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ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ืึทื ืง ืฆื• ื“ืขื ื‘ืœืึธื’ ืžื—ื‘ืจ ืึทื ื˜ืึธืŸ ืขืงื™ืžืขื ืงืึธ ืคึฟืึทืจ ื–ื™ื™ืŸ ื‘ืึทืจื™ื›ื˜

ื”ืงื“ืžื”

ื“ื™ ื“ืื–ื™ืงืข ืฆืขื˜ืœ ืื™ื– ื’ืขืฉืจื™ื‘ืŸ ื’ืขื•ื•ืืจืŸ ื ืืš ื“ืขืจ ืงืื ืคืขืจืขื ืฅ ื•ื•ืึธืœืคืจืึทื ืจื•ืกื™ืฉ ื˜ืขื›ื ืึธืœืึธื’ื™ืข ืงืึธื ืคึฟืขืจืขื ืฅ ืื•ืŸ ืื ื˜ื”ืืœื˜ ื ืงื™ืฆืขืจ ืคื•ืŸ ื“ืขื ื‘ืืจื™ื›ื˜ ืžื™ื˜ ื•ื•ืขืœื›ืŸ ืื™ืš ื”ืื‘ ื’ืขืจืขื“ื˜. ื“ื™ ื’ืขืฉืขืขื ื™ืฉ ืื™ื– ืคืืจื’ืขืงื•ืžืขืŸ ืื™ืŸ ื™ื•ื ื™ ืื™ืŸ ืคืขื˜ืขืจื‘ื•ืจื’. ื•ื•ื™ื™ึทืœ ืื™ืš ืึทืจื‘ืขื˜ ืึท ื‘ืœืึธืง ืึทื•ื•ืขืง ืคื•ืŸ ื“ื™ ืงืึธื ืคึฟืขืจืขื ืฅ ืึธืจื˜, ืื™ืš ืงืขืŸ ื ื™ืฉื˜ ื”ืขืœืคืŸ ืฆื• ืึธื ื˜ื™ื™ืœ ื ืขืžืขืŸ ืื™ืŸ ื“ืขื ื’ืขืฉืขืขื ื™ืฉ. ืื™ืŸ 2016 ืื•ืŸ 2017 ื”ืึธื‘ ืื™ืš ื–ื™ืš ืฆื•ื’ืขื”ืขืจื˜ ืฆื• ื“ื™ ื‘ืึทืจื™ื›ื˜ืŸ ืคึฟื•ืŸ ื“ืขืจ ืงืึธื ืคึฟืขืจืขื ืฅ, ืื•ืŸ ื“ืึธืก ื™ืึธืจ ื”ืึธื‘ ืื™ืš ื’ืขืžืึทื›ื˜ ืึท ื‘ืึทืจื™ื›ื˜. ืขืจืฉื˜ื ืก, ื”ืึธื˜ ื–ื™ืš ื‘ืึทื•ื•ื™ื–ืŸ ืึทืŸ ืื™ื ื˜ืขืจืขืกืึทื ื˜ืข (ื•ื•ื™ ืขืก ืžื™ื™ื ื˜ ืฆื• ืžื™ืจ) ื˜ืขืžืข, ืžื™ื˜ ื•ื•ืึธืก ืžื™ืจ ืึทื ื˜ื•ื•ื™ืงืœืขืŸ ื–ื™ืš ืงื™ืจื™ืœ ื‘ืขืœืึธื•ื•, ืื•ืŸ ืฆื•ื•ื™ื™ื˜ื ืก, ื ืึธืš ืึท ืœืึทื ื’ ืœืขืจื ืขืŸ ืคื•ืŸ ื“ื™ ื’ืขืกืขืฆ - ื’ืขื‘ื•ื ื’ ืคื•ืŸ ื“ื™ ืจื•ืกื™ืฉืข ืคืขื“ืขืจื™ื™ืฉืึทืŸ ืื™ืŸ ื˜ืขืจืžื™ื ืขืŸ ืคื•ืŸ ื“ื™ ืกืึทื ื’ืฉืึทื ื– ืคึผืึธืœื™ื˜ื™ืง, ืื™ืŸ ื“ื™ ืคืึทืจื ืขืžื•ื ื’ ื•ื•ื• ืื™ืš ืึทืจื‘ืขื˜, ืขืก ื–ืขื ืขืŸ ื•ื•ื™ ืคื™ืœืข ื•ื•ื™ ืฆื•ื•ื™ื™ ืœื™ื™ืกืึทื ืกื™ื– ื•ื•ืึธืœืคืจืึทื ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท.

ืื™ื™ื“ืขืจ ืื™ืš ืžืึทืš ืื•ื™ืฃ ืฆื• ื“ืขืจ ื˜ืขืžืข ืคื•ืŸ โ€‹โ€‹ืžื™ื™ืŸ ืจืขื“ืข, ืื™ืš ื•ื•ืึธืœื˜ ื•ื•ื™ ืฆื• ื‘ืึทืžืขืจืงืŸ ื“ื™ ื’ื•ื˜ ืึธืจื’ืึทื ื™ื–ืึทืฆื™ืข ืคื•ืŸ โ€‹โ€‹ื“ืขืจ ื’ืขืฉืขืขื ื™ืฉ. ื“ื™ ื‘ืื–ื•ื›ืŸ ื‘ืœืึทื˜ ืคื•ืŸ ื“ืขืจ ืงืึธื ืคึฟืขืจืขื ืฅ ื ื™ืฆื˜ ื“ื™ ื‘ื™ืœื“ ืคื•ืŸ ื“ื™ ืงืึทื–ืึทืŸ ืงืึทื˜ื”ืขื“ืจืึทืœ. ื“ื™ ืงืึทื˜ื™ื“ืจืึทืœ ืื™ื– ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืกื™ื™ืฅ ืคื•ืŸ ืกื˜ ืคืขื˜ืขืจื‘ื•ืจื’ ืื•ืŸ ืขืก ืื™ื– ื–ื™ื™ืขืจ ืงืœืืจ ืงืขื ื˜ื™ืง ืคื•ืŸ ื“ื™ ื–ืึทืœ ื•ื•ื• ื“ื™ ืงืึธื ืคึฟืขืจืขื ืฅ ืื™ื– ื’ืขื•ื•ืขืŸ ื’ืขื”ืืœื˜ืŸ.

ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื‘ืฒึทื ืึทืจืฒึทื ื’ืึทื ื’ ืื™ืŸ ืคึผืขื˜ืขืจื‘ื•ืจื’ืขืจ ืกื˜ืขื™ื˜ ืขืงืึธื ืึธืžื™ืงึพืื•ื ื™ื•ื•ืขืจืกื™ื˜ืขื˜, ื”ืึธื‘ืŸ ื“ื™ ื‘ืึทื˜ื™ื™ืœื™ืงื˜ืข ื’ืขื˜ืจืึธืคึฟืŸ ืึทืกื™ืกื˜ืขื ื˜ืŸ ืคึฟื•ืŸ ืฆื•ื•ื™ืฉืŸ ื“ื™ ืกื˜ื•ื“ืขื ื˜ืŸ โ€” ื–ื™ื™ ื”ืึธื‘ืŸ ื–ื™ื™ ื ื™ืฉื˜ ื’ืขืœืึธื–ื˜ ืคึฟืึทืจืœื•ื™ืจืขืŸ. ื‘ืขืฉืึทืก ืจืขื’ื™ืกื˜ืจืึทืฆื™ืข, ืงืœื™ื™ืŸ ืกื•ื•ื•ืึทื ื™ืจื– ื–ืขื ืขืŸ ื’ืขื’ืขื‘ืŸ ืื•ื™ืก (ืึท ืฆืึทืฆืงืข - ืึท ืคืœืึทืฉื™ื ื’ ืฉืคึผื™ืฆืœ, ืึท ืคืขื“ืขืจ, ืกื˜ื™ืงืขืจื– ืžื™ื˜ ื•ื•ืึธืœืคืจืึทื ืกื™ืžื‘ืึธืœืก). ืžื™ื˜ืึธื’ ืื•ืŸ ืงืึทื•ื•ืข ื‘ืจื™ื™ืงืก ื–ืขื ืขืŸ ืื•ื™ืš ืึทืจื™ื™ึทื ื’ืขืจืขื›ื ื˜ ืื™ืŸ ื“ื™ ืงืึธื ืคึฟืขืจืขื ืฅ ืคึผืœืึทืŸ. ื•ื•ืขื’ืŸ ื’ืขืฉืžืึทืง ืงืึทื•ื•ืข ืื•ืŸ ืคึผื™ืขืก, ืื™ืš ื”ืึธื‘ืŸ ืฉื•ื™ืŸ ื‘ืืžืขืจืงื˜ ืื•ื™ืฃ ื“ื™ ื•ื•ืึทื ื˜ ืคื•ืŸ ื“ื™ ื’ืจื•ืคึผืข - ื’ืขื–ื•ื ื˜-ื’ืขื˜ืืŸ ืงื•ืงืก. ืžื™ื˜ ื“ืขื ื™ื ื˜ืจืึทื“ืึทืงื˜ืขืจื™ ื˜ื™ื™ืœ, ืื™ืš ื•ื•ืึธืœื˜ ื•ื•ื™ ืฆื• ื•ื ื˜ืขืจืฉื˜ืจื™ื™ึทื›ืŸ ืึทื– ื“ื™ ื’ืขืฉืขืขื ื™ืฉ ื–ื™ืš, ื–ื™ื™ึทืŸ ืคึฟืึธืจืžืึทื˜ ืื•ืŸ ืึธืจื˜ ืฉื•ื™ืŸ ื‘ืจืขื ื’ืขืŸ positive ื™ืžืึธื•ืฉืึทื ื–.

ื“ืขืจ ื‘ืึทืจื™ื›ื˜, ื•ื•ืึธืก ืื™ื– ื’ืขื•ื•ืขืŸ ืฆื•ื’ืขื’ืจื™ื™ื˜ ื“ื•ืจืš ืžื™ืจ ืื•ืŸ ืงื™ืจื™ืœ ื‘ืขืœืึธื•ื•, ืื™ื– ื’ืขืจื•ืคืŸ "ื ื™ืฆืŸ Wolfram Mathematica ืฆื• ืกืึธืœื•ื•ืข ืคึผืจืึธื‘ืœืขืžืก ืื™ืŸ ื’ืขื•ื•ืขื ื“ื˜ ื’ืขืึธืคื™ืกื™ืงืก. ืกืคึผืขืงื˜ืจืึทืœ ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืึธื“ืขืจ "ื•ื•ื• ืืœื˜ืข ืจื™ื•ื•ืขืจืก ื’ืขืœืืคืŸ". ื“ืขืจ ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ื“ืขื ื‘ืึทืจื™ื›ื˜ ืงืึธื•ื•ืขืจืก ืฆื•ื•ื™ื™ ืคึผืึทืจืฅ: ืขืจืฉื˜ืขืจ, ืขืก ืื™ื– ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ืึทืœื’ืขืจื™ื“ืึทืžื– ื‘ื ื™ืžืฆื ืื™ืŸ ื•ื•ืึธืœืคืจืึทื ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท ืคึฟืึทืจ ื“ื™ ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ื“ื–ืฉื™ืึธืคื™ื–ื™ืงืึทืœ ื“ืึทื˜ืŸ, ืื•ืŸ ืฆื•ื•ื™ื™ื˜ื ืก, ื“ืึธืก ืื™ื– ื•ื•ื™ ืฆื• ืฉื˜ืขืœืŸ ื“ื–ืฉื™ืึธืคื™ื–ื™ืงืึทืœ ื“ืึทื˜ืŸ ืื™ืŸ Wolfram Mathematica.

ืกื™ื™ื–ืžื™ืง

ืขืจืฉื˜ืขืจ ืื™ืจ ื“ืึทืจืคึฟืŸ ืฆื• ืžืึทื›ืŸ ืึท ืงื•ืจืฅ ื“ื™ื’ืจืขืฉืึทืŸ ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก. ื’ืขืึธืคื™ื–ื™ืง ืื™ื– ืึท ื•ื•ื™ืกื ืฉืึทืคึฟื˜ ื•ื•ืึธืก ืฉื˜ื•ื“ื™ืจื˜ ื“ื™ ื’ืฉืžื™ื•ืช ืคึผืจืึธืคึผืขืจื˜ื™ืขืก ืคื•ืŸ ืฉื˜ื™ื™ืŸ. ื ื•, ื–ื™ื ื˜ ื“ื™ ืจืึทืงืก ื”ืึธื‘ืŸ ืคืึทืจืฉื™ื“ืขื ืข ืคึผืจืึธืคึผืขืจื˜ื™ืขืก: ืขืœืขืงื˜ืจื™ืงืึทืœ, ืžืึทื’ื ืขื˜ื™ืง, ื’ื•ืžืข, ืขืก ื–ืขื ืขืŸ ืงืึธืจืึทืกืคึผืึทื ื“ื™ื ื’ ืžืขื˜ื”ืึธื“ืก ืคื•ืŸ ื’ืขืึธืคื™ืกื™ืงืก: ืขืœืขืงื˜ืจื™ืงืึทืœ ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ, ืžืึทื’ื ืขื˜ื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ, ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ... ืื™ืŸ ื“ืขื ืงืึธื ื˜ืขืงืกื˜ ืคื•ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ, ืžื™ืจ ื•ื•ืขืœืŸ ื ืึธืจ ืคืึทืจื‘ื™ื ื“ืŸ ืื•ื™ืฃ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ืื™ืŸ ืžืขืจ. ื“ืขื˜ืึทืœ. ืกืขื™ืกืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ืื™ื– ื“ืขืจ ื”ื•ื™ืคึผื˜ ืื•ืคึฟืŸ ืคื•ืŸ ื–ื•ื›ืŸ ืคึฟืึทืจ ื™ื™ืœ ืื•ืŸ ื’ืึทื–. ื“ืขืจ ืื•ืคึฟืŸ ืื™ื– ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ ืขืงืกื™ื™ื˜ื™ื™ืฉืึทืŸ ืคื•ืŸ ื’ื•ืžืข ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื– ืื•ืŸ ื“ื™ ืกืึทื‘ืกืึทืงื•ื•ืึทื ื˜ ืจืขื’ื™ืกื˜ืจืึทืฆื™ืข ืคื•ืŸ โ€‹โ€‹ื“ื™ ืขื ื˜ืคืขืจ ืคื•ืŸ ื“ื™ ืจืึทืงืก ื•ื•ืึธืก ืžืึทื›ืŸ ื“ื™ ืœืขืจื ืขืŸ ื’ืขื’ื ื˜. ืขืงืกื™ื™ื˜ื™ื™ืฉืึทืŸ ืคื•ืŸ ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื– ืื™ื– ื’ืขืคื™ืจื˜ ืื•ื™ืก ืื•ื™ืฃ ืœืึทื ื“ (ื“ื•ืจืš ื“ื™ื™ื ืึทืžื™ื™ื˜ ืึธื“ืขืจ ื ื™ื˜-ื™ืงืกืคึผืœืึธื•ืกื™ื•ื• ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทืŸ ืงื•ื•ืืœืŸ ืคื•ืŸ ื’ื•ืžืข ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื–) ืึธื“ืขืจ ืื™ืŸ ื™ื (ื“ื•ืจืš ืœื•ืคื˜ ื’ืึทื ื–). ืขืœืึทืกื˜ื™ืง ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื– ืคืึทืจืฉืคึผืจื™ื™ื˜ืŸ ื“ื•ืจืš ื“ื™ ื’ืจืขื‘ ืคื•ืŸ ืจืึทืงืก, ืจื™ืคืจืึทืงื˜ื™ื“ ืื•ืŸ ืฉืคื™ื’ืœื˜ ืื™ืŸ ื“ื™ ื‘ืึทื•ื ื“ืจื™ื– ืคื•ืŸ ืœื™ื™ึทืขืจืก ืžื™ื˜ ืคืึทืจืฉื™ื“ืขื ืข ืคึผืจืึธืคึผืขืจื˜ื™ืขืก. ืจืขืคืœืขืงื˜ืขื“ ื›ื•ื•ืืœื™ืขืก ืฆื•ืจื™ืงืงื•ืžืขืŸ ืฆื• ื“ื™ ื™ื™ื‘ืขืจืคืœืึทืš ืื•ืŸ ื–ืขื ืขืŸ ืจืขืงืึธืจื“ืขื“ ื“ื•ืจืš ื’ืขืึธืคืึธื ืขืก ืื•ื™ืฃ ืœืึทื ื“ (ื™ื•ื–ืฉืึทื•ื•ืึทืœื™ ื™ืœืขืงื˜ืจืึธื•ื“ื™ื ืึทืžื™ืง ื“ืขื•ื•ื™ืกืขืก ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ ื‘ืึทื•ื•ืขื’ื•ื ื’ ืคื•ืŸ ืึท ืžืึทื’ื ืขื˜ ืกื•ืกืคึผืขื ื“ืขื“ ืื™ืŸ ืึท ืฉืคึผื•ืœ) ืึธื“ืขืจ ื›ื™ื™ื“ืจืึธื•ืคืึธื•ื ื– ืื™ืŸ ื™ื (ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ ืคึผื™ืขื–ืึธืขืœืขืงื˜ืจื™ืง ื•ื•ื™ืจืงื•ื ื’). ืื™ืŸ ื“ืขืจ ืฆื™ื™ื˜ ืคื•ืŸ ืึธื ืงื•ืžืขืŸ ืคื•ืŸ ื“ื™ ื›ื•ื•ืืœื™ืขืก, ืื™ื™ื ืขืจ ืงืขื ืขืŸ ืจื™ื›ื˜ืขืจ ื“ื™ ื˜ื™ืคืขื ื™ืฉืŸ ืคื•ืŸ ื“ื™ ื’ืขืึธืœืึธื’ื™ืงืึทืœ ืฉื™ื›ื˜ืŸ.

ืกื™ื™ื–ืžื™ืง ืฉื™ืฃ ื˜ืึธื•ื™ื ื’ ื•ื™ืกืจื™ื›ื˜
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ ืœื•ืคื˜ ื‘ื™ืงืก ื™ืงืกื™ื™ืฅ ื’ื•ืžืข ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื–
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื›ื•ื•ืืœื™ืขืก ืคืึธืจืŸ ื“ื•ืจืš ื“ื™ ืฉื˜ื™ื™ืŸ ืžืึทืกืข ืื•ืŸ ื–ืขื ืขืŸ ืจืขืงืึธืจื“ืขื“ ื“ื•ืจืš ื›ื™ื™ื“ืจืึธื•ืคืึธื•ื ื–
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืคืึธืจืฉื•ื ื’ ืฉื™ืฃ ืคื•ืŸ ื“ื–ืฉื™ืึธืคื™ื–ื™ืงืึทืœ ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ "ืื™ื•ื•ืืŸ ื’ื•ื‘ืงื™ืŸ" ื‘ื™ื™ึท ื“ื™ ื‘ืขืจื˜ ืœืขื‘ืŸ ื“ื™ ื‘ืœืึทื’ืึธื•ื•ืขืฉื˜ืฉืขื ืกืงื™ ื‘ืจื™ืง ืื™ืŸ ืกื˜ ืคืขื˜ืขืจื‘ื•ืจื’
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืกื™ื™ื–ืžื™ืง ืกื™ื’ื ืึทืœ ืžืึธื“ืขืœ

ืจืึทืงืก ื”ืึธื‘ืŸ ืคืึทืจืฉื™ื“ืขื ืข ื’ืฉืžื™ื•ืช ืคึผืจืึธืคึผืขืจื˜ื™ืขืก. ืคึฟืึทืจ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ, ืขืจืฉื˜ืขืจ ืคื•ืŸ ืึทืœืข, ื’ื•ืžืข ืคึผืจืึธืคึผืขืจื˜ื™ืขืก ื–ืขื ืขืŸ ื•ื•ื™ื›ื˜ื™ืง - ื“ื™ ื’ื™ื›ืงื™ื™ึทื˜ ืคื•ืŸ ืคึผืจืึทืคึผืึทื’ื™ื™ืฉืึทืŸ ืคื•ืŸ ื’ื•ืžืข ื•ื•ื™ื™ื‘ืจื™ื™ืฉืึทื ื– ืื•ืŸ ื’ืขื“ื™ื›ื˜ืงื™ื™ึทื˜. ืื•ื™ื‘ ืฆื•ื•ื™ื™ ืœื™ื™ึทืขืจืก ื”ืึธื‘ืŸ ื“ื™ ื–ืขืœื‘ืข ืึธื“ืขืจ ื ืึธืขื ื˜ ืคึผืจืึธืคึผืขืจื˜ื™ืขืก, ื“ื™ ื›ื•ื•ืึทืœื™ืข ื•ื•ืขื˜ "ื ื™ื˜ ื‘ืึทืžืขืจืงืŸ" ื“ื™ ื’ืจืขื ืขืฅ ืฆื•ื•ื™ืฉืŸ ื–ื™ื™. ืื•ื™ื‘ ื“ื™ ื›ื•ื•ืึทืœื™ืข ื’ื™ื›ืงื™ื™ึทื˜ ืื™ืŸ ื“ื™ ืœื™ื™ึทืขืจืก ืึทื ื“ืขืจืฉ, ื“ืขืžืึธืœื˜ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ื•ื•ืขื˜ ืคึผืึทืกื™ืจืŸ ื‘ื™ื™ึท ื“ื™ ื’ืจืขื ืขืฅ ืคื•ืŸ ื“ื™ ืœื™ื™ึทืขืจืก. ื“ื™ ื’ืจืขืกืขืจ ื“ื™ ื—ื™ืœื•ืง ืื™ืŸ ืคึผืจืึธืคึผืขืจื˜ื™ืขืก, ื“ื™ ืžืขืจ ื˜ื™ืฃ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’. ื–ื™ื™ึทืŸ ื™ื ื˜ืขื ืกื™ื˜ื™ ื•ื•ืขื˜ ื–ื™ื™ืŸ ื‘ืืฉืœืืกืŸ ื“ื•ืจืš ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ื˜ (ืจืง):

ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื•ื•ื• ฯ ืื™ื– ื“ื™ ืฉื˜ื™ื™ืŸ ื’ืขื“ื™ื›ื˜ืงื™ื™ึทื˜, ฮฝ ืื™ื– ื“ื™ ื›ื•ื•ืึทืœื™ืข ื’ื™ื›ืงื™ื™ึทื˜, 1 ืื•ืŸ 2 ื‘ืึทืฆื™ื™ื›ืขื ืขืŸ ื“ื™ ืื•ื™ื‘ืขืจืฉื˜ืขืจ ืื•ืŸ ื ื™ื“ืขืจื™ืงืขืจ ืฉื™ื›ื˜ืŸ.

ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ืกื™ืžืคึผืœืึทืกื˜ ืื•ืŸ ืžืขืจืกื˜ ืงืึทืžืึทื ืœื™ ื’ืขื ื™ืฆื˜ ืกื™ื™ื–ืžื™ืง ืกื™ื’ื ืึทืœ ืžืึธื“ืขืœืก ืื™ื– ื“ื™ ืงืึธื ื•ื•ืึธืœื•ื˜ื™ืึธื ืึทืœ ืžืึธื“ืขืœ, ื•ื•ืขืŸ ื“ื™ ืจืขืงืึธืจื“ืขื“ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ ืื™ื– ืจืขืคึผืจื™ื–ืขื ื˜ื™ื“ ื•ื•ื™ ื“ืขืจ ืจืขื–ื•ืœื˜ืึทื˜ ืคื•ืŸ ืงืึทื ื•ื•ืึทืœื•ืฉืึทืŸ ืคื•ืŸ ืึท ืกื™ืงื•ื•ืึทื ืก ืคื•ืŸ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ ืžื™ื˜ ืึท ืกืึทื•ื ื“ื™ื ื’ ื“ื•ื™ืคืขืง:

ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื•ื•ื• ืก (ื˜) - ืกื™ื™ื–ืžื™ืฉ ืฉืคึผื•ืจ, ื“.ื”. ืึทืœืฅ ืจืขืงืึธืจื“ืขื“ ื“ื•ืจืš ืึท ื›ื™ื™ื“ืจืึธื•ืคืึธืŸ ืึธื“ืขืจ ื’ืขืึธืคืึธืŸ ื‘ืขืฉืึทืก ืึท ืคืึทืจืคืขืกื˜ื™ืงื˜ ืจืขื’ื™ืกื˜ืจืึทืฆื™ืข ืฆื™ื™ื˜, ื•ื•(ื˜) - ื“ืขืจ ืกื™ื’ื ืึทืœ ื“ื–ืฉืขื ืขืจื™ื™ื˜ืึทื“ ื“ื•ืจืš ื“ื™ ืœื•ืคื˜ ื‘ื™ืงืก, n(ื˜) - ื˜ืจืึทืค ืจืึทืฉ.

ืคึฟืึทืจ ื‘ื™ื™ึทืฉืคึผื™ืœ, ืœืึธืžื™ืจ ืจืขื›ืขื ืขืŸ ืึท ืกื™ื ื˜ืขื˜ื™ืฉ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ. ืžื™ืจ ื•ื•ืขืœืŸ ื ื•ืฆืŸ ื“ื™ ืจื™ืงืขืจ ื“ื•ื™ืคืขืง ื•ื•ื™ื™ื“ืœื™ ื’ืขื ื™ืฆื˜ ืื™ืŸ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ื•ื•ื™ ื“ืขืจ ืขืจืฉื˜ ืกื™ื’ื ืึทืœ. 

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]

ืขืจืฉื˜ ืกื™ื™ื–ืžื™ืง ืฉื˜ื•ืคึผ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืžื™ืจ ืฉื˜ืขืœืŸ ืฆื•ื•ื™ื™ ื‘ืึทื•ื ื“ืจื™ื– ืื™ืŸ ื˜ื™ืคืขื ื™ืฉืŸ ืคื•ืŸ 300 ืžื™ื– ืื•ืŸ 600 ืžื™ื–, ืื•ืŸ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ ื•ื•ืขื˜ ื–ื™ื™ืŸ ื˜ืจืึทืค - ื ื•ืžืขืจืŸ

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]]

ืกื™ืงื•ื•ืึทื ืก ืคื•ืŸ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืจืขื›ืขื ืขืŸ ืื•ืŸ ื•ื•ื™ื™ึทื–ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ. ื–ื™ื ื˜ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ ื”ืึธื‘ืŸ ืคืึทืจืฉื™ื“ืขื ืข ื•ื•ืื•ื ื“ืขืจ, ืžื™ืจ ืื•ื™ืš ื‘ืึทืงื•ืžืขืŸ ืฆื•ื•ื™ื™ ืฆื™ื™ื›ืŸ-ืึธืœื˜ืขืจื ื™ื™ื˜ื™ื ื’ ืจื™ืคืœืขืงืฉืึทื ื– ืื•ื™ืฃ ื“ื™ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ.

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]]

ืกื™ืžื™ืึทืœื™ื™ื˜ื™ื“ ืฉืคึผื•ืจ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืคึฟืึทืจ ื“ืขื ื‘ื™ื™ึทืฉืคึผื™ืœ, ืื™ืจ ื“ืึทืจืคึฟืŸ ืฆื• ืžืึทื›ืŸ ืึท ืจืขื–ืขืจื•ื•ืึทืฆื™ืข - ืื™ืŸ ืคืึทืงื˜, ื“ื™ ื˜ื™ืคืงื™ื™ึทื˜ ืคื•ืŸ ื“ื™ ืœื™ื™ึทืขืจืก ืื™ื– ื‘ืืฉืœืืกืŸ, ืคื•ืŸ ืงื•ืจืก, ืื™ืŸ ืžืขื˜ืขืจ, ืื•ืŸ ื“ื™ ื›ืขื–ืฉื‘ืŸ ืคื•ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ ืึทืงืขืจื– ืคึฟืึทืจ ื“ื™ ืฆื™ื™ื˜ ืคืขืœื“. ืขืก ื•ื•ืืœื˜ ื’ืขื•ื•ืขืŸ ืจื™ื›ื˜ื™ื’ืขืจ ืฆื• ืฉื˜ืขืœืŸ ื“ื™ ื˜ื™ืคืขื ื™ืฉืŸ ืื™ืŸ ืžืขื˜ืขืจ ืื•ืŸ ืื•ื™ืกืจืขื›ืขื ืขืŸ ื“ื™ ืฆื™ื™ื˜ืŸ ืคื•ืŸ ืื ืงื•ืžืขืŸ ื•ื•ื™ืกื ื“ื™ื’ ื“ื™ ืฉื ืขืœืงื™ื™ื˜ืŸ ืื™ืŸ ื“ื™ ืฉื™ื›ื˜ืŸ. ืื™ืŸ ื“ืขื ืคืึทืœ, ืื™ืš ืžื™ื“ ืฉื˜ืขืœืŸ ื“ื™ ืœื™ื™ึทืขืจืก ืื•ื™ืฃ ื“ื™ ืฆื™ื™ื˜ ืึทืงืก.

ืื•ื™ื‘ ืžื™ืจ ืจืขื“ืŸ ื•ื•ืขื’ืŸ ืคืขืœื“ ืฉื˜ื•ื“ื™ื•ื, ื•ื•ื™ ืึท ืจืขื–ื•ืœื˜ืึทื˜ ืคื•ืŸ ืึทื–ืึท ืึทื‘ื–ืขืจื•ื•ื™ื™ืฉืึทื ื–, ืึท ืจื™ื–ื™ืง ื ื•ืžืขืจ ืคื•ืŸ ืึทื–ืึท ืฆื™ื™ื˜ ืกืขืจื™ืข (ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก) ื–ืขื ืขืŸ ืจืขืงืึธืจื“ืขื“. ืคึฟืึทืจ ื‘ื™ื™ึทืฉืคึผื™ืœ, ื•ื•ืขืŸ ืื™ืจ ืœืขืจื ืขืŸ ืึท ืึธืคึผื˜ื™ื™ืœื•ื ื’ 25 ืงื™ืœืืžืขื˜ืขืจ ืœืึทื ื’ ืื•ืŸ 15 ืงื™ืœืืžืขื˜ืขืจ ื‘ืจื™ื™ื˜, ื•ื•ื•, ื•ื•ื™ ืึท ืจืขื–ื•ืœื˜ืึทื˜ ืคื•ืŸ ื“ื™ ืึทืจื‘ืขื˜, ื™ืขื“ืขืจ ืฉืคึผื•ืจ ืงืขืจืึทืงื˜ืขืจื™ื™ื–ืึทื– ืึท ืฆืขืœ ืกื™ื™ื–ื“ 25x25 ืžืขื˜ืขืจ (ืึทื–ืึท ืฆืขืœ ืื™ื– ื’ืขืจื•ืคืŸ ืึท ื‘ื™ืŸ), ื“ื™ ืœืขืฆื˜ ื“ืึทื˜ืŸ ืžืขื ื’ืข ื•ื•ืขื˜ ืึทื ื˜ื”ืึทืœื˜ืŸ 600000 ื˜ืจืึทืกืขืก . ืžื™ื˜ ืึท ืฆื™ื™ื˜ ืžื•ืกื˜ืขืจื•ื ื’ ืฉืจื™ื˜ ืคื•ืŸ 1 ืžื™ื–, ืึท ืจืขืงืึธืจื“ื™ื ื’ ืฆื™ื™ื˜ ืคื•ืŸ 5 ืกืขืงื•ื ื“ืขืก, ื“ื™ ืœืขืฆื˜ ื“ืึทื˜ืŸ ื˜ืขืงืข ื•ื•ืขื˜ ื–ื™ื™ืŸ ืžืขืจ ื•ื•ื™ 11 ื’ื™ื’ืื‘ื™ื™ื˜, ืื•ืŸ ื“ืขืจ ื‘ืึทื ื“ ืคื•ืŸ ื“ืขืจ ืึธืจื™ื’ื™ื ืขืœ "ืจื•ื™" ืžืึทื˜ืขืจื™ืึทืœ ืงืขื ืขืŸ ื–ื™ื™ืŸ ื”ื•ื ื“ืขืจื˜ืขืจ ืคื•ืŸ ื’ื™ื’ืื‘ื™ื™ื˜.

ื•ื•ื™ ืฆื• ืึทืจื‘ืขื˜ืŸ ืžื™ื˜ ื–ื™ื™ ื•ื•ืึธืœืคืจืึทื ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท?

ืคึผืขืงืœ ื’ืขืึธืœืึธื’ื™ื™ืึธ

ื“ื™ ืึทื ื˜ื•ื•ื™ืงืœื•ื ื’ ืคื•ืŸ ื“ื™ ืคึผืขืงืœ ืื ื’ืขื”ื•ื™ื‘ืŸ ืคืจืขื’ืŸ ืื•ื™ืฃ ื“ืขืจ ื•ื•ืง ื•ื•ืึทื ื˜ ืคื•ืŸ ื“ืขืจ ืจื•ืกื™ืฉ-ื’ืขืจืขื“ื˜ ืฉื˜ื™ืฆืŸ ื’ืจื•ืคึผืข. ื ื“ืื  ืง ื“ ื™ ืจืขืืงืฆื™ ืข ืคื• ืŸ ื“ืข ืจ ืงื”ื™ืœ ื” ื”ื ื˜ ืžืข ืŸ ื–ื™ ืš ื’ืขืคื•ื ืข ืŸ ื ืœื™ื™ื–ื•ื ื’ . ืื•ืŸ ื•ื•ื™ ืึท ืจืขื–ื•ืœื˜ืึทื˜, ืขืก ืคืืจืงืขืจื˜ ืื™ืŸ ืึท ืขืจื ืกื˜ ืึทื ื˜ื•ื•ื™ืงืœื•ื ื’. ืงืึธืจืึทืกืคึผืึทื ื“ื™ื ื’ ืคึผืึธืกื˜ืŸ ืื•ื™ืฃ Wolfram ืงืึทืžื™ื•ื ื™ื˜ื™ ื•ื•ืึทื ื˜ ืื™ื– ื’ืขื•ื•ืขืŸ ืืคื™ืœื• ืื ื’ืขืฆื™ื™ื›ื ื˜ ื“ื•ืจืš ื“ื™ ืžืึธื“ืขืจืึทื˜ืึธืจืก. ื“ืขืจื•ื•ื™ื™ึทืœ, ื“ืขืจ ืคึผืขืงืœ ืฉื˜ื™ืฆื˜ ื“ื™ ืคืืœื’ืขื ื“ืข ื˜ื™ื™ืคึผืก ืคื•ืŸ ื“ืึทื˜ืŸ ื•ื•ืึธืก ื–ืขื ืขืŸ ืึทืงื˜ื™ื•ื•ืœื™ ื’ืขื ื™ืฆื˜ ืื™ืŸ ื“ื™ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืื™ื ื“ื•ืกื˜ืจื™ืข:

  1. ืึทืจื™ื™ึทื ืคื™ืจ ืคื•ืŸ ZMAP ืื•ืŸ IRAP ืงืึทืจื˜ืึธื’ืจืึทืคื™ืง ื“ืึทื˜ืŸ
  2. ืึทืจื™ื™ึทื ืคื™ืจ ืคื•ืŸ ื’ืขื–ื•ื ื˜ ืžืขื–ืฉืขืจืžืึทื ืฅ ืื™ืŸ LAS ืคึฟืึธืจืžืึทื˜
  3. ืึทืจื™ื™ึทื ืฉืจื™ื™ึทื‘ ืื•ืŸ ืจืขื–ื•ืœื˜ืึทื˜ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื˜ืขืงืขืก ืคื•ืŸ ื“ืขื ืคึฟืึธืจืžืึทื˜ SEGY

ืฆื• ื™ื ืกื˜ืึทืœื™ืจืŸ ื“ืขื ืคึผืขืงืœ, ืื™ืจ ืžื•ื–ืŸ ื ืึธื›ื’ื™ื™ืŸ ื“ื™ ื™ื ืกื˜ืจืึทืงืฉืึทื ื– ืื•ื™ืฃ ื“ื™ ืืจืืคืงืืคื™ืข ื‘ืœืึทื˜ ืคื•ืŸ ื“ื™ ืงืึทืžืคึผื™ื™ืœื“ ืคึผืขืงืœ, ื“.ื”. ื•ื™ืกืคื™ืจืŸ ื“ื™ ืคืืœื’ืขื ื“ืข ืงืึธื“ ืื™ืŸ ืงื™ื™ืŸ ืžืึทื˜ื”ืขืžืึทื˜ื™ืง ื”ืขืคื˜:

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

ื ืึธืš ื“ืขื, ื“ืขืจ ืคึผืขืงืœ ื•ื•ืขื˜ ื–ื™ื™ืŸ ืื™ื ืกื˜ืึทืœื™ืจืŸ ืื™ืŸ ื“ื™ ืคืขืœื™ืงื™ื™ึทื˜ ื˜ืขืงืข, ื“ืขืจ ื“ืจืš ืฆื• ื•ื•ืึธืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื‘ืืงื•ืžืขืŸ ื•ื•ื™ ื’ื™ื™ื˜:

FileNameJoin[{$UserBasePacletsDirectory, "Repository"}]

ืคึฟืึทืจ ื‘ื™ื™ึทืฉืคึผื™ืœ, ืœืึธื–ืŸ ืื•ื ื“ื– ื‘ืึทื•ื•ื™ื™ึทื–ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืคึฟืขื™ึดืงื™ื™ื˜ืŸ ืคื•ืŸ ื“ืขื ืคึผืขืงืœ. ื“ืขืจ ืจื•ืฃ ืื™ื– ื˜ืจืึทื“ื™ืฉืึทื ืึทืœื™ ื’ืขืžืื›ื˜ ืคึฟืึทืจ ืคึผืึทืงืึทื“ื–ืฉืึทื– ืื™ืŸ ื“ื™ Wolfram ืฉืคึผืจืึทืš:

Get["GeologyIO`"]

ื“ืขืจ ืคึผืขืงืœ ืื™ื– ื“ืขื•ื•ืขืœืึธืคึผืขื“ ื ื™ืฆืŸ ื•ื•ืึธืœืคืจืึทื ื•ื•ืึธืจืงื‘ืขื ื˜ืฉ. ื“ืึธืก ืึทืœืึทื•ื– ืื™ืจ ืฆื• ื‘ืึทื’ืœื™ื™ื˜ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืคืึทื ื’ืงืฉืึทื ืึทืœื™ื˜ื™ ืคื•ืŸ ื“ืขื ืคึผืขืงืœ ืžื™ื˜ ื“ืึทืงื™ื•ืžืขื ื˜ื™ื™ืฉืึทืŸ ื•ื•ืึธืก ืื™ื– ื ื™ืฉื˜ ืึทื ื“ืขืจืฉ ืื™ืŸ ืคึผืจืขื–ืขื ื˜ื™ืจื•ื ื’ ืคึฟืึธืจืžืึทื˜ ืคื•ืŸ ื“ื™ ื“ืึทืงื™ื•ืžืขื ื˜ื™ื™ืฉืึทืŸ ืคื•ืŸ Wolfram Mathematica ื–ื™ืš ืื•ืŸ ืฆื•ืฉื˜ืขืœืŸ ื“ื™ ืคึผืขืงืœ ืžื™ื˜ ืคึผืจื•ื‘ื™ืจืŸ ื˜ืขืงืขืก ืคึฟืึทืจ ืึท ืขืจืฉื˜ืขืจ ื‘ืึทืงืึทื ื˜ืขืจ.

ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืึทื–ืึท ืึท ื˜ืขืงืข, ืื™ืŸ ื‘ืึทื–ื•ื ื“ืขืจ, ืื™ื– ื“ื™ ื˜ืขืงืข "Marmousi.segy" - ื“ืึธืก ืื™ื– ืึท ืกื™ื ื˜ืขื˜ื™ืฉ ืžืึธื“ืขืœ ืคื•ืŸ ืึท ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืึธืคึผื˜ื™ื™ืœื•ื ื’, ื•ื•ืึธืก ืื™ื– ื“ืขื•ื•ืขืœืึธืคึผืขื“ ื“ื•ืจืš ื“ืขืจ ืคืจืื ืฆื•ื™ื–ื™ืฉ ืื™ื ืกื˜ื™ื˜ื•ื˜ ืคื•ืŸ ืคึผืขื˜ืจืึธืœืขื•ื. ืžื™ื˜ ื“ืขื ืžืึธื“ืขืœ, ื“ืขื•ื•ืขืœืึธืคึผืขืจืก ืคึผืจื•ื‘ื™ืจืŸ ื–ื™ื™ืขืจ ืื™ื™ื’ืขื ืข ืึทืœื’ืขืจื™ื“ืึทืžื– ืคึฟืึทืจ ื›ื•ื•ืึทืœื™ืข ืคืขืœื“ ืžืึธื“ืขืœื™ื ื’, ื“ืึทื˜ืŸ ืคึผืจืึทืกืขืกื™ื ื’, ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ ื™ื ื•ื•ืขืจื–ืฉืึทืŸ, ืขื˜ืง. ื“ื™ Marmousi ืžืึธื“ืขืœ ื–ื™ืš ืื™ื– ืกื˜ืึธืจื“ ืื™ืŸ ื“ื™ ืจื™ืคึผืึทื–ืึทื˜ืึธืจื™ ื•ื•ื• ื“ื™ ืคึผืขืงืœ ืื™ื– ื“ืึทื•ื ืœืึธื•ื“ื™ื“. ืฆื• ื‘ืึทืงื•ืžืขืŸ ื“ื™ ื˜ืขืงืข, ืœื•ื™ืคืŸ ื“ื™ ืคืืœื’ืขื ื“ืข ืงืึธื“:

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

ืึทืจื™ื™ึทื ืคื™ืจ ืจืขื–ื•ืœื˜ืึทื˜ - SEGYData ื›ื™ื™ืคืขืฅ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ SEGY ืคึฟืึธืจืžืึทื˜ ื™ื ื•ื•ืึทืœื•ื•ื– ืกื˜ืึธืจื™ื ื’ ืคืึทืจืฉื™ื“ืŸ ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ืึทื‘ื–ืขืจื•ื•ื™ื™ืฉืึทื ื–. ืขืจืฉื˜ืขืจ, ืขืก ื–ืขื ืขืŸ ื˜ืขืงืกื˜ ื‘ืึทืžืขืจืงื•ื ื’ืขืŸ. ื“ื ื–ืขื ืขืŸ ืืจื™ื™ืŸ ืื™ื ืคืืจืžืืฆื™ืข ืื™ื‘ืขืจ ื“ืขื ืืจื˜ ืคื•ืŸ ืืจื‘ืขื˜, ื“ื™ ื ืขืžืขืŸ ืคื•ืŸ ื“ื™ ืคื™ืจืžืขืก ื•ื•ืืก ื”ืื‘ืŸ ื“ื•ืจื›ื’ืขืคื™ืจื˜ ื“ื™ ืžืขืกื˜ืŸ ืืื–"ื• ื•. ืื™ืŸ ืื•ื ื“ื–ืขืจ ืคืึทืœ, ื“ืขื ื›ืขื“ืขืจ ืื™ื– ื’ืขืจื•ืคืŸ ื“ื•ืจืš ืึท ื‘ืงืฉื” ืžื™ื˜ ื“ื™ ื˜ืขืงืกื˜ื”ืขืึทื“ืขืจ ืฉืœื™ืกืœ. ื“ืึธ ืื™ื– ืึท ืคืึทืจืงื™ืจืฆื˜ ื˜ืขืงืกื˜ ื˜ื™ื˜ืœ:

Short[marmousi["TextHeader"]]

"ื“ื™ ืžืึทืจืžืึธื•ืกื™ ื“ืึทื˜ืŸ ืฉื˜ืขืœืŸ ืื™ื– ื“ื–ืฉืขื ืขืจื™ื™ื˜ืึทื“ ืื™ืŸ ื“ืขื ืื™ื ืกื˜ื™ื˜ื•ื˜ ... ืžืึทืงืกื™ืžื•ื ื’ื™ื›ืงื™ื™ึทื˜ ืคื•ืŸ 1500 ืขื / s ืื•ืŸ ืึท ืžืึทืงืกื™ืžื•ื ืคื•ืŸ 5500 ืขื / s)"

ืื™ืจ ืงืขื ืขืŸ ืึทืจื•ื™ืกื•ื•ื™ื™ึทื–ืŸ ื“ื™ ืคืึทืงื˜ื™ืฉ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืžืึธื“ืขืœ ื“ื•ืจืš ืึทืงืกืขืก ื“ื™ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ื ื™ืฆืŸ ื“ื™ "ื˜ืจืึทืกืขืก" ืฉืœื™ืกืœ (ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ืคึฟืขื™ึดืงื™ื™ื˜ืŸ ืคื•ืŸ ื“ืขื ืคึผืขืงืœ ืื™ื– ืคืึทืœ-ื™ื ืกืขื ืกื™ื˜ื™ื•ื• ืฉืœื™ืกืœืขืŸ):

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

ืžืึทืจืžืึธื•ืกื™ ืžืึธื“ืขืœ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ืขืจื•ื•ื™ื™ึทืœ, ื“ืขืจ ืคึผืขืงืœ ืื•ื™ืš ืึทืœืึทื•ื– ืื™ืจ ืฆื• ืึธืคึผืœืึธื“ื™ืจืŸ ื“ืึทื˜ืŸ ืื™ืŸ ืคึผืึทืจืฅ ืคื•ืŸ ื’ืจื•ื™ืก ื˜ืขืงืขืก, ื•ื•ืึธืก ืžืื›ื˜ ืขืก ืžืขื’ืœืขืš ืฆื• ืคึผืจืึธืฆืขืก ื˜ืขืงืขืก ื•ื•ืึธืก ืงืขื ืขืŸ ื“ืขืจื’ืจื™ื™ื›ืŸ ื˜ืขื ืก ืคื•ืŸ ื’ื™ื’ืื‘ื™ื™ื˜ ืื™ืŸ ื’ืจื™ื™ืก. ื“ืขืจ ืคึผืขืงืœ ืื•ื™ืš ื›ื•ืœืœ ืคืึทื ื’ืงืฉืึทื ื– ืคึฟืึทืจ ืขืงืกืคึผืึธืจื˜ื™ื ื’ ื“ืึทื˜ืŸ ืฆื• .ืกืขื’ื™ ืื•ืŸ ืคึผืึทืจื˜ื™ื™ื™ืฉ ืึทื“ื™ื ื’ ืฆื• ื“ื™ ืกื•ืฃ ืคื•ืŸ ื“ืขืจ ื˜ืขืงืข.

ืกืขืคึผืขืจืึทื˜ืœื™, ืขืก ืื™ื– ื›ื“ืื™ ืฆื• ื‘ืืžืขืจืงืŸ ื“ื™ ืคืึทื ื’ืงืฉืึทื ืึทืœื™ื˜ื™ ืคื•ืŸ ื“ืขื ืคึผืขืงืœ ื•ื•ืขืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืึท ืงืึธืžืคึผืœืขืงืก ืกื˜ืจื•ืงื˜ื•ืจ ืคื•ืŸ .ืกืขื’ื™-ืคื™ืœืขืก. ื–ื™ื ื˜ ืขืก ืึทืœืึทื•ื– ื ื™ื˜ ื‘ืœื•ื™ื– ืึทืงืกืขืก ืฆื• ื™ื—ื™ื“ ื˜ืจืึทืกืขืก, ื›ืขื“ืขืจื– ื“ื•ืจืš ืฉืœื™ืกืœืขืŸ ืื•ืŸ ื™ื ื“ืขืงืกื™ื–, ืึธื‘ืขืจ ืื•ื™ืš ื˜ืฉืึทื ื’ื™ื ื’ ื–ื™ื™ ืžื™ื˜ ืกืึทื‘ืกืึทืงื•ื•ืึทื ื˜ ืฉืจื™ื™ื‘ืŸ ืฆื• ืึท ื˜ืขืงืข. ืคื™ืœืข ืคื•ืŸ โ€‹โ€‹ื“ื™ ื˜ืขื›ื ื™ืฉ ื“ืขื˜ืึทื™ืœืก ืคื•ืŸ ื“ื™ ื™ืžืคึผืœืึทืžืขื ื˜ื™ื™ืฉืึทืŸ ืคื•ืŸ GeologyIO ื–ืขื ืขืŸ ื•ื•ื™ื™ึทื˜ืขืจ ืคื•ืŸ ื“ืขื ืคืึทืจื ืขื ืคื•ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ ืื•ืŸ ืžื™ืกื˜ืึธืžืข ืคืึทืจื“ื™ื ืขืŸ ืึท ื‘ืึทื–ื•ื ื“ืขืจ ื‘ืึทืฉืจื™ื™ึทื‘ื•ื ื’.

ื“ื™ ืฉื™ื™ื›ื•ืช ืคื•ืŸ ืกืคึผืขืงื˜ืจืึทืœ ืึทื ืึทืœื™ืกื™ืก ืื™ืŸ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ

ื“ื™ ืคื™ื™ื™ืงื™ื™ื˜ ืฆื• ืึทืจื™ื™ึทื ืคื™ืจ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืื™ืŸ Wolfram Mathematica ืึทืœืึทื•ื– ืื™ืจ ืฆื• ื ื•ืฆืŸ ื“ื™ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืกื™ื’ื ืึทืœ ืคึผืจืึทืกืขืกื™ื ื’ ืคืึทื ื’ืงืฉืึทื ืึทืœื™ื˜ื™ ืคึฟืึทืจ ื™ืงืกืคึผืขืจืžืขื ืึทืœ ื“ืึทื˜ืŸ. ื–ื™ื ื˜ ื™ืขื“ืขืจ ืกื™ื™ื–ืžื™ืง ืฉืคึผื•ืจ ืื™ื– ืึท ืฆื™ื™ื˜ ืกืขืจื™ืข, ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืžื›ืฉื™ืจื™ื ืฆื• ืœืขืจื ืขืŸ ื–ื™ื™ ืื™ื– ืกืคึผืขืงื˜ืจืึทืœ ืึทื ืึทืœื™ืกื™ืก. ืฆื•ื•ื™ืฉืŸ ื“ื™ ืคึผืจื™ืจืขืงื•ื•ืึทื–ืึทืฅ ืคึฟืึทืจ ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ื“ื™ ืึธืคื˜ืงื™ื™ึทื˜ ืื™ื ื”ืึทืœื˜ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ื–ืขื ืขืŸ, ืœืžืฉืœ, ื“ื™ ืคืืœื’ืขื ื“ืข:

  1. ืคืึทืจืฉื™ื“ืขื ืข ื˜ื™ื™ืคึผืก ืคื•ืŸ ื›ื•ื•ืืœื™ืขืก ื–ืขื ืขืŸ ืงืขืจืึทืงื˜ืขืจื™ื™ื–ื“ ื“ื•ืจืš ืคืึทืจืฉื™ื“ืขื ืข ืึธืคื˜ืงื™ื™ึทื˜ ื–ืึทืฅ. ื“ืึธืก ืึทืœืึทื•ื– ืื™ืจ ืฆื• ืื•ื™ืกืงืœื™ื™ึทื‘ืŸ ื ื•ืฆื™ืง ื›ื•ื•ืืœื™ืขืก ืื•ืŸ ืคืึทืจืฉื˜ื™ืงืŸ ื™ื ื˜ืขืจืคื™ืจืึทื ืก ื›ื•ื•ืืœื™ืขืก.
  2. ืฉื˜ื™ื™ืŸ ืคึผืจืึธืคึผืขืจื˜ื™ืขืก ืึทื–ืึท ื•ื•ื™ ืคึผืึธืจืึธืกื™ื˜ื™ ืื•ืŸ ื–ืขื˜ื™ืงื•ื ื’ ืงืขื ืขืŸ ื•ื•ื™ืจืงืŸ ื“ื™ ืึธืคื˜ืงื™ื™ึทื˜ ืื™ื ื”ืึทืœื˜. ื“ืึธืก ืึทืœืึทื•ื– ืื™ืจ ืฆื• ืื•ื™ืกืงืœื™ื™ึทื‘ืŸ ืจืึทืงืก ืžื™ื˜ ื‘ืขืกืขืจ ืคึผืจืึธืคึผืขืจื˜ื™ืขืก.
  3. ืœื™ื™ึทืขืจืก ืžื™ื˜ ืคืึทืจืฉื™ื“ืขื ืข ื’ืจืขื‘ ื’ืจื•ื ื˜ ืึทื ืึทืžืึทืœื™ื– ืื™ืŸ ืคืึทืจืฉื™ื“ืขื ืข ืึธืคื˜ืงื™ื™ึทื˜ ืจื™ื™ื ื“ื–ืฉืึทื–.

ื“ื™ ื“ืจื™ื˜ ืคื•ื ื˜ ืื™ื– ื“ืขืจ ื”ื•ื™ืคึผื˜ ืื™ืŸ ื“ืขื ืงืึธื ื˜ืขืงืกื˜ ืคื•ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ. ื•ื ื˜ืขืจ ืื™ื– ืึท ืงืึธื“ ืคืจืึทื’ืžืขื ื˜ ืคึฟืึทืจ ืงืึทืœืงื™ืึทืœื™ื™ื˜ื™ื ื’ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ืื™ืŸ ื“ื™ ืคืึทืœ ืคื•ืŸ ืึท ืฉื™ื›ื˜ืข ืžื™ื˜ ื•ื•ืขืจื™ื™ื ื’ ื’ืจืขื‘ - ืึท ื•ื•ืขื“ื–ืฉ ืžืึธื“ืขืœ. ื“ืขืจ ืžืึธื“ืขืœ ืื™ื– ื˜ืจืึทื“ื™ืฉืึทื ืึทืœื™ ื’ืขืœืขืจื ื˜ ืื™ืŸ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ืคึฟืึทืจ ื“ื™ ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ื™ื ื˜ืขืจืคื™ืจืึทื ืก ื™ืคืขืงืฅ ื•ื•ืขืŸ ื›ื•ื•ืืœื™ืขืก ืฉืคื™ื’ืœื˜ ืคื•ืŸ ืคื™ืœืข ืœื™ื™ึทืขืจืก ื–ืขื ืขืŸ ืกื•ืคึผืขืจืึทืžืคึผืึธื•ื–ื“ ืื•ื™ืฃ ื™ืขื“ืขืจ ืื ื“ืขืจืขืจ.

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]]

ืคึผื™ื ื˜ืฉืึธื•ื˜ ืžืึธื“ืขืœ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ ื›ื•ื•ืึทืœื™ืข ื’ื™ื›ืงื™ื™ึทื˜ ื™ืŸ ื“ืขืจ ื•ื•ืขื“ื–ืฉ ืื™ื– 4500 ืขื / s, ืึทืจื•ื™ืก ื“ื™ ื•ื•ืขื“ื–ืฉ 4000 ืขื / s, ืื•ืŸ ื“ื™ ื’ืขื“ื™ื›ื˜ืงื™ื™ึทื˜ ืื™ื– ืื ื’ืขื ื•ืžืขืŸ ืฆื• ื–ื™ื™ืŸ ืงืขืกื™ื™ื“ืขืจื“ื™ืง 2200 ื’ / ืกืขื ื˜ื™ืžืขื˜ืขืจ XNUMX. ืคึฟืึทืจ ืึทื–ืึท ืึท ืžืึธื“ืขืœ, ืžื™ืจ ืจืขื›ืขื ืขืŸ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ ืื•ืŸ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก.

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]

ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ืคึฟืึทืจ ื“ื™ ื•ื•ืขื“ื–ืฉ ืžืึธื“ืขืœ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ ืกื™ืงื•ื•ืึทื ืก ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ื“ื™ืคึผื™ืงื˜ื™ื“ ืื™ืŸ ื“ืขื ืคื™ื’ื•ืจ ืื™ื– ื’ืขืจื•ืคืŸ ืึท ืกื™ื™ื–ืžื™ืง ืึธืคึผื˜ื™ื™ืœื•ื ื’. ื•ื•ื™ ืื™ืจ ืงืขื ืขืŸ ื–ืขืŸ, ื–ื™ื™ึทืŸ ื™ื ื˜ืขืจืคึผืจื™ื˜ื™ื™ืฉืึทืŸ ืงืขื ืขืŸ ืื•ื™ืš ื–ื™ื™ืŸ ื’ืขื˜ืืŸ ืื•ื™ืฃ ืึท ื™ื ื˜ื•ืึทื˜ื™ื•ื• ืžื“ืจื’ื”, ื•ื•ื™ื™ึทืœ ื“ื™ ื“ื–ืฉื™ืึทืžืึทื˜ืจื™ ืคื•ืŸ ื“ื™ ืฉืคื™ื’ืœื˜ ื›ื•ื•ืืœื™ืขืก ื™ื•ื ื™ืงืœื™ ืงืึธืจืึทืกืคึผืึทื ื“ื– ืฆื• ื“ื™ ืžืึธื“ืขืœ ื•ื•ืึธืก ืื™ื– ื’ืขื•ื•ืขืŸ ืกืคึผืขืกื™ืคื™ืขื“ ืคืจื™ืขืจ. ืื•ื™ื‘ ืžื™ืจ ืคื•ื ืึทื ื“ืขืจืงืœื™ื™ึทื‘ืŸ ื“ื™ ื˜ืจืึทืกืขืก ืื™ืŸ ืžืขืจ ื“ืขื˜ืึทืœ, ืžื™ืจ ืงืขื ืขืŸ ื–ืขืŸ ืึทื– ื“ื™ ื˜ืจืึทืกืขืก ืคื•ืŸ 1 ืฆื•, ื‘ืขืขืจืขืš 30, ื˜ืึธืŸ ื ื™ื˜ ืึทื ื“ืขืจืฉ - ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืคื•ืŸ ื“ื™ ืฉืคึผื™ืฅ ืคื•ืŸ ื“ื™ ืคืึธืจืžื™ืจื•ื ื’ ืื•ืŸ ืคื•ืŸ ื“ื™ ืคึผื™ืึทื˜ืข ื˜ืึธืŸ ื ื™ื˜ ืึธื•ื•ื•ืขืจืœืึทืคึผ ื™ืขื“ืขืจ ืื ื“ืขืจืขืจ. ืกื˜ืึทืจื˜ื™ื ื’ ืคื•ืŸ ื“ื™ 31 ืฉืคึผื•ืจ, ื“ื™ ืจื™ืคืœืขืงืฉืึทื ื– ืึธื ื”ื™ื™ื‘ืŸ ืฆื• ืึทืจื™ื™ึทื ืžื™ืฉื  ื–ื™ืš. ืื•ืŸ ื›ืึธื˜ืฉ, ืื™ืŸ ื“ื™ ืžืึธื“ืขืœ, ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืงืึธื•ืึทืคื™ืฉืึทื ืฅ ื˜ืึธืŸ ื ื™ื˜ ื˜ื•ื™ืฉืŸ ื›ืึธืจื™ื–ืึทื ื˜ืึทืœื™ - ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ื˜ื•ื™ืฉืŸ ื–ื™ื™ืขืจ ื™ื ื˜ืขื ืกื™ื˜ื™ ื•ื•ืขืŸ ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ื’ืจืขื‘ ืขื ื“ืขืจื•ื ื’ืขืŸ.

ื‘ืึทื˜ืจืึทื›ื˜ืŸ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“ ืคื•ืŸ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืคื•ืŸ ื“ืขืจ ืื•ื™ื‘ืขืจืฉื˜ืขืจ ื’ืจืขื ืขืฅ ืคื•ืŸ ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ. ืกื˜ืึทืจื˜ื™ื ื’ ืคื•ืŸ ื“ื™ 60 ืฉืคึผื•ืจ, ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ื™ื ื˜ืขื ืกื™ื˜ื™ ื”ื™ื™ื‘ื˜ ืฆื• ืคืึทืจื’ืจืขืกืขืจืŸ ืื•ืŸ ื•ื•ืขืจื˜ ืžืึทืงืกื™ืžื•ื ืื•ื™ืฃ ื“ื™ 70 ืฉืคึผื•ืจ. ื“ืึธืก ืื™ื– ื•ื•ื™ ื“ื™ ื™ื ื˜ืขืจืคื™ืจืึทื ืก ืคื•ืŸ ื›ื•ื•ืืœื™ืขืก ืคื•ืŸ ื“ื™ ืฉืคึผื™ืฅ ืื•ืŸ ื“ื ืึธ ืคื•ืŸ ื“ื™ ืœื™ื™ึทืขืจืก ืžืึทื ืึทืคืขืกืฅ ื–ื™ืš, ื•ื•ืึธืก ืคื™ืจืŸ ืื™ืŸ ืขื˜ืœืขื›ืข ืคืืœืŸ ืฆื• ื‘ืึทื˜ื™ื™ึทื˜ื™ืง ืึทื ืึทืžืึทืœื™ื– ืื™ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ืจืขืงืึธืจื“.

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]

ื’ืจืึทืคื™ืง ืคื•ืŸ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“ ืคื•ืŸ ื“ื™ ืฉืคื™ื’ืœื˜ ื›ื•ื•ืึทืœื™ืข ืคื•ืŸ โ€‹โ€‹ื“ืขืจ ืื•ื™ื‘ืขืจืฉื˜ืขืจ ื‘ืจืขื’ ืคื•ืŸ ื“ื™ ื•ื•ืขื“ื–ืฉ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืขืก ืื™ื– ืœืึทื“ื–ืฉื™ืงืึทืœ ืึทื– ื•ื•ืขืŸ ื“ืขืจ ืกื™ื’ื ืึทืœ ืื™ื– ื ื™ื“ืขืจื™ืงืขืจ-ืึธืคื˜ืงื™ื™ึทื˜, ื“ื™ ื™ื ื˜ืขืจืคื™ืจืึทื ืก ื”ื™ื™ื‘ื˜ ืฆื• ื“ืขืจืฉื™ื™ึทื ืขืŸ ืื™ืŸ ื’ืจื•ื™ืก ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ื’ืขื“ื™ื›ื˜ืงื™ื™ึทื˜, ืื•ืŸ ืื™ืŸ ื“ืขื ืคืึทืœ ืคื•ืŸ ืึท ื”ื•ื™ืš-ืึธืคื˜ืงื™ื™ึทื˜ ืกื™ื’ื ืึทืœ, ื™ื ื˜ืขืจืคื™ืจืึทื ืก ืึทืงืขืจื– ืื™ืŸ ืงืœืขื ืขืจืขืจ ื’ืจืขื‘. ื“ื™ ืคืืœื’ืขื ื“ืข ืงืึธื“ ืกื ื™ืคึผืึทื˜ ืงืจื™ื™ื™ืฅ ืึท ืกื™ื’ื ืึทืœ ื‘ื™ื™ 35 ื”ื–, 55 ื”ื– ืื•ืŸ 85 ื”ื–.

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]

ื’ืึทื ื’ ืคื•ืŸ ืขืจืฉื˜ ืกื™ื’ื ืึทืœื– ืžื™ื˜ ืคืจื™ืงื•ื•ืึทื ืกื™ื– 35 ื”ื–, 55 ื”ื–, 85 ื”ื–
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื ืึธืš ืคึผืขืจืคืึธืจืžื™ื ื’ ื“ื™ ื›ืขื–ืฉื‘ืŸ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ืื•ืŸ ืคึผืœืึทื˜ื™ื ื’ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“ื– ืคื•ืŸ ื“ื™ ืจืขืคืœืขืงื˜ืขื“ ื›ื•ื•ืึทืœื™ืข, ืžื™ืจ ืงืขื ืขืŸ ื–ืขืŸ ืึทื– ืคึฟืึทืจ ืคืึทืจืฉื™ื“ืขื ืข ืคืจื™ืงื•ื•ืึทื ืกื™ื– ื“ื™ ืึทื ืึทืžืึทืœื™ ืื™ื– ื‘ืืžืขืจืงื˜ ืื™ืŸ ืคืึทืจืฉื™ื“ืขื ืข ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ื˜ื”ื™ืงื ืขืกืกืขืก.

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]

ื’ืจืึทืคืก ืคื•ืŸ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“ื– ืคื•ืŸ ื“ื™ ืฉืคื™ื’ืœื˜ ื›ื•ื•ืึทืœื™ืข ืคื•ืŸ โ€‹โ€‹ื“ืขืจ ืื•ื™ื‘ืขืจืฉื˜ืขืจ ื‘ืจืขื’ ืคื•ืŸ ื“ื™ ื•ื•ืขื“ื–ืฉ ืคึฟืึทืจ ืคืึทืจืฉื™ื“ืขื ืข ืคืจื™ืงื•ื•ืึทื ืกื™ื–
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ ืคื™ื™ื™ืงื™ื™ื˜ ืฆื• ืฆื™ืขืŸ ืงืึทื ืงืœื•ื–ืฉืึทื ื– ื•ื•ืขื’ืŸ ื“ื™ ื’ืจืขื‘ ืคื•ืŸ ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ืคึฟื•ืŸ ื“ื™ ืจืขื–ื•ืœื˜ืึทื˜ืŸ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ืึทื‘ื–ืขืจื•ื•ื™ื™ืฉืึทื ื– ืื™ื– ื’ืึธืจ ื ื•ืฆื™ืง, ื•ื•ื™ื™ึทืœ ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ื˜ืึทืกืงืก ืื™ืŸ ื“ื™ ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ืคื•ืŸ ืึท ื™ื™ืœ ืคืขืœื“ ืื™ื– ืฆื• ืึธืคึผืฉืึทืฆืŸ ื“ื™ ืžืขืจืกื˜ ืคึผืจืึทืžืึทืกื™ื ื’ ืคื•ื ืงื˜ืŸ ืคึฟืึทืจ ืืจื•ื™ืคืœื™ื™ื’ืŸ ืึท ื’ืขื–ื•ื ื˜ (ื“"ื”, ื“ื™ ื’ืขื‘ื™ื˜ืŸ) ื•ื•ื• ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ื”ืื˜ ืึท ื’ืจื•ื™ืก ื’ืจืขื‘). ืื™ืŸ ื“ืขืจืฆื•, ืื™ืŸ ื“ื™ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืึธืคึผื˜ื™ื™ืœื•ื ื’ ืขืก ืงืขืŸ ื–ื™ื™ืŸ ืึทื–ืึท ืึทื‘ื“ื–ืฉืขืงืฅ ื•ื•ืึธืก, ื“ื•ืจืš ื–ื™ื™ืขืจ ื’ืขื ืขืกื™ืก, ื’ืจื•ื ื˜ ืึท ืฉืึทืจืฃ ืขื ื“ืขืจื•ื ื’ ืื™ืŸ ื“ื™ ื’ืจืขื‘ ืคื•ืŸ ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ. ื“ืึธืก ืžืื›ื˜ ืกืคึผืขืงื˜ืจืึทืœ ืึทื ืึทืœื™ืกื™ืก ืึท ืขืคืขืงื˜ื™ื•ื• ื’ืขืฆื™ื™ึทื’ ืคึฟืึทืจ ืœืขืจื ืขืŸ ื–ื™ื™. ืื™ืŸ ื“ืขืจ ื•ื•ื™ื™ึทื˜ืขืจ ื˜ื™ื™ืœ ืคื•ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ, ืžื™ืจ ื•ื•ืขืœืŸ ื‘ืึทื˜ืจืึทื›ื˜ืŸ ืึทื–ืึท ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืึทื‘ื“ื–ืฉืขืงืฅ ืื™ืŸ ืžืขืจ ื“ืขื˜ืึทืœ.

ืขืงืกืคึผืขืจื™ืžืขื ื˜ืึทืœ ื“ืึทื˜ืŸ. ื•ื•ื• ื–ืขื ืขืŸ ื–ื™ื™ ื‘ืืงื•ืžืขืŸ ืื•ืŸ ื•ื•ืึธืก ืฆื• ืงื•ืงืŸ ืคึฟืึทืจ ืื™ืŸ ื–ื™ื™?

ื“ื™ ืžืึทื˜ืขืจื™ืึทืœืก ืึทื ืึทืœื™ื™ื–ื“ ืื™ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ ื–ืขื ืขืŸ ื‘ืืงื•ืžืขืŸ ืื•ื™ืฃ ื“ื™ ื˜ืขืจื™ื˜ืึธืจื™ืข ืคื•ืŸ โ€‹โ€‹ืžืขืจื‘ ืกื™ื‘ื™ืจ. ื“ื™ ื’ืขื’ื ื˜, ื•ื•ื™ ืึทืœืขืžืขืŸ ืึธืŸ ื•ื™ืกื ืขื ืžื™ืกื˜ืึธืžืข ื•ื•ื™ืกืŸ, ืื™ื– ื“ื™ ื”ื•ื™ืคึผื˜ ื™ื™ืœ-ืคึผืจืึธื“ื•ืกื™ื ื’ ื’ืขื’ื ื˜ ืคื•ืŸ ืื•ื ื“ื–ืขืจ ืœืึทื ื“. ืึทืงื˜ื™ื•ื• ืึทื ื˜ื•ื•ื™ืงืœื•ื ื’ ืคื•ืŸ ื“ื™ืคึผืึทื–ืึทืฅ ืื ื’ืขื”ื•ื™ื‘ืŸ ืื™ืŸ ื“ืขืจ ื’ืขื’ื ื˜ ืื™ืŸ ื“ื™ 60 ืก ืคื•ืŸ ื“ื™ ืœืขืฆื˜ืข ื™ืึธืจื”ื•ื ื“ืขืจื˜. ื“ืขืจ ื”ื•ื™ืคึผื˜ ืื•ืคึฟืŸ ืคื•ืŸ ื–ื•ื›ืŸ ืคึฟืึทืจ ื™ื™ืœ ื“ื™ืคึผืึทื–ืึทืฅ ืื™ื– ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ. ืขืก ืื™ื– ื˜ืฉื™ืงืึทื•ื•ืข ืฆื• ื‘ืึทื˜ืจืึทื›ื˜ืŸ ืกืึทื˜ืขืœื™ื˜ ื‘ื™ืœื“ืขืจ ืคื•ืŸ ื“ืขื ื˜ืขืจื™ื˜ืึธืจื™ืข. ืื™ืŸ ืึท ืงืœื™ื™ืŸ ื•ื•ืึธื’, ืึท ืจื™ื–ื™ืง ื ื•ืžืขืจ ืคื•ืŸ ืกื•ื•ืึทืžืคึผืก ืื•ืŸ ืœืึทืงืขืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื‘ืืžืขืจืงื˜, ื“ื•ืจืš ื–ื•ืžื™ื ื’ ืื•ื™ืฃ ื“ืขืจ ืžืึทืคึผืข, ืื™ืจ ืงืขื ืขืŸ ื–ืขืŸ ื’ืขื–ื•ื ื˜ ื“ืจื™ืœื™ื ื’ ื–ื™ื™ื˜ืœืขืš, ืื•ืŸ ื“ื•ืจืš ื–ื•ืžื™ื ื’ ืฆื• ื“ื™ ืฉื™ืขื•ืจ, ืื™ืจ ืงืขื ืขืŸ ืื•ื™ืš ื•ื™ืกื˜ื™ื™ืœืŸ ื“ื™ ืงืœื™ืจื™ื ื’ ืคื•ืŸ ื“ื™ ืคึผืจืึธื•ืคื™ื™ืœื– ืื•ื™ืฃ ื•ื•ืึธืก ืกื™ื™ื–ืžื™ืง. ืึทื‘ื–ืขืจื•ื•ื™ื™ืฉืึทื ื– ื–ืขื ืขืŸ ื’ืขืžืื›ื˜.

ืกืึทื˜ืขืœื™ื˜ ื‘ื™ืœื“ ืคื•ืŸ ื™ืึทื ื“ืขืงืก ืžืึทืคึผืก - ื’ืขื’ื ื˜ ืคื•ืŸ ื“ืขืจ ืฉื˜ืึธื˜ ืคื•ืŸ ื ื•ื™ืึทื‘ืจืกืง
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื ืขืฅ ืคื•ืŸ ื’ืขื–ื•ื ื˜ ืคึผืึทื“ืก ืื™ืŸ ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ืคืขืœื“ืขืจ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืึธื™ืœ-ืฉื™ื™ึทื›ืขืก ืจืึทืงืก ืคื•ืŸ ืžืขืจื‘ ืกื™ื‘ื™ืจ ืคืึทืœืŸ ืื™ืŸ ืึท ื‘ืจื™ื™ื˜ ืงื™ื™ื˜ ืคื•ืŸ ื˜ื™ืคืขื ื™ืฉืŸ - ืคื•ืŸ 1 ืงื™ืœืืžืขื˜ืขืจ ืฆื• 5 ืงื™ืœืืžืขื˜ืขืจ. ื“ืขืจ ื”ื•ื™ืคึผื˜ ื‘ืึทื ื“ ืคื•ืŸ ืจืึทืงืก ืžื™ื˜ ื™ื™ืœ ืื™ื– ื’ืขืฉืืคืŸ ืื™ืŸ ื“ื™ ื“ื–ืฉื•ืจืึทืกืกื™ืง ืื•ืŸ ืงืจืขื˜ืึทืกืขืึธื•ืก. ื“ื™ ื“ื–ืฉื•ืจืึทืกืกื™ืง ืฆื™ื™ึทื˜ ืื™ื– ืžื™ืกื˜ืึธืžืข ื‘ืืงืื ื˜ ืฆื• ืคื™ืœืข ืคื•ืŸ โ€‹โ€‹ื“ื™ ืคื™ืœื ืžื™ื˜ ื“ื™ ื–ืขืœื‘ืข ื ืึธืžืขืŸ. ื“ื–ืฉื•ืจืึทืกื™ืง ืงืœื™ืžืึทื˜ ื‘ืื˜ื™ื™ื˜ื™ืง ืึทื ื“ืขืจืฉ ืคื•ืŸ ื”ื™ื™ึทื ื˜. ื“ื™ ืขื ืฆื™ืงืœืึธืคึผืขื“ื™ืข ื‘ืจื™ื˜ืึทื ื™ืงืึท ื”ืื˜ ืึท ืกืขืจื™ืข ืคื•ืŸ โ€‹โ€‹ืคึผืึทืœืขืึธ-ืžืึทืคึผืก ื•ื•ืึธืก ืงืขืจืึทืงื˜ืขืจื™ื™ื– ื™ืขื“ืขืจ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืขืคึผืึธื›ืข.

ืคืึธืจืฉื˜ืขืœืŸ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก
ื“ื–ืฉื•ืจืึทืกื™ืง ืฆื™ื™ึทื˜
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื‘ื™ื˜ืข ื˜ืึธืŸ ืึทื– ืื™ืŸ ื“ื™ ื“ื–ืฉื•ืจืึทืกื™ืง, ื“ื™ ื˜ืขืจื™ื˜ืึธืจื™ืข ืคื•ืŸ โ€‹โ€‹ืžืขืจื‘ ืกื™ื‘ื™ืจ ืื™ื– ื’ืขื•ื•ืขืŸ ืึท ื™ื ื‘ืจืขื’ (ืœืึทื ื“, ืงืจืึธืกื˜ ื“ื•ืจืš ืจื™ื•ื•ืขืจืก ืื•ืŸ ืึท ืคึผืœื™ื˜ืงืข ื™ื). ื–ื™ื ื˜ ื“ื™ ืงืœื™ืžืึทื˜ ืื™ื– ื’ืขื•ื•ืขืŸ ื‘ืึทืงื•ื•ืขื, ืขืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ืื ื’ืขื ื•ืžืขืŸ ืึทื– ืึท ื˜ื™ืคึผื™ืฉ ืœืึทื ื“ืฉืึทืคื˜ ืคื•ืŸ ืึทื– ืฆื™ื™ึทื˜ ื”ืื˜ ื•ื•ื™ ื“ืึธืก:

ื“ื–ืฉื•ืจืึทืกืกื™ืง ืกื™ื‘ื™ืจ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืื™ืŸ ื“ืขื ื‘ื™ืœื“, ืขืก ื–ืขื ืขืŸ ื ื™ืฉื˜ ืึทื–ื•ื™ ืคื™ืœ ืึทื ื™ืžืึทืœืก ืื•ืŸ ืคื™ื™ื’ืœ ื•ื•ืึธืก ื–ืขื ืขืŸ ื•ื•ื™ื›ื˜ื™ืง ืคึฟืึทืจ ืื•ื ื“ื–, ืึธื‘ืขืจ ื“ื™ ื‘ื™ืœื“ ืคื•ืŸ ื“ื™ ื˜ื™ื™ึทืš ืื™ืŸ ื“ืขืจ ื”ื™ื ื˜ืขืจื’ืจื•ื ื˜. ื“ืขืจ ื˜ื™ื™ืš ืื™ื– ื“ืขืจ ื–ืขืœื‘ืขืจ ื’ืขืืœืื’ื™ืฉืŸ ืื‘ื™ืขืงื˜ ื•ื•ืืก ืžื™ืจ ื”ืื‘ืŸ ืคืจื™ืขืจ ืืคื’ืขืฉื˜ืขืœื˜. ื“ืขืจ ืคืึทืงื˜ ืื™ื– ืึทื– ื“ื™ ื˜ืขื˜ื™ืงื™ื™ื˜ ืคื•ืŸ ื“ื™ ืจื™ื•ื•ืขืจืก ืึทืœืึทื•ื– ื“ื™ ืึทืงื™ื•ืžื™ืึทืœื™ื™ืฉืึทืŸ ืคื•ืŸ ื’ืขื–ื•ื ื˜-ืกืึธืจื˜ื™ื“ ืกืึทื ื“ืกื˜ืึธื•ื ื–, ื•ื•ืึธืก ื“ืขืžืึธืœื˜ ื•ื•ืขืจืŸ ืึท ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ืคึฟืึทืจ ื™ื™ืœ. ื“ื™ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจื– ืงืขื ืขืŸ ื”ืึธื‘ืŸ ืึท ื˜ืฉื•ื“ื ืข, ืงืึธืžืคึผืœืขืงืก ืคืึธืจืขื (ื•ื•ื™ ืึท ื˜ื™ื™ึทืš ื‘ืขื˜) ืื•ืŸ ื–ื™ื™ ื”ืึธื‘ืŸ ืึท ื‘ื™ื™ึทื˜ืขื•ื•ื“ื™ืง ื’ืจืขื‘ - ื“ื™ ื’ืจืขื‘ ืื™ื– ืงืœื™ื™ืŸ ืœืขื‘ืŸ ื“ื™ ื‘ืจืขื’, ืื•ืŸ ื™ื ืงืจื™ืกื™ื– ื ืขืขื ื˜ืขืจ ืฆื• ื“ื™ ืฆืขื ื˜ืขืจ ืคื•ืŸ ื“ืขื ืงืึทื ืึทืœ ืึธื“ืขืจ ืื™ืŸ ืžื™ืึทื ื“ืขืจ ื’ืขื‘ื™ื˜ืŸ. ืึทื–ื•ื™, ื“ื™ ืจื™ื•ื•ืขืจืก ื’ืขืฉืืคืŸ ืื™ืŸ ื“ื™ ื“ื–ืฉื•ืจืึทืกืกื™ืง ื–ืขื ืขืŸ ืื™ืฆื˜ ืื™ืŸ ืึท ื˜ื™ืคืขื ื™ืฉ ืคื•ืŸ ื•ื•ืขื’ืŸ ื“ืจื™ื™ึท ืงื™ืœืึธืžืขื˜ืขืจืก ืื•ืŸ ื–ืขื ืขืŸ ื“ื™ ื›ื™ื™ืคืขืฅ ืคื•ืŸ ืึท ื–ื•ื›ืŸ ืคึฟืึทืจ ื™ื™ืœ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจื–.

ืขืงืกืคึผืขืจื™ืžืขื ื˜ืึทืœ ื“ืึทื˜ืŸ. ืคึผืจืึทืกืขืกื™ื ื’ ืื•ืŸ ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทืŸ

ื–ืืœ ืื•ื ื“ื– ืžื™ื“ ืžืึทื›ืŸ ืึท ืจืขื–ืขืจื•ื•ืึทืฆื™ืข ื•ื•ืขื’ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ืžืึทื˜ืขืจื™ืึทืœืก ื’ืขื•ื•ื™ื–ืŸ ืื™ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ - ืจืขื›ื˜ ืฆื• ื“ืขื ืคืึทืงื˜ ืึทื– ื“ื™ ืกื•ืžืข ืคื•ืŸ โ€‹โ€‹ื“ืึทื˜ืŸ ื’ืขื ื™ืฆื˜ ืคึฟืึทืจ ืึทื ืึทืœื™ืกื™ืก ืื™ื– ื‘ืึทื˜ื™ื™ึทื˜ื™ืง - ื‘ืœื•ื™ื– ืึท ืคืจืึทื’ืžืขื ื˜ ืคื•ืŸ ื“ืขืจ ืึธืจื™ื’ื™ื ืขืœ ื’ืึทื ื’ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ืื™ื– ืึทืจื™ื™ึทื ื’ืขืจืขื›ื ื˜ ืื™ืŸ ื“ืขื ืึทืจื˜ื™ืงืœ. ื“ืึธืก ื•ื•ืขื˜ ืœืึธื–ืŸ ืึทืœืขืžืขืŸ ืฆื• ืจืขืคึผืจืึธื“ื•ืฆื™ืจืŸ ื“ื™ ืื•ื™ื‘ืŸ ื—ืฉื‘ื•ื ื•ืช.

ื•ื•ืขืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ, ืึท ื’ืขืึธืคื™ืกื™ืกื™ืกื˜ ื™ื•ื–ืฉืึทื•ื•ืึทืœื™ ื ื™ืฆื˜ ืกืคึผืขืฉืึทืœื™ื™ื–ื“ ื•ื•ื™ื™ื›ื•ื•ืืจื’ (ืขืก ื–ืขื ืขืŸ ืขื˜ืœืขื›ืข ื™ื ื“ืึทืกื˜ืจื™ ืคื™ืจืขืจ ื•ื•ืขืžืขื ืก ื“ื™ื•ื•ืขืœืึทืคึผืžืึทื ืฅ ื–ืขื ืขืŸ ืึทืงื˜ื™ื•ื•ืœื™ ื’ืขื ื™ืฆื˜, ืึทื–ืึท ื•ื•ื™ ืคึผืขื˜ืจืขืœ ืึธื“ืขืจ ืคึผืึทืจืึทื“ื™ื’ื), ื•ื•ืึธืก ืึทืœืึทื•ื– ืื™ืจ ืฆื• ืคื•ื ืึทื ื“ืขืจืงืœื™ื™ึทื‘ืŸ ืคืึทืจืฉื™ื“ืขื ืข ื˜ื™ื™ืคึผืก ืคื•ืŸ ื“ืึทื˜ืŸ ืื•ืŸ ื”ืื˜ ืึท ื‘ืึทืงื•ื•ืขื ื’ืจืึทืคื™ืงืึทืœ ืฆื•ื‘ื™ื ื“. ื˜ืจืึธืฅ ืึทืœืข ื“ื™ ืงืึทื ื•ื•ื™ื ื™ืึทื ืก, ืึทื–ืึท ื˜ื™ื™ืคึผืก ืคื•ืŸ ื•ื•ื™ื™ื›ื•ื•ืืจื’ ืื•ื™ืš ื”ืึธื‘ืŸ ื–ื™ื™ืขืจ ื“ื™ืกืึทื“ื•ื•ืึทื ื˜ื™ื“ื–ืฉื™ื– - ืœืžืฉืœ, ื“ื™ ื”ืงื“ืžื” ืคื•ืŸ ืžืึธื“ืขืจืŸ ืึทืœื’ืขืจื™ื“ืึทืžื– ืื™ืŸ ืกื˜ืึทื‘ื™ืœ ื•ื•ืขืจืกื™ืขืก ื ืขืžื˜ ืึท ืคึผืœืึทืฅ ืคื•ืŸ ืฆื™ื™ื˜, ืื•ืŸ ื“ื™ ืคึผืึทืกืึทื‘ื™ืœืึทื˜ื™ื– ืคึฟืึทืจ ืึธื˜ืึทืžื™ื™ื˜ื™ื ื’ ื—ืฉื‘ื•ื ื•ืช ื–ืขื ืขืŸ ื™ื•ื–ืฉืึทื•ื•ืึทืœื™ ืœื™ืžื™ื˜ืขื“. ืื™ืŸ ืึทื–ืึท ืึท ืกื™ื˜ื•ืึทืฆื™ืข, ืขืก ื•ื•ืขืจื˜ ื–ื™ื™ืขืจ ื‘ืึทืงื•ื•ืขื ืฆื• ื ื•ืฆืŸ ืงืึธืžืคึผื™ื•ื˜ืขืจ ืžืื˜ืขืžืื˜ื™ืง ืกื™ืกื˜ืขืžืขืŸ ืื•ืŸ ื”ื•ื™ืš-ืžื“ืจื’ื” ืคึผืจืึธื’ืจืึทืžืžื™ื ื’ ืฉืคึผืจืึทื›ืŸ ื•ื•ืึธืก ืœืึธื–ืŸ ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ืึท ื‘ืจื™ื™ื˜ ืึทืœื’ืขืจื™ื“ืึทืžื™ืง ื‘ืึทื–ืข ืื•ืŸ, ืื™ืŸ ื“ืขืจ ื–ืขืœื‘ื™ืงืขืจ ืฆื™ื™ื˜, ื ืขืžืขืŸ ืึท ืคึผืœืึทืฅ ืคื•ืŸ ืจื•ื˜ื™ืŸ. ื“ืขืจ ืคึผืจื™ื ืฆื™ืคึผ ืื™ื– ื’ืขื ื™ืฆื˜ ืฆื• ืึทืจื‘ืขื˜ืŸ ืžื™ื˜ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืื™ืŸ Wolfram Mathematica. ืขืก ืื™ื– ื ื™ืฉื˜ ืงืขื“ื™ื™ึทื™ืง ืฆื• ืฉืจื™ื™ึทื‘ืŸ ืจื™ื™ึทืš ืคืึทื ื’ืงืฉืึทื ืึทืœื™ื˜ื™ ืคึฟืึทืจ ื™ื ื˜ืขืจืึทืงื˜ื™ื•ื• ืึทืจื‘ืขื˜ ืžื™ื˜ ื“ืึทื˜ืŸ - ืขืก ืื™ื– ืžืขืจ ื•ื•ื™ื›ื˜ื™ืง ืฆื• ืฆื•ืฉื˜ืขืœืŸ ืœืึธื•ื“ื™ื ื’ ืคื•ืŸ ืึท ื‘ื›ืœืœ ืื ื’ืขื ื•ืžืขืŸ ืคึฟืึธืจืžืึทื˜, ืฆื•ืœื™ื™ื’ืŸ ื“ื™ ื’ืขื‘ืขื˜ืŸ ืึทืœื’ืขืจื™ื“ืึทืžื– ืฆื• ื–ื™ื™ ืื•ืŸ ืฆื•ืคึฟืขืœื™ืงืขืจ ื–ื™ื™ ืฆื•ืจื™ืง ืฆื• ืึท ืคื•ื ื“ืจื•ื™ืกื ื“ื™ืง ืคึฟืึธืจืžืึทื˜.

ื ืึธืš ื“ื™ ืคืืจื’ืขืœื™ื™ื’ื˜ ืกื›ืขืžืข, ืžื™ืจ ื•ื•ืขืœืŸ ืœืึธื“ืŸ ื“ื™ ืึธืจื™ื’ื™ื ืขืœ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืื•ืŸ ื•ื•ื™ื™ึทื–ืŸ ื–ื™ื™ ืื™ืŸ ื•ื•ืึธืœืคืจืึทื ืžืึทื˜ื”ืขืžืึทื˜ื™ืงืึท:

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]

ื“ื™ ื“ืึทื˜ืŸ ืœืึธื•ื“ื™ื“ ืื•ืŸ ื™ืžืคึผืึธืจื˜ื™ื“ ืื™ืŸ ื“ืขื ื•ื•ืขื’ ื–ืขื ืขืŸ ื“ื™ ื˜ืจืึทืกืขืก ืจืขืงืึธืจื“ืขื“ ืื™ืŸ ืึท ืึธืคึผื˜ื™ื™ืœื•ื ื’ ืคื•ืŸ 10 ื“ื•ืจืš 5 ืงื™ืœืึธืžืขื˜ืขืจืก. ืื•ื™ื‘ ื“ื™ ื“ืึทื˜ืŸ ื–ืขื ืขืŸ ื‘ืืงื•ืžืขืŸ ืžื™ื˜ ื“ื™ XNUMXD ืกื™ื™ื–ืžื™ืง ื™ื‘ืขืจื‘ืœื™ืง ืื•ืคึฟืŸ (ื›ื•ื•ืืœื™ืขืก ื–ืขื ืขืŸ ืจืขืงืึธืจื“ืขื“ ื ื™ืฉื˜ ืฆื•ื–ืืžืขืŸ ื™ื—ื™ื“ ื’ืขืึธืคื™ืกื™ืงืึทืœ ืคึผืจืึธื•ืคื™ื™ืœื–, ืึธื‘ืขืจ ืื™ื‘ืขืจ ื“ื™ ื’ืื ืฆืข ื’ืขื’ื ื˜ ืกื™ื™ืžืึทืœื˜ื™ื™ื ื™ืึทืกืœื™), ืขืก ืื™ื– ืžืขื’ืœืขืš ืฆื• ื‘ืึทืงื•ืžืขืŸ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืงื™ื•ื‘ื–. ื“ืืก ื–ืขื ืขืŸ ื“ืจื™ื™-ื“ื™ืžืขื ืฉืึทื ืึทืœ ืึทื‘ื“ื–ืฉืขืงืฅ, ื•ื•ืขืจื˜ื™ืงืึทืœ ืื•ืŸ ื”ืึธืจื™ื–ืึธื ื˜ืึทืœ ืกืขืงืฉืึทื ื– ื•ื•ืึธืก ืœืึธื–ืŸ ืื™ืจ ืฆื• ืœืขืจื ืขืŸ ื“ื™ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืกื•ื•ื™ื•ื•ืข ืื™ืŸ ื“ืขื˜ืึทืœ. ืื™ืŸ ื“ืขื ื‘ืึทื˜ืจืึทื›ื˜ ื‘ื™ื™ืฉืคึผื™ืœ, ืžื™ืจ ื”ืึทื ื“ืœืขืŸ ืžื™ื˜ ื‘ืœื•ื™ื– ื“ืจื™ื™-ื“ื™ืžืขื ืฉืึทื ืึทืœ ื“ืึทื˜ืŸ. ืžื™ืจ ืงืขื ืขืŸ ื‘ืึทืงื•ืžืขืŸ ืขื˜ืœืขื›ืข ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืคื•ืŸ โ€‹โ€‹ื“ื™ ื˜ืขืงืกื˜ ื›ืขื“ืขืจ, ื•ื•ื™ ื“ืึธืก 

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

C 1 ื“ืึธืก ืื™ื– ื“ืขืžืึธ ื˜ืขืงืข ืคึฟืึทืจ ื’ืขืึธืœืึธื’ื™ื™ืึธ ืคึผืขืงืœ ืคึผืจื•ื‘ื™ืจืŸ
C ืงืกื ื•ืžืงืก
C ืงืกื ื•ืžืงืก
C ืงืกื ื•ืžืงืก
C 5 ื“ืึทื˜ืข ื‘ืึทื ื™ืฆืขืจ ื ืึธืžืขืŸ: WOLFRAM USER
C6 ื™ื‘ืขืจื‘ืœื™ืง ื ืึธืžืขืŸ: ืขืจื’ืขืฅ ืื™ืŸ ืกื™ื‘ื™ืจ
C 7 ื˜ืขืงืข ื˜ื™ืคึผ 3 ื“ ืกืขื™ืกืžื™ืง ื‘ืึทื ื“
C ืงืกื ื•ืžืงืก
C ืงืกื ื•ืžืงืก
C10 ื– ืงื™ื™ื˜: ืขืจืฉื˜ืขืจ 2200 ื ืœืขืฆื˜ืข 2400 ื

ื“ื™ ื“ืึทื˜ืŸ ืฉื˜ืขืœืŸ ื•ื•ืขื˜ ื–ื™ื™ืŸ ื’ืขื ื•ื’ ืคึฟืึทืจ ืื•ื ื“ื– ืฆื• ื‘ืึทื•ื•ื™ื™ึทื–ืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืกื˜ืึทื’ืขืก ืคื•ืŸ ื“ืึทื˜ืŸ ืึทื ืึทืœื™ืกื™ืก. ื“ื™ ื˜ืจืึทืกืขืก ืื™ืŸ ื“ืขืจ ื˜ืขืงืข ื–ืขื ืขืŸ ืจืขืงืึธืจื“ืขื“ ืกืึทืงื•ื•ืขื ื˜ืฉืึทืœื™ ืื•ืŸ ื™ืขื“ืขืจ ืคื•ืŸ ื–ื™ื™ ืงื•ืงื˜ ื•ื•ื™ ื“ื™ ืคืืœื’ืขื ื“ืข ืคื™ื’ื•ืจ - ื“ืึธืก ืื™ื– ื“ื™ ืคืึทืจืฉืคึผืจื™ื™ื˜ื•ื ื’ ืคื•ืŸ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“ื– ืคื•ืŸ ื“ื™ ืฉืคื™ื’ืœื˜ ื›ื•ื•ืืœื™ืขืก ืฆื•ื–ืืžืขืŸ ื“ื™ ื•ื•ืขืจื˜ื™ืงืึทืœ ืึทืงืก (ื˜ื™ืคืงื™ื™ึทื˜ ืึทืงืก).

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]

ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ื˜ืจืึทืกืขืก ืคื•ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ืึธืคึผื˜ื™ื™ืœื•ื ื’
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื•ื•ื™ืกืŸ ื•ื•ื™ ืคื™ืœืข ื˜ืจืึทืกืขืก ื–ืขื ืขืŸ ืœื™ื’ืŸ ืื™ืŸ ื™ืขื“ืขืจ ืจื™ื›ื˜ื•ื ื’ ืคื•ืŸ ื“ื™ ื’ืขืœืขืจื ื˜ ื’ืขื’ื ื˜, ืื™ืจ ืงืขื ืขืŸ ืคืึธืจืขื ืึท ื“ืจื™ื™-ื“ื™ืžืขื ืฉืึทื ืึทืœ ื“ืึทื˜ืŸ ืžืขื ื’ืข ืื•ืŸ ื•ื•ื™ื™ึทื–ืŸ ืขืก ืžื™ื˜ ื“ื™ Image3D [] ืคื•ื ืงืฆื™ืข. 

traces=seismic3DSEGY["traces"];
startIL=1050;EndIL=2000;stepIL=2; (*ะบะพะพั€ะดะธะฝะฐั‚ะฐ ะฅ ะฝะฐั‡ะฐะปะฐ ะธ ะบะพะฝั†ะฐ ััŠั‘ะผะบะธ ะธ ัˆะฐะณ ั‚ั€ะฐัั*)
startXL=1165;EndXL=1615;stepXL=2; (*ะบะพะพั€ะดะธะฝะฐั‚ะฐ Y ะฝะฐั‡ะฐะปะฐ ะธ ะบะพะฝั†ะฐ ััŠั‘ะผะบะธ ะธ ัˆะฐะณ ั‚ั€ะฐัั*)
numIL=(EndIL-startIL)/stepIL+1;   (*ะบะพะปะธั‡ะตัั‚ะฒะพ ั‚ั€ะฐัั ะฟะพ ะพะธั ะฅ*)
numXL=(EndXL-startXL)/stepIL+1;   (*ะบะพะปะธั‡ะตัั‚ะฒะพ ั‚ั€ะฐัั ะฟะพ ะพะธั Y*)
Image3D[ArrayReshape[Abs[traces/Max[Abs[traces[[All,1;;;;4]]]]],{numIL,numXL,101}],ViewPoint->{-1, 0, 0},Background->RGBColor[0,0,0]]

XNUMX ื“ ื‘ื™ืœื“ ืคื•ืŸ ืึท ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืงื•ื‘. (ื•ื•ืขืจื˜ื™ืงืึทืœ ืึทืงืก - ื˜ื™ืคืงื™ื™ึทื˜)
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืื™ืŸ ื“ืขืจ ื’ืขืฉืขืขื ื™ืฉ ืึทื– ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ืึทื‘ื“ื–ืฉืขืงืฅ ืคื•ืŸ ืื™ื ื˜ืขืจืขืก ืžืึทื›ืŸ ื˜ื™ืฃ ืกื™ื™ื–ืžื™ืง ืึทื ืึทืžืึทืœื™ื–, ื•ื•ื™ื–ืฉื•ื•ืึทืœืึทื–ื™ื™ืฉืึทืŸ ืžื›ืฉื™ืจื™ื ืžื™ื˜ ื“ื•ืจื›ื–ืขื™ืงื™ื™ึทื˜ ืงืขื ืขืŸ ื–ื™ื™ืŸ ื’ืขื•ื•ื™ื™ื ื˜. "ื•ื ื™ืžืคึผืึธืจื˜ืึทื ื˜" ืกืขืงืฉืึทื ื– ืคื•ืŸ ื“ื™ ืจืขืงืึธืจื“ื™ื ื’ ืงืขื ืขืŸ ื–ื™ื™ืŸ ื•ืžื–ืขื™ืง, ืื•ืŸ ื‘ืœื•ื™ื– ืึทื ืึทืžืึทืœื™ื– ืงืขื ืขืŸ ื–ื™ื™ืŸ ืงืขื ื˜ื™ืง. ืื™ืŸ Wolfram Mathematica, ื“ืึธืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื’ืขื˜ืืŸ ืžื™ื˜ ืึธื•ืคึผืึทืกืึทื˜ื™[] ะธ 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]

ื‘ื™ืœื“ ืคื•ืŸ ืึท ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืงื•ื‘ ื ื™ืฆืŸ ืึธื•ืคึผืึทืกืึทื˜ื™ [] ืื•ืŸ Raster3D [] ืคืึทื ื’ืงืฉืึทื ื– ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื•ื•ื™ ืื™ืŸ ื“ื™ ืกื™ื ื˜ืขื˜ื™ืฉ ื‘ื™ื™ึทืฉืคึผื™ืœ, ืขื˜ืœืขื›ืข ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ื‘ืึทื•ื ื“ืจื™ื– (ืœื™ื™ึทืขืจืก) ืžื™ื˜ ื•ื•ืขืจื™ืึทื‘ืึทืœ ืจืขืœื™ืขืฃ ืงืขื ืขืŸ ื–ื™ื™ืŸ ืื•ื ื˜ืขืจืฉื™ื™ื“ืŸ ืื•ื™ืฃ ื“ื™ ืกืœื™ื™ืกื™ื– ืคื•ืŸ ื“ืขืจ ืึธืจื™ื’ื™ื ืขืœ ืงื•ื‘.

ื“ื™ ื”ื•ื™ืคึผื˜ ื’ืขืฆื™ื™ึทื’ ืคึฟืึทืจ ืกืคึผืขืงื˜ืจืึทืœ ืึทื ืึทืœื™ืกื™ืก ืื™ื– ื“ื™ ืคืึธืจื™ืขืจ ื™ื‘ืขืจืžืึทื›ืŸ. ืขืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื’ืขื ื•ืฆื˜ ืฆื• ืึธืคึผืฉืึทืฆืŸ ื“ื™ ืึทืžืคึผืœื™ื˜ื•ื“-ืึธืคื˜ืงื™ื™ึทื˜ ืกืคึผืขืงื˜ืจื•ื ืคื•ืŸ ื™ืขื“ืขืจ ืฉืคึผื•ืจ ืึธื“ืขืจ ื’ืจื•ืคึผืข ืคื•ืŸ โ€‹โ€‹ื˜ืจืึทืกืขืก. ืึธื‘ืขืจ, ื ืึธืš ื˜ืจืึทื ืกืคืขืจื™ื ื’ ื“ื™ ื“ืึทื˜ืŸ ืฆื• ื“ื™ ืึธืคื˜ืงื™ื™ึทื˜ ืคืขืœื“, ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ืื™ื– ืคืึทืจืคืึทืœืŸ ื•ื•ืขื’ืŸ ืื™ืŸ ื•ื•ืึธืก ืฆื™ื™ื˜ (ืœื™ื™ืขื ืขืŸ, ืื™ืŸ ื•ื•ืึธืก ื˜ื™ืคืขื ื™ืฉืŸ) ื“ื™ ืึธืคื˜ืงื™ื™ึทื˜ ืขื ื“ืขืจื•ื ื’ืขืŸ. ื›ึผื“ื™ ืฆื• ืงืขื ืขืŸ ืœืึธืงืึทืœื™ื–ื™ืจืŸ ืกื™ื’ื ืึทืœ ืขื ื“ืขืจื•ื ื’ืขืŸ ืื•ื™ืฃ ื“ืขืจ ืฆื™ื™ื˜ (ื˜ื™ืคืงื™ื™ึทื˜) ืึทืงืก, ื“ื™ ื•ื•ื™ื ื“ืึธื•ื“ ืคืึธื•ืจื™ืขืจ ื™ื‘ืขืจืžืึทื›ืŸ ืื•ืŸ ื•ื•ืึทื•ื•ืึทืœืขื˜ ื“ื™ืงืึทืžืคึผืึธื•ื–ื™ืฉืึทืŸ ื–ืขื ืขืŸ ื’ืขื ื™ืฆื˜. ื“ืขืจ ืึทืจื˜ื™ืงืœ ื ื™ืฆื˜ ื•ื•ืึทื•ื•ืึทืœืขื˜ ื“ื™ืงืึทืžืคึผืึธื•ื–ื™ืฉืึทืŸ. ื•ื•ืึทื•ื•ืขืœืขื˜ ืึทื ืึทืœื™ืกื™ืก ื˜ืขื›ื ืึธืœืึธื’ื™ืข ืื ื’ืขื”ื•ื™ื‘ืŸ ืฆื• ื–ื™ื™ืŸ ืึทืงื˜ื™ื•ื•ืœื™ ื’ืขื ื™ืฆื˜ ืื™ืŸ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ ืื™ืŸ ื“ื™ 90 ืก. ื“ื™ ืžื™ื™ึทืœืข ืื™ื‘ืขืจ ื“ื™ ื•ื•ื™ื ื“ืึธื•ื“ ืคืึธื•ืจื™ืขืจ ื™ื‘ืขืจืžืึทื›ืŸ ืื™ื– ื’ืขื”ืืœื˜ืŸ ืฆื• ื–ื™ื™ืŸ ื‘ืขืกืขืจ ืฆื™ื™ื˜ ื”ืึทื›ืœืึธื˜ืข.

ื ื™ืฆืŸ ื“ื™ ืคืืœื’ืขื ื“ืข ืงืึธื“ ืคืจืึทื’ืžืขื ื˜, ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ื˜ืจืึทืกืขืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื“ื™ืงืึทืžืคึผืึธื•ื–ื“ ืื™ืŸ ื™ื—ื™ื“ ืงืึทืžืคึผืึธื•ื ืึทื ืฅ:

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]

ื“ื™ืงืึทืžืคึผืึธื•ื–ื™ื ื’ ืึท ืฉืคึผื•ืจ ืื™ืŸ ืงืึทืžืคึผืึธื•ื ืึทื ืฅ
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืฆื• ืึธืคึผืฉืึทืฆืŸ ื•ื•ื™ ื“ื™ ืึธืคึผืฉืคึผื™ื’ืœื•ื ื’ ืขื ืขืจื’ื™ืข ืื™ื– ืคื•ื ืื ื“ืขืจื’ืขื˜ื™ื™ืœื˜ ืื™ืŸ ืคืึทืจืฉื™ื“ืขื ืข ื›ื•ื•ืึทืœื™ืข ืึธื ืงื•ืžืขืŸ ืฆื™ื™ื˜, ืกืงืึทืœืึทื’ืจืึทืžื– (ืึทื ืึทืœืึธื’ ืฆื• ืึท ืกืคึผืขืงื˜ืจืึธื’ืจืึทื) ื–ืขื ืขืŸ ื’ืขื ื™ืฆื˜. ื•ื•ื™ ืึท ื”ืขืจืฉืŸ, ืื™ืŸ ืคื™ืจ ืขืก ืื™ื– ื ื™ื˜ ื ื™ื™ื˜ื™ืง ืฆื• ืคื•ื ืึทื ื“ืขืจืงืœื™ื™ึทื‘ืŸ ืึทืœืข ื“ื™ ืงืึทืžืคึผืึธื•ื ืึทื ืฅ. ื™ื•ื–ืฉืึทื•ื•ืึทืœื™ ืงืœื™ื™ึทื‘ืŸ ืึท ื ื™ื“ืขืจื™ืง-, ืžื™ื˜ืœ- ืื•ืŸ ื”ื•ื™ืš-ืึธืคื˜ืงื™ื™ึทื˜ ืงืึธืžืคึผืึธื ืขื ื˜.

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]

ืกืงืึทืœืึทื’ืจืึทื. ืคื•ื ืงืฆื™ืึธื ื™ืจืŸ ืจืขื–ื•ืœื˜ืึทื˜ ื•ื•ืึทื•ื•ืขืœืขื˜ ืกืงืึทืœืึธื’ืจืึทื[]
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ื“ื™ Wolfram ืฉืคึผืจืึทืš ื ื™ืฆื˜ ื“ื™ ื•ื•ืึทื•ื•ืขืœืขื˜ ื™ื‘ืขืจืžืึทื›ืŸ ืคึฟื•ื ืงืฆื™ืข ContinuousWaveletTransform[]. ืื•ืŸ ื“ื™ ืึทืคึผืœืึทืงื™ื™ืฉืึทืŸ ืคื•ืŸ ื“ืขื ืคื•ื ืงืฆื™ืข ืฆื• ื“ื™ ื’ืื ืฆืข ื’ืึทื ื’ ืคื•ืŸ ื˜ืจืึทืกืขืก ื•ื•ืขื˜ ื–ื™ื™ืŸ ื“ื•ืจื›ื’ืขืงืึธื›ื˜ ืžื™ื˜ ื“ื™ ืคื•ื ืงืฆื™ืข ื˜ื™ืฉ[]. ื“ืึธ ืขืก ืื™ื– ื›ื“ืื™ ืฆื• ื‘ืืžืขืจืงืŸ ืื™ื™ื ืขืจ ืคื•ืŸ ื“ื™ ืกื˜ืจืขื ื’ืงื˜ืก ืคื•ืŸ Wolfram Mathematica, ื“ื™ ืคื™ื™ื™ืงื™ื™ื˜ ืฆื• ื ื•ืฆืŸ ืคึผืึทืจืึทืœืขืœื™ื–ืึทื˜ื™ืึธืŸ ืคึผืึทืจืึทืœืขืœ ื˜ืึทื‘ืœืข[]. ืื™ืŸ ื“ื™ ืื•ื™ื‘ืŸ ื‘ื™ื™ึทืฉืคึผื™ืœ, ืขืก ืื™ื– ื ื™ื˜ ื“ืึทืจืคึฟืŸ ืคึฟืึทืจ ืคึผืึทืจืึทืœืขืœื™ื–ืึทื˜ื™ืึธืŸ - ื“ื™ ืกื•ืžืข ืคื•ืŸ โ€‹โ€‹ื“ืึทื˜ืŸ ืื™ื– ื ื™ืฉื˜ ื’ืจื•ื™ืก, ืึธื‘ืขืจ ื•ื•ืขืŸ ืืจื‘ืขื˜ืŸ ืžื™ื˜ ื™ืงืกืคึผืขืจืžืขื ืึทืœ ื“ืึทื˜ืŸ ืฉื˜ืขืœื˜ ืžื™ื˜ ื”ื•ื ื“ืขืจื˜ืขืจ ืคื•ืŸ ื˜ื•ื™ื–ื ื˜ืขืจ ืคื•ืŸ ื˜ืจืึทืกืขืก, ื“ืึธืก ืื™ื– ืึท ื ื™ื™ื˜ื™ืงื™ื™ึทื˜.

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

ื ืึธืš ืึทืคึผืœื™ื™ื™ื ื’ ื“ื™ ืคึฟื•ื ืงืฆื™ืข ContinuousWaveletTransform[] ื ื™ื™ึท ื“ืึทื˜ืข ืฉื˜ืขืœื˜ ื“ืขืจืฉื™ื™ึทื ืขืŸ ืงืึธืจืึทืกืคึผืึทื ื“ื™ื ื’ ืฆื• ื“ื™ ืื•ื™ืกื’ืขืงืœื™ื‘ืŸ ืคืจื™ืงื•ื•ืึทื ืกื™ื–. ืื™ืŸ ื“ืขื ื‘ื™ื™ึทืฉืคึผื™ืœ ืื•ื™ื‘ืŸ, ื“ืึธืก ื–ืขื ืขืŸ ื“ื™ ืคืจื™ืงื•ื•ืึทื ืกื™ื–: 38 ื”ื–, 33 ื”ื–, 27 ื”ื–. ื“ื™ ื‘ืจื™ืจื” ืคื•ืŸ ืคืจื™ืงื•ื•ืึทื ืกื™ื– ืื™ื– ื’ืขืคื™ืจื˜ ืื•ื™ืก ืจื•ื‘ึฟ ืึธืคื˜ ืื•ื™ืฃ ื“ื™ ื™ืงืขืจ ืคื•ืŸ ื˜ืขืกื˜ื™ื ื’ - ื–ื™ื™ ื‘ืึทืงื•ืžืขืŸ ืจืขื–ื•ืœื˜ืึทื˜ ืžืึทืคึผืก ืคึฟืึทืจ ืคืึทืจืฉื™ื“ืขื ืข ืึธืคื˜ืงื™ื™ึทื˜ ืงืึทืžื‘ืึทื ื™ื™ืฉืึทื ื– ืื•ืŸ ืงืœื™ื™ึทื‘ืŸ ื“ื™ ืžืขืจืกื˜ ื™ื ืคืึธืจืžืึทื˜ื™ื•ื• ืคื•ืŸ ื“ื™ ืคื•ื ื˜ ืคื•ืŸ ืžื™ื™ื ื•ื ื’ ืคื•ืŸ ืึท ื’ืขืึธืœืึธื’ื™ืกื˜.

ืื•ื™ื‘ ื“ื™ ืจืขื–ื•ืœื˜ืึทื˜ืŸ ื“ืึทืจืคึฟืŸ ืฆื• ื–ื™ื™ืŸ ืฉืขืจื“ ืžื™ื˜ ื—ื‘ืจื™ื ืึธื“ืขืจ ืฆื•ื’ืขืฉื˜ืขืœื˜ ืฆื• ื“ืขืจ ืงื•ื ื”, ืื™ืจ ืงืขื ื˜ ื ื•ืฆืŸ ื“ื™ SEGYExport [] ืคื•ื ืงืฆื™ืข ืคื•ืŸ โ€‹โ€‹โ€‹โ€‹ื“ื™ GeologyIO ืคึผืขืงืœ

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];

ืžื™ื˜ ื“ืจื™ื™ ืคื•ืŸ ื“ื™ ืงื™ื•ื‘ื– ื‘ื ื™ืžืฆื (ื ื™ื“ืขืจื™ืง, ืžื™ื˜ืŸ ืื•ืŸ ื”ื•ื™ืš), ืขืก ืื™ื– ืคึผืจืึธืกื˜ ืฆื• ื ื•ืฆืŸ RGB ื‘ืœืขื ื“ื™ื ื’ ืฆื• ื•ื•ื™ื–ืฉื•ื•ืึทืœื™ื™ื– ื“ื™ ื“ืึทื˜ืŸ ืฆื•ื–ืึทืžืขืŸ. ื™ืขื“ืขืจ ืงืึธืžืคึผืึธื ืขื ื˜ ืื™ื– ืึทืกื™ื™ื ื“ ื–ื™ื™ึทืŸ ืื™ื™ื’ืŸ ืงืึธืœื™ืจ - ืจื•ื™ื˜, ื’ืจื™ืŸ, ื‘ืœื•ื™. ืื™ืŸ Wolfram Mathematica, ื“ืึธืก ืงืขืŸ ื–ื™ื™ืŸ ื’ืขื˜ืืŸ ืžื™ื˜ ื“ื™ ืคื•ื ืงืฆื™ืข ืงืึธืœืึธืจืงืึธืžื‘ื™ื ืข[].

ื“ืขืจ ืจืขื–ื•ืœื˜ืึทื˜ ืื™ื– ื‘ื™ืœื“ืขืจ ื•ื•ืึธืก ืงืขื ืขืŸ ื–ื™ื™ืŸ ื’ืขื•ื•ื™ื™ื ื˜ ืคึฟืึทืจ ื“ื–ืฉื™ืึทืœืึทื“ื–ืฉื™ืงืึทืœ ื™ื ื˜ืขืจืคึผืจื™ื˜ื™ื™ืฉืึทืŸ. ืžื™ืึทื ื“ืขืจื–, ื•ื•ืึธืก ื–ืขื ืขืŸ ืคืึทืจืคืขืกื˜ื™ืงื˜ ืื•ื™ืฃ ื“ื™ ื“ื•ืจื›ืฉื ื™ื˜, ืžืึทื›ืŸ ืขืก ืžืขื’ืœืขืš ืฆื• ื•ื™ืกื˜ื™ื™ืœืŸ ืคึผืึทืœืขืึธื˜ืฉืึทื ืึทืœื–, ื•ื•ืึธืก ื–ืขื ืขืŸ ืžืขืจ ืžืกืชึผืžื ืฆื• ื–ื™ื™ืŸ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจื– ืื•ืŸ ืึทื ื˜ื”ืึทืœื˜ืŸ ื™ื™ืœ ืจื™ื–ืขืจื•ื•ื–. ื–ื•ื›ืŸ ืื•ืŸ ืึทื ืึทืœื™ืกื™ืก ืคื•ืŸ ืžืึธื“ืขืจืŸ ืึทื ืึทืœืึธื’ื•ืขืก ืคื•ืŸ ืึทื–ืึท ืึท ื˜ื™ื™ึทืš ืกื™ืกื˜ืขื ืžืื›ื˜ ืขืก ืžืขื’ืœืขืš ืฆื• ื‘ืึทืฉืœื™ืกืŸ ื“ื™ ืžืขืจืกื˜ ืคึผืจืึทืžืึทืกื™ื ื’ ื˜ื™ื™ืœืŸ ืคื•ืŸ ื“ื™ ืžื™ืึทื ื“ืขืจื–. ื“ื™ ื˜ืฉืึทื ืึทืœื– ื–ื™ืš ื–ืขื ืขืŸ ืงืขืจืึทืงื˜ืขืจื™ื™ื–ื“ ื“ื•ืจืš ื“ื™ืง ืœื™ื™ึทืขืจืก ืคื•ืŸ ื’ืขื–ื•ื ื˜-ืกืึธืจื˜ื™ื“ ืกืึทื ื“ืกื˜ืึธื•ืŸ ืื•ืŸ ื–ืขื ืขืŸ ืึท ื’ื•ื˜ ืจืขื–ืขืจื•ื•ื•ื•ืึทืจ ืคึฟืึทืจ ื™ื™ืœ. ื’ืขื‘ื™ื˜ืŸ ืึทืจื•ื™ืก ื“ื™ "ืฉื˜ืจื™ืงืœ" ืึทื ืึทืžืึทืœื™ื– ื–ืขื ืขืŸ ืขื ืœืขืš ืฆื• ืžืึธื“ืขืจืŸ ืคืœืึทื“ืคึผืœืึทื™ืŸ ื“ื™ืคึผืึทื–ืึทืฅ. ืคืœืึธืึธื“ืคึผืœืึทื™ืŸ ื“ื™ืคึผืึทื–ืึทืฅ ื–ืขื ืขืŸ ื“ืขืจ ื”ื•ื™ืคึผื˜ ืจืขืคึผืจื™ื–ืขื ื˜ื™ื“ ื“ื•ืจืš ืœื™ื™ื ืจืึทืงืก ืื•ืŸ ื“ืจื™ืœื™ื ื’ ืื™ืŸ ื“ื™ ื–ืึธื ืขืก ื•ื•ืขื˜ ื–ื™ื™ืŸ ื‘ืึทื˜ืœืึธื ื™ืฉ.

RGB ืจืขืคื˜ืœ ืคื•ืŸ ื“ื™ ื“ืึทื˜ืŸ ืงื•ื‘. ืื™ืŸ ืฆืขื ื˜ืขืจ (ืึท ื‘ื™ืกืœ ืœื™ื ืงืก ืคื•ืŸ ืฆืขื ื˜ืขืจ) ืงืขื ืขืŸ ื–ื™ื™ืŸ ื˜ืจื™ื™ืกื˜ ืึท ืžื™ืึทื ื“ืขืจื™ื ื’ ื˜ื™ื™ึทืš.
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก
RGB ืจืขืคื˜ืœ ืคื•ืŸ ื“ื™ ื“ืึทื˜ืŸ ืงื•ื‘. ืื•ื™ืฃ ื“ื™ ืœื™ื ืงืก ื–ื™ื™ึทื˜ ืื™ืจ ืงืขื ืขืŸ ืฉืคึผื•ืจ ื“ื™ ืžื™ืึทื ื“ืขืจื™ื ื’ ื˜ื™ื™ึทืš.
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืื™ืŸ ืขื˜ืœืขื›ืข ืงืึทืกืขืก, ื“ื™ ืงื•ื•ืึทืœื™ื˜ืขื˜ ืคื•ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืึทืœืึทื•ื– ื‘ืื˜ื™ื™ื˜ื™ืง ืฉืึทืจืคึผืขืจ ื‘ื™ืœื“ืขืจ. ืขืก ื“ืขืคึผืขื ื“ืก ืื•ื™ืฃ ื“ืขืจ ืื•ืคึฟืŸ ืคื•ืŸ ืคืขืœื“ ืึทืจื‘ืขื˜, ื“ื™ ื•ื™ืกืจื™ื›ื˜ ื’ืขื ื™ืฆื˜ ื“ื•ืจืš ื“ื™ ืจืึทืฉ ืจืขื“ื•ืงืฆื™ืข ืึทืœื’ืขืจื™ื“ืึทื. ืื™ืŸ ืึทื–ืึท ืงืึทืกืขืก, ื ื™ื˜ ื‘ืœื•ื™ื– ืคืจืึทื’ืžืึทื ืฅ ืคื•ืŸ ื˜ื™ื™ึทืš ืกื™ืกื˜ืขืžืขืŸ ื–ืขื ืขืŸ ืงืขื ื˜ื™ืง, ืึธื‘ืขืจ ืื•ื™ืš ื’ืึทื ืฅ ืขืงืกื˜ืขื ื“ืขื“ ืคึผืึทืœืขืึธ ืจื™ื•ื•ืขืจืก.

RGB ื‘ืœืขื ื“ื™ื ื’ ืคื•ืŸ ื“ื™ ื“ืจื™ื™ ืงืึทืžืคึผืึธื•ื ืึทื ืฅ ืคื•ืŸ ื“ื™ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืงื•ื‘ (ื”ืึธืจื™ื–ืึธื ื˜ืึทืœ ืจืขืคื˜ืœ). ื˜ื™ืคืงื™ื™ึทื˜ ืื™ื– ื‘ืขืขืจืขืš 2 ืงื™ืœืืžืขื˜ืขืจ.
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก
ืกืึทื˜ืขืœื™ื˜ ื‘ื™ืœื“ ืคื•ืŸ ื“ื™ ื•ื•ืึธืœื’ืึท ื˜ื™ื™ืš ืœืขื‘ืŸ ืกืึทืจืึทื˜ืึธื•ื•
ื•ื•ืึธืœืคืจืึทื ืžืื˜ืขืžืื˜ื™ืง ืื™ืŸ ื’ืขืึธืคื™ืกื™ืงืก

ืกืึธืฃ

ืื™ืŸ Wolfram Mathematica, ืื™ืจ ืงืขื ืขืŸ ืคื•ื ืึทื ื“ืขืจืงืœื™ื™ึทื‘ืŸ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืื•ืŸ ืกืึธืœื•ื•ืข ื’ืขื•ื•ืขื ื“ื˜ ืคึผืจืึธื‘ืœืขืžืก ืฉื™ื™ึทื›ื•ืช ืฆื• ื“ืขืจ ื–ื•ื›ืŸ ืคึฟืึทืจ ืžื™ื ืขืจืึทืœืก, ืื•ืŸ ื“ื™ GeologyIO ืคึผืขืงืœ ืžืื›ื˜ ื“ืขื ืคึผืจืึธืฆืขืก ืžืขืจ ื‘ืึทืงื•ื•ืขื. ื“ื™ ืกื˜ืจื•ืงื˜ื•ืจ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ื“ืึทื˜ืŸ ืื™ื– ืึทื–ื•ื™ ืึทื– ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ื’ืขื‘ื•ื™ื˜-ืื™ืŸ ืžืขื˜ื”ืึธื“ืก ืคึฟืึทืจ ืึทืงืกืขืœืขืจื™ื™ื˜ื™ื ื’ ื—ืฉื‘ื•ื ื•ืช (ืคึผืึทืจืึทืœืขืœ ื˜ืึทื‘ืœืข[], ParallelDo[],...) ืื™ื– ื–ื™ื™ืขืจ ืขืคืขืงื˜ื™ื•ื• ืื•ืŸ ืึทืœืึทื•ื– ืื™ืจ ืฆื• ืคึผืจืึธืฆืขืก ื’ืจื•ื™ืก ืึทืžืึทื•ื ืฅ ืคื•ืŸ ื“ืึทื˜ืŸ. ืื™ืŸ ืึท ื’ืจื•ื™ืก ืžืึธืก, ื“ืึธืก ืื™ื– ืคืึทืกื™ืœืึทื˜ื™ื™ื˜ื™ื“ ื“ื•ืจืš ื“ื™ ื“ืึทื˜ืŸ ืกื˜ืึธืจื™ื“ื–ืฉ ืคึฟืขื™ึดืงื™ื™ื˜ืŸ ืคื•ืŸ ื“ื™ GeologyIO ืคึผืขืงืœ. ื“ื•ืจืš ื“ืขื ื•ื•ืขื’, ื“ื™ ืคึผืขืงืœ ืงืขื ืขืŸ ื–ื™ื™ืŸ ื’ืขื•ื•ื™ื™ื ื˜ ื ื™ื˜ ื‘ืœื•ื™ื– ืื™ืŸ ื“ื™ ืคืขืœื“ ืคื•ืŸ ืกื™ื™ื–ืžื™ืง ืขืงืกืคึผืœืขืจื™ื™ืฉืึทืŸ. ื›ึผืžืขื˜ ื“ื™ ื–ืขืœื‘ืข ื˜ื™ื™ืคึผืก ืคื•ืŸ ื“ืึทื˜ืŸ ื–ืขื ืขืŸ ื’ืขื ื™ืฆื˜ ืื™ืŸ ื’ืคึผืจ ืื•ืŸ ืกื™ื™ื–ืžืึธืœืึธื’ื™. ืื•ื™ื‘ ืื™ืจ ื”ืึธื˜ ืคึฟื™ืจืœื™ื™ื’ืŸ ื•ื•ื™ ืฆื• ืคึฟืึทืจื‘ืขืกืขืจืŸ ื“ื™ ืจืขื–ื•ืœื˜ืึทื˜, ื•ื•ืึธืก ืกื™ื’ื ืึทืœ ืึทื ืึทืœื™ืกื™ืก ืึทืœื’ืขืจื™ื“ืึทืžื– ืคื•ืŸ ื“ื™ Wolfram Mathematica ืึทืจืกืขื ืึทืœ ื–ืขื ืขืŸ ืึธื ื•ื•ืขื ื“ืœืขืš ืฆื• ืึทื–ืึท ื“ืึทื˜ืŸ, ืึธื“ืขืจ ืื•ื™ื‘ ืื™ืจ ื”ืึธื˜ ืงืจื™ื˜ื™ืฉ ื‘ืึทืžืขืจืงื•ื ื’ืขืŸ, ื‘ื™ื˜ืข ืœืึธื–ืŸ ื‘ืึทืžืขืจืงื•ื ื’ืขืŸ.

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ืœื™ื™ื’ืŸ ืึท ื‘ืึทืžืขืจืงื•ื ื’