO Wolfram Mathematica ma Geophysics

Ma ka puka komo i ke Kulanui ʻOihana Moku'āina ʻo St. Petersburg, ua hui ʻia nā mea komo e nā mea kōkua mai waena o nā haumāna - ʻaʻole lākou i ʻae iā lākou e nalowale. I ka wā o ka hoʻopaʻa inoa ʻana, hāʻawi ʻia nā mea hoʻomanaʻo liʻiliʻi (kahi pāʻani - he spike uila, peni, nā mea hoʻopaʻa me nā hōʻailona Wolfram). Ua hoʻokomo pū ʻia ka ʻaina awakea a me ka hoʻomaha kofe i ka papa kūkā. Ua ʻike mua wau e pili ana i ka kofe maikaʻi a me nā pies ma ka pā o ka hui - maikaʻi nā chefs. Me kēia ʻāpana hoʻomaka, makemake wau e hoʻoikaika i ka hanana ponoʻī, kona ʻano a me kona wahi e lawe mai nei i nā manaʻo maikaʻi.

ʻO ka hōʻike i hoʻomākaukau ʻia e aʻu a me Kirill Belov ua kapa ʻia ʻo "Ke hoʻohana nei iā Wolfram Mathematica e hoʻoponopono i nā pilikia i ka geophysics noiʻi. Ka nānā ʻana i nā ʻikepili seismic a i ʻole "kahi i holo ai nā muliwai kahiko." ʻO ka ʻike o ka hōʻike e uhi i ʻelua mau ʻāpana: ʻo ka mea mua, ka hoʻohana ʻana i nā algorithms i loaʻa ma ʻO Wolfram Mathematica no ke kālailai ʻana i ka ʻikepili geophysical, a ʻo ka lua, eia ke ʻano o ka hoʻokomo ʻana i ka ʻikepili geophysical i loko o Wolfram Mathematica.

Ka ʻimi ʻana i ka seismic

Pono ʻoe e hana i kahi huakaʻi pōkole i ka geophysics. ʻO Geophysics ka ʻepekema e aʻo ana i nā waiwai kino o nā pōhaku. ʻAe, no ka mea he ʻokoʻa nā waiwai o nā pōhaku: uila, magnetic, elastic, aia nā ʻano like o ka geophysics: electro prospecting, magnetic prospecting, seismic prospect... ʻO ka ʻimi seismic ke ʻano nui o ka ʻimi ʻana i ka aila a me ke kinoea. Hoʻokumu ʻia ke ʻano hana i ka hoʻoulu ʻia o nā haʻalulu elastic a me ka hoʻopaʻa ʻana o ka pane mai nā pōhaku i haku i ka wahi haʻawina. Hauʻoli nā haʻalulu ma ka ʻāina (me nā dynamite a i ʻole nā ​​kumu haʻalulu pahū ʻole o nā haʻalulu elastic) a i ʻole ma ke kai (me nā pū ea). Hoʻolaha ʻia nā haʻalulu elastic ma o ka nui o ka pōhaku, e hoʻohuli ʻia a ʻike ʻia ma nā palena o nā papa me nā waiwai like ʻole. Hoʻi hou nā nalu i hoʻohālikelike ʻia i ka ʻili a hoʻopaʻa ʻia e nā geophones ma ka ʻāina (ʻo ia ka mea maʻamau i nā mea electrodynamic e pili ana i ka neʻe ʻana o kahi magnet i hoʻokuʻu ʻia i loko o kahi coil) a i ʻole hydrophones i ke kai (ma muli o ka hopena piezoelectric). I ka hiki ʻana mai o nā nalu, hiki i kekahi ke hoʻoholo i ka hohonu o nā papa honua.

Lako huki moku seismic
ʻO Wolfram Mathematica ma Geophysics

Hoʻoulu ka pū ea i nā haʻalulu elastic
ʻO Wolfram Mathematica ma Geophysics

Hele nā ​​nalu i ka pōhaku a hoʻopaʻa ʻia e nā hydrophones
ʻO Wolfram Mathematica ma Geophysics

ʻO ka moku noiʻi noiʻi Geophysical "Ivan Gubkin" ma ka uapo kokoke i ka Blagoveshchensky Bridge ma St.
ʻO Wolfram Mathematica ma Geophysics

Ke hoʻohālike hōʻailona seismic

He ʻokoʻa ko nā pōhaku. No ka ʻimi seismic, he mea nui ka waiwai elastic - ka wikiwiki o ka hoʻolaha ʻana o nā haʻalulu elastic a me ka nui. Inā loaʻa i nā ʻāpana ʻelua nā waiwai like a like paha, a laila "ʻaʻole ʻike" ka nalu i ka palena ma waena o lākou. Inā ʻokoʻa ka wikiwiki o ka nalu ma nā papa, a laila e ʻike ʻia ka noʻonoʻo ma ka palena o nā papa. ʻOi aku ka ʻokoʻa o nā waiwai, ʻoi aku ka ikaika o ka noʻonoʻo. E hoʻoholo ʻia kona ikaika e ka huina hoʻohālikelike (rc):

ʻO Wolfram Mathematica ma Geophysics

kahi o ρ ka mānoanoa pōhaku, ν ka wikiwiki o ka nalu, 1 a me 2 e kuhikuhi i ka papa luna a me lalo.

ʻO kekahi o nā hiʻohiʻona hōʻailona seismic maʻalahi a hoʻohana pinepine ʻia ʻo ia ke kumu hoʻohālikelike, ke hōʻike ʻia ke ʻano seismic i hoʻopaʻa ʻia ma ke ʻano he hopena o ka hoʻohui ʻana o ke kaʻina o nā coefficient noʻonoʻo me kahi pulse probing.

ʻO Wolfram Mathematica ma Geophysics

ma hea s(t) - he seismic trace, i.e. nā mea a pau i hoʻopaʻa ʻia e kahi hydrophone a i ʻole geophone i ka manawa hoʻopaʻa paʻa, w(t) - ka hōʻailona i hana ʻia e ka pū ea, n(t) - walaʻau leo.

E helu kākou i kahi la'ana seismic synthetic. E hoʻohana mākou i ka pulse Ricker, i hoʻohana nui ʻia i ka ʻimi seismic, ma ke ʻano he hōʻailona mua.

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]

Hoʻomaka mua seismic impulse
ʻO Wolfram Mathematica ma Geophysics

E hoʻonoho mākou i ʻelua mau palena ma ka hohonu o 300 ms a me 600 ms, a ʻo nā helu noʻonoʻo he helu maʻamau.

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]]

Ke kaʻina o nā mea hoʻohālikelike
ʻO Wolfram Mathematica ma Geophysics

E helu a hōʻike i ke ʻano seismic. No ka mea he ʻokoʻa nā hōʻailona hoʻohālikelike, loaʻa iā mākou ʻelua mau manaʻo noʻonoʻo ʻana ma ke ʻano 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]]

Ala hoʻohālike
ʻO Wolfram Mathematica ma Geophysics

No kēia hiʻohiʻona, pono e hana i kahi hoʻopaʻa - ʻo ka ʻoiaʻiʻo, ua hoʻoholo ʻia ka hohonu o nā papa, ʻoiaʻiʻo, i nā mika, a ʻo ka helu ʻana o ka seismic trace e loaʻa ana no ka manawa domain. ʻOi aku ka pololei o ka hoʻonohonoho ʻana i ka hohonu i nā mika a helu i nā manawa hōʻea me ka ʻike i ka wikiwiki o nā papa. I kēia hihia, hoʻonohonoho koke wau i nā papa ma ka axis manawa.

Inā mākou e kamaʻilio e pili ana i ka noiʻi kahua, a ma muli o ia mau ʻike ʻana, ua hoʻopaʻa ʻia kahi helu nui o nā manawa like (seismic traces). No ka laʻana, i ka wā e aʻo ai i kahi pūnaewele 25 km ka lōʻihi a me 15 km ākea, kahi, ma muli o ka hana, e hōʻike ana kēlā me kēia meheu i kahi cell i ana ʻia he 25x25 mika (kapa ʻia kēlā cell he bin), ʻo ka ʻikepili hope loa he 600000 traces. Me ka manawa hoʻohālike o 1 ms a me ka manawa hoʻopaʻa ʻana o 5 kekona, ʻoi aku ka nui o ka faila ʻikepili hope ma mua o 11 GB, a ʻo ka nui o ka mea kumu "raw" hiki ke lilo i mau haneli gigabytes.

Pehea e hana pū ai me lākou ʻO Wolfram Mathematica?

Hoʻolapala GeologyIO

Ua hoʻomaka ka hoʻomohala ʻana o ka pūʻolo pilikia ma ka pā VK o ka hui kākoʻo ʻōlelo Lūkini. Mahalo i nā pane o ke kaiāulu, ua loaʻa koke kahi hoʻonā. A ʻo ka hopena, ua ulu aʻe i kahi ulu koʻikoʻi. Pili ana pou paia kaiaulu Wolfram Ua hōʻailona ʻia e nā mea hoʻoponopono. I kēia manawa, kākoʻo ka pūʻolo i ka hana ʻana me nā ʻano ʻikepili i hoʻohana ikaika ʻia i ka ʻoihana geological:

  1. lawe mai i ka ʻikepili palapala ma nā ʻano ZMAP a me IRAP
  2. lawe mai i nā ana ma nā pūnāwai LAS format
  3. hoʻokomo a me ka hoʻopuka ʻana o nā faila seismic SEGY

No ka hoʻouka ʻana i ka pūʻolo, pono ʻoe e hahai i nā ʻōlelo aʻoaʻo ma ka ʻaoʻao download o ka pūʻolo i hui ʻia, ʻo ia. e hoʻokō i kēia code ma kekahi puke puke Mathematica:

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

Ma hope o ka hoʻokomo ʻia ʻana o ka pūʻolo i loko o ka waihona paʻamau, ke ala e hiki ai ke loaʻa penei:

FileNameJoin[{$UserBasePacletsDirectory, "Repository"}]

Ma keʻano he laʻana, e hōʻike mākou i nā mana nui o ka pūʻolo. Hana ʻia ke kelepona no nā pūʻolo ma ka ʻōlelo Wolfram:

Get["GeologyIO`"]

Kūkulu ʻia ka pūʻolo me ka hoʻohana ʻana ʻO Wolfram Workbench. ʻAe kēia iā ʻoe e hele pū me ka hana nui o ka puʻupuʻu me nā palapala, ʻaʻole ʻokoʻa ka ʻano o ka hōʻike hōʻike mai ka palapala a Wolfram Mathematica ponoʻī, a hāʻawi i ka pūʻolo me nā faila hoʻāʻo no ka ʻike mua.

ʻO Wolfram Mathematica ma Geophysics

ʻO Wolfram Mathematica ma Geophysics

ʻO ia faila, ʻo ia hoʻi, ka faila "Marmousi.segy" - he kumu hoʻohālike kēia o kahi ʻāpana geological, i hoʻomohala ʻia e ka French Petroleum Institute. Ke hoʻohana nei i kēia ʻano hoʻohālike, hoʻāʻo nā mea hoʻomohala i kā lākou iho algorithms no ka hoʻohālikelike ʻana i ke kahua nalu, ka hoʻoili ʻikepili, ka hoʻohuli ʻana i ka seismic trace, etc. Mālama ʻia ka hiʻohiʻona Marmousi i loko o ka waihona mai kahi i hoʻoiho ʻia ai ka pōʻai ponoʻī. No ka loaʻa ʻana o ka faila, e holo i kēia code:

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

Hoʻokomo i ka hopena - SEGYData mea
ʻO Wolfram Mathematica ma Geophysics

ʻO ka SEGY format e pili ana i ka mālama ʻana i nā ʻike like ʻole e pili ana i nā nānā. ʻO ka mea mua, he mau manaʻo kikokikona kēia. Aia kēia i ka ʻike e pili ana i kahi o ka hana, nā inoa o nā hui i hana i nā ana, etc. I kā mākou hihia, kāhea ʻia kēia poʻo e kahi noi me ke kī TextHeader. Eia kahi poʻomanaʻo kikokikona pōkole:

Short[marmousi["TextHeader"]]

"Ua hana ʻia ka ʻikepili Marmousi ma ke Keʻena ... ʻoi loa ka wikiwiki o 1500 m/s a ʻoi aku ka nui o 5500 m/s)"

Hiki iā ʻoe ke hōʻike i ke ʻano hoʻohālike maoli ma ke komo ʻana i nā ʻāpana seismic me ka hoʻohana ʻana i ke kī "traces" (ʻo kekahi o nā hiʻohiʻona o ka pūʻolo ʻo ia nā kī ʻaʻole hihia):

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

ʻO Marmousi hoʻohālike
ʻO Wolfram Mathematica ma Geophysics

I kēia manawa, hiki iā ʻoe ke hoʻouka i ka ʻikepili i nā ʻāpana mai nā faila nui, e hiki ai ke hana i nā faila i hiki i ka nui o nā gigabytes. Hoʻokomo pū ʻia nā hana o ka pūʻolo i nā hana no ka lawe ʻana i ka ʻikepili i .segy a hoʻopili hapa i ka hope o ka faila.

Ma kahi kaʻawale, pono e ʻike i ka hana o ka pūʻolo i ka wā e hana ai me ka hoʻolālā paʻakikī o nā faila .segy. No ka mea ʻaʻole hiki iā ʻoe ke komo i nā ʻāpana a me nā poʻomanaʻo me ka hoʻohana ʻana i nā kī a me nā kuhikuhi, akā e hoʻololi pū iā lākou a laila kākau iā lākou i kahi faila. ʻO ka nui o nā kikoʻī loea o ka hoʻokō ʻana o GeologyIO ma waho o ke kiko o kēia ʻatikala a pono paha e wehewehe ʻokoʻa.

Ka pili ana o ka anaana spectral i ka imi seismic

ʻO ka hiki ke hoʻokomo i ka ʻikepili seismic i loko o Wolfram Mathematica hiki iā ʻoe ke hoʻohana i ka hana hoʻoili hōʻailona i kūkulu ʻia no ka ʻikepili hoʻokolohua. No ka mea, ʻo kēlā me kēia meheu seismic e hōʻike ana i kahi kaʻina manawa, ʻo kekahi o nā mea hana nui no ke aʻo ʻana iā lākou ʻo ia ka loiloi spectral. Ma waena o nā mea e pono ai no ka nānā ʻana i ka haku mele ʻana o ka ʻikepili seismic, hiki iā mākou ke inoa, no ka laʻana, penei:

  1. Hōʻike ʻia nā ʻano nalu like ʻole e ka haku mele ʻana. ʻAe kēia iā ʻoe e hōʻike i nā nalu pono a kāpae i nā nalu interference.
  2. Hiki i nā waiwai pōhaku e like me ke porosity a me ka saturation ke hoʻopili i ka haku mele pinepine. ʻO kēia ka mea hiki ke ʻike i nā pōhaku me nā waiwai maikaʻi loa.
  3. ʻO nā papa me nā mānoanoa like ʻole ke kumu i nā anomalies i nā pae alapine like ʻole.

ʻO ka helu ʻekolu ka mea nui ma ka pōʻaiapili o kēia ʻatikala. Aia ma lalo iho kahi ʻāpana code no ka helu ʻana i nā meheu seismic i ke ʻano o kahi papa me ka mānoanoa like ʻole - he kumu hoʻohālike. Ua aʻo kuʻuna ʻia kēia kŘkohu i ka ʻimi seismic no ka nānā ʻana i nā hopena hoʻopilikia ke ʻike ʻia nā nalu mai nā papa he nui ma luna o kekahi.

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]]

ʻO ke kumu hoʻohālike o ka hoʻokumu ʻana i waho
ʻO Wolfram Mathematica ma Geophysics

He 4500 m/s ka mama o ka nalu i loko o ka wedge, ma waho o ka wedge 4000 m/s, a ua manaʻo ʻia ʻo ka mānoanoa he 2200 g/cm³ mau. No ia ʻano hoʻohālike, helu mākou i nā coefficient noʻonoʻo a me nā ʻāpana seismic.

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]

Nā meheu seismic no ke kŘkohu wedge
ʻO Wolfram Mathematica ma Geophysics

Ua kapa ʻia ke kaʻina o nā meheu seismic i hōʻike ʻia ma kēia kiʻi he ʻāpana seismic. E like me kāu e ʻike ai, hiki ke hoʻokō ʻia kāna wehewehe ʻana ma kahi pae intuitive, ʻoiai ʻo ka geometry o nā nalu i hōʻike ʻia e pili pono ana i ke kumu hoʻohālike i hōʻike mua ʻia. Inā ʻoe e loiloi i nā ʻano kikoʻī, e ʻike ʻoe ʻaʻole ʻokoʻa nā ʻāpana mai ka 1 a hiki i ka 30 - ʻaʻole ʻokoʻa ka noʻonoʻo ʻana mai ka hale o ka hoʻokumu ʻana a mai lalo. E hoʻomaka ana mai ka trace 31st, hoʻomaka nā noʻonoʻo e hoʻopilikia. A, ʻoiai i loko o ke kŘkohu, ʻaʻole e hoʻololi ʻia nā coefficients noʻonoʻo - hoʻololi ke ʻano seismic i ko lākou ikaika e like me ka hoʻololi ʻana o ka mānoanoa o ka hoʻokumu ʻana.

E noʻonoʻo kākou i ka amplitude o ka noʻonoʻo ʻana mai ka palena o luna o ka hoʻokumu ʻana. E hoʻomaka ana mai ke ala 60th, hoʻomaka ka ikaika o ka noʻonoʻo e hoʻonui a ma ke ala 70th e lilo i mea kiʻekiʻe. ʻO kēia ke ʻano o ka hoʻopili ʻana o nā nalu mai ka hale a me lalo o nā papa e hōʻike iā ia iho, e alakaʻi ana i kekahi mau mea i nā anomalies koʻikoʻi i ka mooolelo 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]

Kiʻikuhi o ka amplitude o ka nalu i ʻike ʻia mai ka ʻaoʻao o luna o ka wili
ʻO Wolfram Mathematica ma Geophysics

Maikaʻi ka manaʻo o ka hōʻailona haʻahaʻa-frequency, hoʻomaka ka hoʻopili ʻana i nā mānoanoa hoʻokumu nui, a i ke ʻano o kahi hōʻailona alapine kiʻekiʻe, hiki ke keakea i nā mānoanoa liʻiliʻi. Hoʻokumu ka snippet code ma lalo i kahi hōʻailona me nā alapine o 35 Hz, 55 Hz a me 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]

He pūʻulu o nā hōʻailona kumu me nā alapine o 35 Hz, 55Hz, 85Hz
ʻO Wolfram Mathematica ma Geophysics

Ma ka helu ʻana i nā ʻāpana seismic a me ka hoʻolālā ʻana i nā kiʻi o nā amplitudes nalu i ʻike ʻia, hiki iā mākou ke ʻike no nā alapine like ʻole ke ʻike ʻia kahi anomaly ma nā mānoanoa hoʻokumu like ʻole.

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]

Nā kaha kiʻi o nā amplitudes o ka nalu i hōʻike ʻia mai ka lihi luna o ka wedge no nā alapine like ʻole.
ʻO Wolfram Mathematica ma Geophysics

ʻO ka hiki ke huki i nā manaʻo e pili ana i ka mānoanoa o ka hoʻokumu ʻana mai nā hopena o ka nānā ʻana i ka seismic he mea maikaʻi loa ia, no ka mea, ʻo kekahi o nā hana nui i ka ʻimi ʻaila ʻo ia ka loiloi i nā wahi maikaʻi loa no ka hoʻomoe ʻana i kahi pūnāwai (ʻo ia hoʻi, nā wahi kahi i hoʻokumu ʻia ai. mānoanoa). Eia kekahi, ma ka ʻāpana geological aia paha nā mea nona ka genesis e hoʻololi nui i ka mānoanoa o ka hoʻokumu ʻana. Hana kēia i ka nānā ʻana spectral i mea hana pono no ke aʻo ʻana iā lākou. Ma ka ʻaoʻao aʻe o ka ʻatikala e noʻonoʻo mākou i kēlā mau mea geological i nā kikoʻī hou aku.

ʻikepili hoʻokolohua. Ma hea ʻoe i loaʻa ai a he aha kāu e ʻimi ai i loko o lākou?

Loaʻa nā mea i kālailai ʻia ma ka ʻatikala ma Western Siberia. ʻO ka ʻāina, e like me ka mea i ʻike ʻole ʻia e ka poʻe āpau, ʻo ia ka ʻāina hana ʻaila nui o ko mākou ʻāina. Hoʻomaka ka hoʻomohala ʻana o nā waihona i ka ʻāina i nā makahiki 60 o ke kenekulia i hala. ʻO ke ala nui o ka ʻimi ʻana i nā waihona aila ʻo ia ka ʻimi seismic. He mea hoihoi ke nana aku i na kii ukali o keia teritore. Ma kahi ʻano liʻiliʻi, hiki iā ʻoe ke ʻike i ka nui o nā swamps a me nā loko; ma ka hoʻonui ʻana i ka palapala ʻāina, hiki iā ʻoe ke ʻike i nā kahua hoʻoheheʻe pūnāwai, a ma ka hoʻonui ʻana i ka palapala ʻāina i ka palena, hiki iā ʻoe ke ʻike i ka wehe ʻana o nā profiles e pili ana i ka seismic. ua hana ʻia nā ʻike.

Kiʻi Satellite o nā palapala 'āina Yandex - Noyabrsk wahi kūlanakauhale
ʻO Wolfram Mathematica ma Geophysics

ʻO kahi pūnaewele o nā pūnāwai ma kekahi o nā māla
ʻO Wolfram Mathematica ma Geophysics

Aia nā pōhaku ʻaila o Western Siberia ma kahi ākea o ka hohonu - mai 1 km a 5 km. Ua hoʻokumu ʻia ka nui o nā pōhaku i loko o ka ʻaila i ka wā Jurassic a me Cretaceous. ʻIke ʻia paha ka manawa Jurassic e nā mea he nui mai ka kiʻiʻoniʻoni o ka inoa like. ʻElima Jurassic ʻokoʻa loa ia mai ko kēia wā. He ʻano paleomaps ka Encyclopedia Britannica e hōʻike ana i kēlā me kēia au helogical.

E hōʻike nei i ka manaʻo
ʻO Wolfram Mathematica ma Geophysics
Ka wā Jurassic
ʻO Wolfram Mathematica ma Geophysics

E ʻoluʻolu e hoʻomaopopo i ka wā Jurassic, ʻo ka ʻāina o Western Siberia he kahakai kai ('āina i hele ʻia e nā muliwai a me ke kai pāpaʻu). Ma muli o ka ʻoluʻolu o ke aniau, hiki iā mākou ke manaʻo ua like ke ʻano o ka ʻāina maʻamau o ia manawa:

Jurassic Siberia
ʻO Wolfram Mathematica ma Geophysics

Ma kēia kiʻi, ʻo ka mea nui iā mākou ʻaʻole nā ​​holoholona a me nā manu, akā ʻo ke kiʻi o ka muliwai ma hope. ʻO ka muliwai ka mea honua like a mākou i kū ai ma mua. ʻO ka mea ʻoiaʻiʻo, ʻo ka hana o nā muliwai e ʻae i nā pōhaku i hoʻonohonoho maikaʻi ʻia e hōʻiliʻili, a laila e lilo i waihona no ka aila. Hiki ke ʻano ʻano ʻano ʻē a paʻakikī kēia mau loko (e like me ka moena o ka muliwai) a he ʻano mānoanoa ko lākou - kokoke i nā kapa liʻiliʻi ka mānoanoa, akā kokoke i ke kikowaena o ke kahawai a i ʻole ma nā wahi meander e piʻi ai. No laila, ʻo nā muliwai i hoʻokumu ʻia i ka Jurassic i kēia manawa ma kahi hohonu o ʻekolu mau kilomita a ʻo ia ke kumu o ka ʻimi ʻana i nā waihona aila.

ʻikepili hoʻokolohua. Ka hana a me ka nānā ʻana

E hoʻopaʻa koke mākou e pili ana i nā mea seismic i hōʻike ʻia ma ka ʻatikala - ma muli o ka nui o ka nui o ka ʻikepili i hoʻohana ʻia no ka nānā ʻana he mea koʻikoʻi - ʻo kahi ʻāpana wale nō o ka pūʻulu kumu o nā ʻāpana seismic i hoʻokomo ʻia i loko o ka kikokikona o ka ʻatikala. ʻAe kēia i kekahi e hana hou i nā helu ʻana ma luna.

I ka hana ʻana me ka ʻikepili seismic, hoʻohana maʻamau ka geophysicist i nā polokalamu kūikawā (he nui nā alakaʻi o ka ʻoihana i hoʻohana ikaika ʻia, no ka laʻana ʻo Petrel a i ʻole Paradigm), kahi e hiki ai iā ʻoe ke kālailai i nā ʻano ʻikepili like ʻole a loaʻa iā ʻoe kahi interface kiʻi kūpono. ʻOiai ʻo ka ʻoluʻolu a pau, loaʻa i kēia mau ʻano polokalamu i kā lākou drawbacks - no ka laʻana, ʻo ka hoʻokō ʻana i nā algorithms hou i nā mana paʻa he nui ka manawa, a ʻo nā mea hiki ke hoʻololi i ka helu ʻana he mea maʻamau. Ma ia kūlana, lilo ia i mea maʻalahi ka hoʻohana ʻana i nā ʻōnaehana makemakika lolouila a me nā ʻōlelo hoʻolālā kiʻekiʻe, e ʻae ai i ka hoʻohana ʻana i kahi waihona algorithmic ākea a, i ka manawa like, lawe i nā hana maʻamau. ʻO kēia ke kumu i hoʻohana ʻia e hana me ka ʻikepili seismic ma Wolfram Mathematica. ʻAʻole kūpono ke kākau i nā hana waiwai no ka hana pili me ka ʻikepili - ʻoi aku ka mea nui e hōʻoia i ka hoʻouka ʻana mai kahi ʻano i ʻae ʻia, e noi ana i nā algorithm i makemake ʻia iā lākou a hoʻouka hou iā lākou i kahi ʻano waho.

Ma hope o ka papahana i manaʻo ʻia, e hoʻouka mākou i ka ʻikepili seismic kumu a hōʻike iā lākou i loko ʻO 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]

ʻO ka ʻikepili i hoʻoiho ʻia a lawe ʻia ma kēia ala ʻo ia nā ala i hoʻopaʻa ʻia ma kahi ʻāpana he 10 a 5 mau kilomita. Inā loaʻa ka ʻikepili me ka hoʻohana ʻana i ke ʻano loiloi seismic ʻekolu-dimensional (ʻaʻole i hoʻopaʻa ʻia nā nalu ma nā ʻaoʻao geophysical pākahi, akā ma luna o ka wahi holoʻokoʻa i ka manawa like), hiki ke loaʻa nā cubes data seismic. ʻO kēia nā mea ʻekolu-dimensional, nā ʻāpana kū a me nā ʻāpana e hiki ai ke aʻo kikoʻī i ke kaiapuni honua. Ma ka laʻana i manaʻo ʻia, ke hana nei mākou i nā ʻikepili ʻekolu. Hiki iā mākou ke loaʻa kekahi ʻike mai ke poʻo kikokikona, e like me kēia

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

C 1 EIA KEIA DEMO FILE NO GEOLOGYIO PACKAGE HOA'O
C 2
C 3
C 4
C 5 KA LĀ MEA NĀ MEA HOʻohana: WOLFRAM USER
C 6 NANA INOA: MAKAHI MA SIBERIA
C 7 KE ANO FILE 3D SEISMIC VOLUME
C 8
C 9
C10 Z RANGE: MUA 2200M HOPE 2400M

E lawa kēia pūʻulu ʻikepili iā mākou e hōʻike i nā pae nui o ka ʻikepili ʻikepili. Hoʻopaʻa ʻia nā ʻōkuhi i loko o ka faila a ʻike ʻia kēlā me kēia me ke kiʻi ma lalo nei - ʻo ia ka puʻunaue o nā amplitudes o nā nalu i ʻike ʻia ma ke koʻikoʻi kūpaʻa (axis depth).

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]

ʻO kekahi o nā ʻāpana seismic
ʻO Wolfram Mathematica ma Geophysics

I ka ʻike ʻana i ka nui o nā meheu i kēlā me kēia ʻaoʻao o ka wahi i aʻo ʻia, hiki iā ʻoe ke hana i kahi ʻikepili ʻekolu-dimensional a hōʻike iā ia me ka hoʻohana ʻana i ka hana 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]]

Kiʻi XNUMXD o kahi cube data seismic. (Axi Vertical - hohonu)
ʻO Wolfram Mathematica ma Geophysics

Inā hoʻokumu nā hiʻohiʻona honua o ka hoihoi i nā anomali seismic ikaika, a laila hiki ke hoʻohana ʻia nā mea hana ʻike me ka ʻike. Hiki ke ʻike ʻole ʻia nā wahi "mea ʻole" o ka hoʻopaʻa ʻana, waiho wale i nā anomalies e ʻike ʻia. Ma Wolfram Mathematica hiki ke hana i kēia me ka hoʻohana ʻana 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]

Ke kiʻi cube data Seismic me ka hoʻohana ʻana i nā hana Opacity[] a me Raster3D[]. ʻO Wolfram Mathematica ma Geophysics

E like me ka laʻana synthetic, ma nā ʻāpana o ka cube kumu hiki ke ʻike i kekahi mau palena ʻāina (nā papa) me ka hoʻololi ʻana.

ʻO ka mea hana nui no ka loiloi spectral ʻo ka hoʻololi Fourier. Me kona kōkua, hiki iā ʻoe ke loiloi i ka amplitude-frequency spectrum o kēlā me kēia meheu a i ʻole pūʻulu o nā traces. Eia nō naʻe, ma hope o ka hoʻoili ʻana i ka ʻikepili i ka domain frequency, nalowale ka ʻike e pili ana i nā manawa (heluhelu i ka hohonu) e loli ka alapine. I mea e hiki ai ke hoʻokaʻawale i nā hoʻololi hōʻailona ma ke axis o ka manawa (hohonu), hoʻohana ʻia ka hoʻololi ʻana o Fourier windowed a me ka decomposition wavelet. Hoʻohana kēia ʻatikala i ka decomposition wavelet. Ua hoʻomaka ka ʻenehana loiloi Wavelet e hoʻohana ikaika ʻia i ka ʻimi seismic i nā makahiki 90. ʻO ka maikaʻi ma luna o ka puka makani Fourier transform i manaʻo ʻia ʻoi aku ka maikaʻi o ka hoʻonā manawa.

Me ka hoʻohana ʻana i kēia ʻāpana code, hiki iā ʻoe ke hoʻokaʻawale i kekahi o nā ʻāpana seismic i nā ʻāpana pākahi:

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]

ʻO ka hoʻoheheʻe ʻana o kahi meheu i mau ʻāpana
ʻO Wolfram Mathematica ma Geophysics

No ka nānā ʻana i ke ʻano o ka puʻunaue ʻana o ka ikehu noʻonoʻo i nā manawa hōʻea nalu like ʻole, hoʻohana ʻia nā scalograms (e like me kahi spectrogram). Ma keʻano he kūlana, ma ka hoʻomaʻamaʻa ʻaʻole pono e nānā i nā ʻāpana āpau. ʻO ka mea maʻamau, koho ʻia nā ʻāpana haʻahaʻa, waena a kiʻekiʻe.

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. Ka hopena hana WaveletScalogram[]
ʻO Wolfram Mathematica ma Geophysics

Hoʻohana ka Wolfram Language i ka hana no ka hoʻololi wavelet Hoʻololi Wavelet[]. A e hoʻokō ʻia ka hoʻohana ʻana i kēia hana i ka pūʻulu holoʻokoʻa o nā traces me ka hoʻohana ʻana i ka hana Papa []. Eia ka mea pono e ʻike i kekahi o nā ikaika o Wolfram Mathematica - ka hiki ke hoʻohana i ka parallelization Pākuʻi Parallel[]. Ma ka laʻana i luna, ʻaʻohe pono no ka parallelization - ʻaʻole nui ka nui o ka ʻikepili, akā i ka hana ʻana me nā pūʻulu ʻikepili hoʻokolohua i loaʻa i nā haneli he mau tausani, he mea pono kēia.

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

Ma hope o ka hoʻohana ʻana i ka hana Hoʻololi Wavelet[] Hōʻike ʻia nā pūʻulu ʻikepili hou e pili ana i nā alapine i koho ʻia. I ka laʻana ma luna, ʻo kēia mau alapine: 38Hz, 33Hz, 27Hz. Hoʻohana pinepine ʻia ke koho ʻana i nā alapine ma ke kumu o ka hoʻāʻo - loaʻa iā lākou nā palapala ʻāina kūpono no nā hui like ʻole a koho i ka mea ʻike loa mai ka ʻike o kahi kanaka geologist.

Inā pono ʻoe e kaʻana like i nā hopena me nā hoa hana a hāʻawi iā lākou i ka mea kūʻai aku, hiki iā ʻoe ke hoʻohana i ka SEGYExport[] hana o ka pūʻolo GeologyIO

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];

Me ʻekolu o kēia mau cubes (nā haʻahaʻa haʻahaʻa, waena waena, a me nā ʻāpana kiʻekiʻe), hoʻohana maʻamau ka hui ʻana o RGB e nānā i ka ʻikepili. Hāʻawi ʻia kēlā me kēia ʻāpana i kona kala ponoʻī - ʻulaʻula, ʻōmaʻomaʻo, uliuli. Ma Wolfram Mathematica hiki ke hana i kēia me ka hana ColorCombine[].

ʻO ka hopena, ʻo ia nā kiʻi i hiki ke hana i ka wehewehe ʻāina. ʻO nā meanders i hoʻopaʻa ʻia ma ka ʻāpana e hiki ke wehewehe i nā paleochannels, ʻoi aku ka nui o nā waihona a loaʻa nā ʻaila. ʻO ka ʻimi a me ka nānā ʻana o nā analogues hou o ia ʻano kahawai e hiki ai iā mākou ke hoʻoholo i nā ʻāpana ʻoi loa o nā meanders. Hōʻike ʻia nā kahawai ponoʻī e nā ʻāpana mānoanoa o ke one i hoʻokaʻawale maikaʻi ʻia a he waihona maikaʻi no ka ʻaila. ʻO nā wahi ma waho o nā anomalies "lace" e like me nā waihona waikahe hou. Hōʻike nui ʻia ka waiho ʻana o Floodplain e nā pōhaku pālolo a ʻaʻole pono ka ʻeli ʻana i loko o kēia mau ʻāpana.

ʻāpana RGB o ka pahu ʻikepili. Ma ke kikowaena (ma ka hema iki o ke kikowaena) hiki iā ʻoe ke ʻimi i ke kahawai ʻala.
ʻO Wolfram Mathematica ma Geophysics
ʻāpana RGB o ka pahu ʻikepili. Ma ka ʻaoʻao hema hiki iā ʻoe ke ʻimi i ke kahawai ʻala.
ʻO Wolfram Mathematica ma Geophysics

I kekahi mau hihia, hiki i ka maikaʻi o ka ʻikepili seismic ke loaʻa nā kiʻi ʻoi aku ka maopopo. Pili kēia i ke ʻano hana o ke kahua, nā mea hana i hoʻohana ʻia e ka algorithm noise reduction. Ma ia mau hihia, ʻaʻole ʻike wale ʻia nā ʻāpana o nā ʻōnaehana kahawai, akā ʻo nā paleo-nā kahawai holoʻokoʻa.

ʻO ka hui pū ʻana o RGB o ʻekolu mau ʻāpana o kahi cube data seismic (ʻāpana ʻākau). Ka hohonu ma kahi o 2 km.
ʻO Wolfram Mathematica ma Geophysics
Kiʻi Satellite o ka muliwai Volga kokoke i Saratov
ʻO Wolfram Mathematica ma Geophysics

hopena

ʻAe ʻo Wolfram Mathematica iā ʻoe e kālailai i ka ʻikepili seismic a hoʻoponopono i nā pilikia pili e pili ana i ka ʻimi mineral, a ʻoi aku ka maʻalahi o ka pūʻolo GeologyIO i kēia kaʻina hana. ʻO ke ʻano o ka ʻikepili seismic e like me ka hoʻohana ʻana i nā ʻano hana i kūkulu ʻia e wikiwiki i ka helu ʻana (Pākuʻi Parallel[], ParallelDo[],…) maikaʻi loa a hiki iā ʻoe ke hana i ka nui o ka ʻikepili. Ma kahi nui, hoʻomaʻamaʻa ʻia kēia e nā hiʻohiʻona mālama ʻikepili o ka pūʻulu GeologyIO. Ma ke ala, hiki ke hoʻohana ʻia ka pūʻolo ʻaʻole wale ma ke kahua o ka noiʻi seismic noiʻi. ʻAneʻane like nā ʻano ʻikepili i hoʻohana ʻia ma ka honua penetrating radar a me ka seismology. Inā loaʻa iā ʻoe nā manaʻo e pili ana i ka hoʻomaikaʻi ʻana i ka hopena, ʻo ia nā algorithms analysis signal mai ka Wolfram Mathematica arsenal e pili ana i ia ʻikepili, a i ʻole he manaʻo koʻikoʻi kāu, e ʻoluʻolu. waiho i ka manao.

Source: www.habr.com

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