ͳͳͳ
’”‘˜‡†“—ƒ–‹–ƒ–‹˜‡…ƒŽ‹„”ƒ–‹‘‘ˆ”‘…
’Š›•‹…•‘†‡Ž•
‡”ƒ”†‘‘›ƒ‘ͳǡ”Ž‹‰—‰‘‡•‡ͳǡ‘””‡‘Šƒ•‡ͳǡʹǤ
 ”‡•‡”˜‘‹” …Šƒ”ƒ…–‡”‹œƒ–‹‘ǡ ”‘…Ǧ’Š›•‹…• ‘†‡Ž• ’”‘˜‹†‡ –Š‡ Ž‹ „‡–™‡‡ •‡‹•‹…
‘„•‡”˜ƒ„Ž‡•ȋ†‡•‹–›ǡ…‘’”‡••‹‘ƒŽƒ†•Š‡ƒ”™ƒ˜‡•’‡‡†•Ȍƒ†”‡•‡”˜‘‹”’ƒ”ƒ‡–‡”••—…Š
ƒ• ’‘”‘•‹–›ǡ Ž‹–Š‘Ž‘‰› ƒ† ˆŽ—‹† •ƒ–—”ƒ–‹‘Ǥ ‘™‡˜‡”ǡ –Š‡ ƒ……—”ƒ…› ‘ˆ –Š‡•‡ ’”‡†‹…–‹‘• ‹•
”ƒ”‡Ž›‡š’Ž‘”‡†Ǥˆƒ…–ǡ–Š‡˜ƒŽ‹†ƒ–‹‘‘ˆƒ‘†‡Ž”‡’”‡•‡–‹‰ƒ†ƒ–ƒ•‡–‹•‘ˆ–‡Ž‹‹–‡†–‘
–Š‡ ƒƒŽ›•‹• ‘ˆ ƒ …”‘••Ǧ’Ž‘– ‘ˆ –™‘ ƒ”„‹–”ƒ”› ƒ‰‹–—†‡•Ǥ Š‡ ‘„Œ‡…–‹˜‡ ‘ˆ –Š‹• ’ƒ’‡” ‹• –‘
‹’”‘˜‡ –Š‡ …ƒŽ‹„”ƒ–‹‘ ’”‘…‡†—”‡ –Š”‘—‰Š ƒ “—ƒ–‹–ƒ–‹˜‡ ƒ••‡••‡– ‘ˆ –Š‡ ”‡•‡”˜‘‹”
’”‘’‡”–›’”‡†‹…–‹‘•—•‹‰˜ƒ”‹‘—•”‘…Ǧ’Š›•‹…•‘†‡Ž•ǤŠ‡ƒƒŽ›•‹•‹•„ƒ•‡†‘ƒ‹˜‡”•‡
”‘…Ǧ’Š›•‹…•‘†‡ŽŽ‹‰–Šƒ–‘”‰ƒ‹œ‡•–Š‡”‘…Ǧ’Š›•‹…• –”ƒ•ˆ‘”•‹–‘…‘•–”ƒ‹–†ƒ–ƒ•‘
–Šƒ– –Š‡ •‡‹•‹… ˜ƒ”‹ƒ„Ž‡• ƒ”‡ †‹”‡…– ˆ—…–‹‘• ‘ˆ –Š‡ ”‡•‡”˜‘‹” ’ƒ”ƒ‡–‡”•Ǥ – ‹• ”‡˜‡ƒŽ‡†
–Šƒ– –Š‡ ’”‡†‹…–‹‘• ‘ˆ ”‡•‡”˜‘‹” “—ƒŽ‹–› …ƒ ƒ••‹•– ‹ –Š‡ †‹ƒ‰‘•‹• ‘ˆ –Š‡ ”‘…
‹…”‘•–”—…–—”‡ ‹–•‡Žˆǡ •—…Š ƒ• –Š‡ Ž‘…ƒ–‹‘ ‘ˆ …Žƒ› ’ƒ”–‹…Ž‡• ‹ …Žƒ›Ǧ”‹…Š •‡†‹‡–•Ǥ 
ƒ††‹–‹‘ǡ ™‡ ˆ‘—† –Šƒ– ƒ “—ƒ–‹–ƒ–‹˜‡ ƒƒŽ›•‹• ‹• –Š‡ ‘Ž› ™ƒ› –‘ ‡˜ƒŽ—ƒ–‡ ƒ……—”ƒ–‡Ž› –Š‡
’‡”ˆ‘”ƒ…‡‘ˆ˜ƒ”‹‘—•‘†‡Ž•™Š‡•–—†›‹‰Š‡–‡”‘‰‡‡‘—•†ƒ–ƒ•‡–•Ǥ
‡Ž‡…–‹‰ƒ†…ƒŽ‹„”ƒ–‹‰–Š‡‘•– •—‹–ƒ„Ž‡”‘…Ǧ’Š›•‹…•‘†‡Žˆ‘” ƒ ‰‹˜‡†ƒ–ƒ•‡–‹•
ƒ ‡š‡”…‹•‡ ™‹–Š ƒ ‘Ǧ—‹“—‡ •‘Ž—–‹‘Ǥ ‘…Ǧ’Š›•‹…• ‘†‡Ž• …ƒ’–—”‡ ‘‡ ‘” ƒ •‡Ž‡…– ˆ‡™
ˆƒ…–‘”•–Šƒ–‹ˆŽ—‡…‡–Š‡‡Žƒ•–‹…’”‘’‡”–‹‡•‘ˆ–Š‡”‘…•Ǥƒ††‹–‹‘ǡ–Š‡•‡‘†‡Ž•–›’‹…ƒŽŽ›
ƒ”‡ …ƒŽ‹„”ƒ–‡† –‘ ƒ Ž‹‹–‡† •‡– ‘ˆ ’Š›•‹…ƒŽ †ƒ–ƒ ȋ‡Ǥ‰Ǥ …‘’”‡••‹‘ƒŽ ȋȌ ˜‡Ž‘…‹–› †ƒ–ƒȌǤ ‡
‰”‘—’ ‘ˆ ‘†‡Ž• „ƒ•‡† ‘ …‘–ƒ…– –Š‡‘”› ȋ‹†Ž‹ ͳͻͶͻȌ –”‡ƒ–• ”‘…• ƒ• ƒ …‘ŽŽ‡…–‹‘ ‘ˆ
‰”ƒ‹•ƒ†‡•–‹ƒ–‡•–Š‡‹”•–‹ˆˆ‡••‡•ˆ”‘–Š‡…‘–ƒ…–•–”‡••„‡–™‡‡–™‘•’Š‡”‡•‘ˆ‡“—ƒŽ
•‹œ‡Ǥ–Š‡‘–Š‡”Šƒ†ǡ‹…Ž—•‹‘‘†‡Ž•ȋ‡””›ƒͳͻͺͲȌ–”‡ƒ––Š‡”‘…ƒ•ƒ‡Žƒ•–‹…•‘Ž‹†
™‹–Š …ƒ˜‹–‹‡• ƒ† ƒ……‘—–• ˆ‘” –Š‡ ‡ˆˆ‡…–• ‘ˆ •Šƒ’‡• ‘ˆ —Ž–‹’Ž‡ ’‘”‡• ‘ ‡Žƒ•–‹…‹–›Ǥ 
’”ƒ…–‹…‡ǡ‰‡‡”ƒŽ‰—‹†‡Ž‹‡•ƒ†ƒ††‹–‹‘ƒŽ‘„•‡”˜ƒ–‹‘•Š‡Ž’–‘…‘•–”ƒ‹–Š‡‘†‡Ž•’ƒ…‡
–‘ ƒ ”‡Žƒ–‹˜‡Ž› •ƒŽŽ —„‡” ‘ˆ ’Žƒ—•‹„Ž‡ ‘’–‹‘•Ǥ ‘” ‡šƒ’Ž‡ǡ …‘–ƒ…– ‘†‡Ž• Šƒ˜‡ „‡‡
—•‡†•—……‡••ˆ—ŽŽ›–‘•–—†›–Š‡’”‡••—”‡†‡’‡†‡…‡‘ˆ˜‡Ž‘…‹–›‘ˆ—…‘•‘Ž‹†ƒ–‡†•‡†‹‡–•
ȋ˜‘”‹ Ƭ —” ͳͻͻ͸ȌǤ …Ž—•‹‘ ‘†‡Ž• ƒ”‡ ‘ˆ–‡ ’”‡ˆ‡”ƒ„Ž‡ ™Š‡ ƒƒŽ›œ‹‰ ™‡ŽŽǦ
ͳ‡’ƒ”–‡–‘ˆƒ”–Š…‹‡…‡ǡ‹˜‡”•‹–›‘ˆ‡”‰‡ǡ‡”‰‡ǡ‘”™ƒ›Ǥ
ʹǡ‡”‰‡ǡ‘”™ƒ›Ǥ
ͳͳʹ
…‘•‘Ž‹†ƒ–‡† ”‘…• ȋŠ‡‰ ͳͻͻͲǢ ‡”‰‡ ‡– ƒŽǤ ͳͻͻ͵ȌǤ ‘™‡˜‡”ǡ ƒˆ–‡” •‡Ž‡…–‹‰ ƒ ‘†‡ŽŽ‹‰
•–”ƒ–‡‰›ǡ ™‡ ƒ”‡ ˆ”‡“—‡–Ž› Ž‡ˆ– ™‹–Š •‡˜‡”ƒŽ ’‘••‹„Ž‡ ‘†‡Ž• –Šƒ– •‡‡ –‘ ”‡’”‡•‡–
‡š’‡”‹‡–ƒŽ†ƒ–ƒ‡“—ƒŽŽ›™‡ŽŽǤ
”‡•‡”˜‘‹”…Šƒ”ƒ…–‡”‹œƒ–‹‘ǡ–Š‡—Ž–‹ƒ–‡‰‘ƒŽ‘ˆƒ”‘…Ǧ’Š›•‹…•‘†‡Ž‹•–‘ƒ••‹•–‹
–Š‡ ‹˜‡”•‹‘ ‘ˆ •‡‹•‹… †ƒ–ƒ ˆ‘” ’‘”‘•‹–›ǡ Ž‹–Š‘Ž‘‰› ƒ† ’‘”‡ ˆŽ—‹† ȋȌǤ Š‡•‡ ‘†‡Ž•
†‡ˆ‹‡ –Š‡ –”ƒ•ˆ‘”• „‡–™‡‡ •‡‹•‹… ‘„•‡”˜ƒ„Ž‡• ƒ† ”‡•‡”˜‘‹” ’ƒ”ƒ‡–‡”•Ǥ ‡Ž‡…–‹‰ ƒ
•’‡…‹ˆ‹…‘†‡Ž‹’Ž‹…‹–Ž›†‡ˆ‹‡•–Š‡†‘‹ƒ–’ƒ”ƒ‡–‡”•–Šƒ–…‘–”‘Ž–Š‡•‡”‡Žƒ–‹‘•Š‹’•
ƒ††‡–‡”‹‡•–Š‡ƒ……—”ƒ…›‘ˆ–Š‡’”‡†‹…–‹‘•ǤŠ‡”‡ˆ‘”‡ǡƒ…”—…‹ƒŽ•–‡’‹•–‘…ƒŽ‹„”ƒ–‡ƒ†
–‘…‘’ƒ”‡–Š‡’”‡†‹…–‹‘•“—ƒ–‹–ƒ–‹˜‡Ž›™Š‡‘”‡–Šƒ‘‡‘†‡Žƒ’’‡ƒ”•‡“—‹˜ƒŽ‡–Ž›
˜ƒŽ‹†ˆ‘”ƒ‰‹˜‡ƒ”‡ƒǤ
ƒ”‹‘—• ‘†‡Ž• ƒ”‡ —•‡† –‘ ƒ……‘—– ˆ‘” –Š‡ †‡’‡†‡…‡ ‘ˆ ‡Žƒ•–‹… ’”‘’‡”–‹‡• ‘
†‹ˆˆ‡”‡–’Š›•‹…ƒŽ…‘†‹–‹‘•Ǥ”‡••—”‡†‡’‡†‡…‡Šƒ•„‡‡…ƒ’–—”‡†„›‘†‡Ž•„ƒ•‡†‘
…‘–ƒ…––Š‡‘”›ȋ‹†Ž‹ͳͻͶͻǢ‹‰„›ͳͻͺͳǢƒŽ–‘ͳͻͺ͹ȌǤŠ‡•–‹ˆˆ‡••‡ˆˆ‡…–†—‡–‘…‡‡–
Ž‘…ƒ–‡†ƒ––Š‡‰”ƒ‹…‘–ƒ…–•‹•‘ˆ–‡…ƒŽ…—Žƒ–‡†—•‹‰…‘–ƒ…–…‡‡––Š‡‘”›ȋ˜‘”‹Ƭ—”
ͳͻͻ͸Ȍǡ™Š‡”‡ƒ•’‘”‡‹…”‘•–”—…–—”‡‡ˆˆ‡…–•…ƒ„‡‘†‡ŽŽ‡†„›‹…Ž—•‹‘‘†‡Ž•ȋ—•–‡”Ƭ
‘•‘œ ͳͻ͹ͶǢ ‡””›ƒ ͳͻͺͲȌǤ ‡ŽˆǦ…‘•‹•–‡– ƒ’’”‘š‹ƒ–‹‘• ȋǯ‘‡ŽŽ Ƭ —†‹ƒ•›
ͳͻ͹ͶǢ‘”„›‡–ƒŽǤͳͻͻͶǢ‡””›ƒͳͻͻͷȌƒ††‹ˆˆ‡”‡–‹ƒŽ‡ˆˆ‡…–‹˜‡‡†‹—ȋȌ‘†‡Ž•
ȋ‡””›ƒ ͳͻͻʹȌ Šƒ˜‡ „‡‡ †‡˜‡Ž‘’‡† •’‡…‹ˆ‹…ƒŽŽ› –‘ ‡š–‡† ‹…Ž—•‹‘ ‘†‡Ž• –‘ Šƒ†Ž‡
Š‹‰Š‡”…‘…‡–”ƒ–‹‘•‘ˆ‹…Ž—•‹‘•ǤŠƒŽ‡•ǡ†—‡–‘–Š‡‹”…‘’Ž‡šŽ‹–Š‘Ž‘‰›ƒ†”‡†—…‡†’‘”‡
•‹œ‡• Šƒ˜‡ „‡‡ ‹†‡ƒŽ‹œ‡† –Š”‘—‰Š ‹…Ž—•‹‘ ‘†‡Ž•ǡ ȋ‘”„› ‡– ƒŽǤ ͳͻͻͶǢ ƒ‘„•‡ ‡– ƒŽǤ
ʹͲͲ͵Ǣ ‘Šƒ•‡ ‡– ƒŽǤ ʹͲͲͶƒǢ ”ƒ‡‰‡ ‡– ƒŽǤ ʹͲͲ͸ȌǤ Š‡ ‡“—ƒ–‹‘• ‘ˆ ƒ••ƒ ȋͳͻͷͳȌ
•‹—Žƒ–‡–Š‡Ž‘™Ǧˆ”‡“—‡…›‡ˆˆ‡…–•‘ˆ†‹ˆˆ‡”‡–’‘”‡ˆŽ—‹†•‘•‡‹•‹…˜‡Ž‘…‹–‹‡•Ǥ˜•‡–Š‡–ƒŽǤ
ȋʹͲͳͲȌ ’”‘˜‹†‡ ƒ ‘˜‡”˜‹‡™ ‘ˆ –Š‡‘”‡–‹…ƒŽǡ ‡’‹”‹…ƒŽǡ Š‡—”‹•–‹… ƒ† Š›„”‹† •–”ƒ–‡‰‹‡• –‘
‘†‡Ž†‹ƒ‰‡‡–‹…ƒ††‡’‘•‹–‹‘ƒŽ–”‡†•‹—…‘•‘Ž‹†ƒ–‡†Š‹‰ŠǦ’‘”‘•‹–›•‡†‹‡–•ǤŠ—•ǡ
ƒ„‹‰—‹–‹‡•…ƒƒ”‹•‡™Š‡™‡ƒ’’Ž›˜ƒ”‹‘—•‘†‡Ž•–‘‡•–‹ƒ–‡•‹—Ž–ƒ‡‘—•Ž›”‡•‡”˜‘‹”
’”‘’‡”–‹‡••—…Šƒ•Ž‹–Š‘Ž‘‰›ǡ’‘”‘•‹–›ƒ†•ƒ–—”ƒ–‹‘Ǥ‹––Ž‡™‘”Šƒ•„‡‡†‘‡–‘‡˜ƒŽ—ƒ–‡
•›•–‡ƒ–‹…ƒŽŽ› ’ƒ”ƒ‡–‡”• ‘„–ƒ‹‡† —•‹‰ †‹ˆˆ‡”‡– ‘†‡Ž•Ǥ ‘” ƒ ‰‹˜‡ †ƒ–ƒ•‡–ǡ –Š‡
•‡Ž‡…–‹‘ ‘ˆ ƒ ”‘…Ǧ’Š›•‹…• ‘†‡Ž ‹• —…‡”–ƒ‹ǡ ‹ –‡”• ‘ˆ ’”‘˜‹†‹‰ –Š‡ ‘•– •—‹–ƒ„Ž‡
”‡Žƒ–‹‘•Š‹’„‡–™‡‡–Š‡•‡‹•‹…ƒ†’ƒ”ƒ‡–‡”•ǤŠ‡‰‘ƒŽ‘ˆ–Š‹•’ƒ’‡”‹•–‘’”‡•‡–ƒ
™ƒ› –‘ •‡Ž‡…– ƒ† …ƒŽ‹„”ƒ–‡ –Š‡ ‘•– •—‹–ƒ„Ž‡ ”‘…Ǧ’Š›•‹…• ‘†‡Ž ˆ‘” ƒ ‰‹˜‡ †ƒ–ƒ•‡– ƒ†
”‡†—…‡ –Š‡ ‘Ǧ—‹“—‡‡•• ‘ˆ –Š‡ ”‡•‡”˜‘‹” …Šƒ”ƒ…–‡”‹œƒ–‹‘ ’”‘„Ž‡Ǥ ‡ †‘ –Š‹• „›
“—ƒ–‹ˆ›‹‰ –Š‡ ƒ……—”ƒ…› ‘ˆ †‹ˆˆ‡”‡– ”‘…Ǧ’Š›•‹…• ‘†‡Ž• ‹ –Š‡ ’”‡†‹…–‹‘ ‘ˆ ”‡•‡”˜‘‹”
’ƒ”ƒ‡–‡”• ™Š‡ …ƒŽ‹„”ƒ–‡† –‘ ‡š’‡”‹‡–ƒŽ †ƒ–ƒǤ ‡ —•‡ ƒ ƒ’’”‘ƒ…Š ȋ‘Šƒ•‡ ‡– ƒŽǤ
ʹͲͲͶ„Ȍ–Šƒ– ‘”‰ƒ‹œ‡•–Š‡”‘…Ǧ’Š›•‹…•–”ƒ•ˆ‘”•‹–‘…‘•–”ƒ‹–†ƒ–ƒ™Š‡”‡–Š‡•‡‹•‹…
˜ƒ”‹ƒ„Ž‡•ȋ‡Ǥ‰Ǥǡ˜‡Ž‘…‹–›ƒ††‡•‹–›Ȍƒ”‡†‹”‡…–ˆ—…–‹‘•‘ˆ–Š‡•‡Ž‡…–‡†’ƒ”ƒ‡–‡”•Ǥ‡
•–ƒ”–™‹–Šƒ”‡˜‹‡™‘ˆ–Š‹••–”ƒ–‡‰›ǡƒ†–Š‡™‡†‡‘•–”ƒ–‡–Š‡…ƒŽ‹„”ƒ–‹‘’”‘…‡†—”‡‹
–™‘…ƒ•‡•—•‹‰”‡ƒŽ†ƒ–ƒǤ…ƒ•‡ ͳ™‡—•‡–Š‡’”‘…‡†—”‡–‘‹ŽŽ—•–”ƒ–‡–Š‡•Š‘”–…‘‹‰‘ˆ
–Š‡ –”ƒ†‹–‹‘ƒŽ …”‘••Ǧ’Ž‘– –›’‡ ‘ˆ …ƒŽ‹„”ƒ–‹‘Ǥ ‡ †‘ –Š‹• „› …‘’ƒ”‹‰ –Š‡ ”‡•‡”˜‘‹”
’”‘’‡”–› ’”‡†‹…–‹‘• ƒ†‡ ™‹–Š ƒ ‘†‡Ž ˆ‘” †‹•’‡”•‡† …Žƒ› ȋ˜‘”‹ Ƭ —–‹‡””‡œ ʹͲͲͳȌ
ͳͳ͵
˜‡”•—•ƒ‘†‡Žˆ‘”•–”—…–—”ƒŽ…Žƒ›ȋ˜•‡–Š‡–ƒŽǤʹͲͲͷȌ‘ƒ•‡–‘ˆŽƒ„‘”ƒ–‘”›‡ƒ•—”‡‡–•
‘ˆ …Žƒ›Ǧ•ƒ† …‘’‘•‹–‡• ȋ‹ ͳͻͻʹȌǤ  …ƒ•‡ ʹ ™‡ ‡š’Ž‘”‡ –Š‡ ƒ……—”ƒ…› ‘ˆ ˜ƒ”‹‘—• ”‘…Ǧ
’Š›•‹…•’”‡†‹…–‹‘•‘ˆ”‡•‡”˜‘‹”’”‘’‡”–‹‡•…‘•‹†‡”‹‰ƒ‘”‡‡š–‡•‹˜‡†ƒ–ƒ•‡–ȋƒ‡–ƒŽǤ
ͳͻͺ͸ȌǤ —„•‡“—‡–Ž›ǡ ™‡ •‡Ž‡…– –Š‡ ‘•– •—‹–ƒ„Ž‡ ‘†‡Ž• ƒ† –Š‡ ’‡”–—”„ ‹†‹˜‹†—ƒŽ
’ƒ”ƒ‡–‡”•–‘‘’–‹‹œ‡–Š‡ˆ‹ƒŽ’”‡†‹…–‹‘•Ǥ
…‘‘’”ƒ…–‹…‡‹”‘…Ǧ’Š›•‹…•ƒƒŽ›•‹•‹•–‘—•‡…”‘••’Ž‘–•–‘•–—†›–”‡†•ƒ†
’”‘’‡”–› †‡’‡†‡…‹‡•Ǥ‘” ‡šƒ’Ž‡ǡ‹‰—”‡ ͳƒ•Š‘™•–Š‡’”‡†‹…–‡† „—Ž‘†—Ž—•˜‡”•—•
’‘”‘•‹–› –”‡†• ˆ‘” ƒ ’ƒ”–‹…—Žƒ” ˆŽ—‹† •ƒ–—”ƒ–‹‘ ƒ† †‹ˆˆ‡”‡– Ž‹–Š‘Ž‘‰‹‡• —•‹‰ ƒ ”‘…
’Š›•‹…•‘†‡ŽǤ–Š‡•–”ƒ–‡‰› ‘ˆ‘Šƒ•‡‡–ƒŽǤȋʹͲͲͶ„Ȍ•—…Š‘†‡ŽŽ‡††‡’‡†‡…‹‡•ƒ”‡
”‡•ƒ’Ž‡† ‹–‘ ƒ •…ƒŽƒ” ˆ‹‡Ž† ‘ˆ –Š‡ ”‡•‡”˜‘‹” ’”‘’‡”–‹‡•Ǥ ‹‰—”‡ ͳ„ ‹ŽŽ—•–”ƒ–‡• –Š‡
”‡•ƒ’Ž‹‰‘ˆ–™‘„—Ž‘†—Ž‹˜ƒŽ—‡•‹–‘ƒŽ‹–Š‘Ž‘‰›˜‡”•—•’‘”‘•‹–›…”‘••’Ž‘–Ǥ‡’‡ƒ–‹‰
–Š‹•ˆ‘”–Š‡‘–Š‡”‘†—Ž‹˜ƒŽ—‡•ƒ†˜ƒ”‹‘—•ˆŽ—‹†•ƒ–—”ƒ–‹‘•‰‹˜‡•—•–Š‡͵…—„‡‹‹‰—”‡
ʹǤŠ‡”‡•ƒ’Ž‡†„—Ž‘†—Ž—•…ƒ„‡–Š‘—‰Š–ƒ•ƒ•…ƒŽƒ”ˆ‹‡Ž†Ǥ–Š‹•…ƒ•‡ǡαȋφǡǡȌǡ
™Š‡”‡ φǡ ƒ† †‡‘–‡ –Š‡ ’‘”‘•‹–›ǡ …Žƒ› ƒ† ˆŽ—‹† ˜‘Ž—‡ ˆ”ƒ…–‹‘•ǡ ”‡•’‡…–‹˜‡Ž› ˆ‘” ƒ
’ƒ”–‹…—Žƒ” ”‘… ’Š›•‹…• ‘†‡ŽǤ ”‘ ȋφǡǡȌǡ ™‡ …ƒŽ…—Žƒ–‡ ƒ —‡”‹…ƒŽ ”‡Žƒ–‹‘•Š‹’
„‡–™‡‡φǡƒ†™Š‹…Š…‘””‡•’‘†•–‘ƒ•’‡…‹ˆ‹…„—Ž‘†—Ž—•˜ƒŽ—‡Ǥ‘”–Š‡͵…—„‡–Š‹•
–›’‹…ƒŽŽ›’”‘†—…‡•ƒ•—”ˆƒ…‡–Šƒ–™‡†‡‘–‡ƒ‹•‘Ǧ•—”ˆƒ…‡„‡…ƒ—•‡ƒŽŽ’‘‹–•‘–Š‹••—”ˆƒ…‡
…‘””‡•’‘†–‘–Š‡•ƒ‡‘†—Ž—•Ǥ
Figure 1 Resampling of a rock-physics model from velocity-porosity to lithology-porosity space. Ci are model
results for various clay contents.
ͳͳͶ
•–‹ƒ–‹‰”‡•‡”˜‘‹”’”‘’‡”–‹‡•
‹•‘Ǧ•—”ˆƒ…‡…ƒ„‡—•‡†–‘•–—†›’”‡†‹…–‡†”‡•‡”˜‘‹”’”‘’‡”–›†‡’‡†‡…‹‡•ˆ‘”ƒ
’ƒ”–‹…—Žƒ”•‡‹•‹…’ƒ”ƒ‡–‡”˜ƒŽ—‡ƒ†ƒ‰‹˜‡”‘…’Š›•‹…•‘†‡ŽǤ›…‘„‹ƒ–‹‘‘ˆ φǡ
ƒ† …‘””‡•’‘†‹‰ –‘ ƒ ’‘‹– ‘ •—…Š ƒ •—”ˆƒ…‡ ‹• ƒ ’‘••‹„Ž‡ •‘Ž—–‹‘ ˆ‘” –Š‡ ’ƒ”–‹…—Žƒ”
•‡‹•‹…’ƒ”ƒ‡–‡”˜ƒŽ—‡Ǥ›’‹…ƒŽŽ›ǡ™‡Šƒ˜‡†ƒ–ƒ‘ˆ‘”‡–Šƒ‘‡•‡‹•‹…’ƒ”ƒ‡–‡”ȋ…‘Ǧ
’”‡••‹‘ƒŽ ƒ† •Š‡ƒ” ™ƒ˜‡•’‡‡†•ǡ ’ ƒ† •ǡ ƒ† „—Ž †‡•‹–› ρȌǡ ƒ† „› …‘„‹‹‰ –Š‡‹”
‹†‹˜‹†—ƒŽ ‹•‘Ǧ•—”ˆƒ…‡• ™‡ …‘•–”ƒ‹ –Š‡ ’‘••‹„Ž‡ •‘Ž—–‹‘•Ǥ …‘„‹ƒ–‹‘ ‘ˆ –™‘
•‡‹•‹… ‘„•‡”˜ƒ„Ž‡• ȋ‡Ǥ‰Ǥ ’ ƒ† ρȌ ™‹ŽŽ ‘”ƒŽŽ› Ž‡ƒ† –‘ ‘‡ ‘” ‘”‡ …—”˜‹‰ Ž‹‡• ‹ –Š‡
†‘ƒ‹Ǥ—”–Š‡”‘”‡ǡƒ…‘„‹ƒ–‹‘ ‘ˆ–Š”‡‡ ‘„•‡”˜ƒ„Ž‡•Ž‡ƒ†•–‘‘‡‘”‘”‡’‘‹–
•‘Ž—–‹‘• „‡…ƒ—•‡ ™‡ ƒ”‡ †‡ƒŽ‹‰ ™‹–Š ƒ ‘ǦŽ‹‡ƒ” ’”‘„Ž‡ ȋ•‡‡ ‹‰—”‡ ͵ȌǤ ‘–Š‡”
’‘••‹„Ž‡ ‘—–…‘‡ ‘ˆ –Š‡ ‹˜‡”•‹‘ ‹• –Šƒ– ‘ ‹–‡”•‡…–‹‘ ‹• ˆ‘—†ǡ ‹Ǥ‡Ǥǡ ‘ …‘„‹ƒ–‹‘ ‘ˆ
”‡•‡”˜‘‹”’”‘’‡”–‹‡•‹•…‘•‹•–‡–™‹–Š–Š‡•‡–‘ˆ‘„•‡”˜ƒ„Ž‡•ǤŠ‹•‡ƒ•–Šƒ––Š‡•‡Ž‡…–‡†
”‘…’Š›•‹…•‘†‡Žˆƒ‹Ž•–‘”‡’”‘†—…‡–Š‡†ƒ–ƒƒ†‘–Š‡”’‘••‹„Ž‡‘†‡Ž…ƒ†‹†ƒ–‡••Š‘—Ž†
„‡–‡•–‡†Ǥ
Š‡™‘”‹‰™‹–Š”‡ƒŽ†ƒ–ƒǡ‹–‹•†‹ˆˆ‹…—Ž––‘ˆ‹†ƒ”‘…’Š›•‹…•‘†‡Ž–Šƒ–‹•ƒ„Ž‡–‘
’”‡†‹…––Š‡…‘””‡…–”‡•‡”˜‘‹”’”‘’‡”–‹‡•ˆ‘”‡˜‡”›†ƒ–ƒ’‘‹–—Ž‡••—…‡”–ƒ‹–›‹•‹…Ž—†‡†Ǥ
…ƒ•‡‘‡ǡ™‡‹…Ž—†‡ƒˆ‡™’‡”–—”„‡†˜ƒŽ—‡•‘ˆ–Š‡‹’—–†ƒ–ƒ‹ƒ††‹–‹‘–‘–Š‡‘„•‡”˜‡†
†ƒ–ƒƒ†’‡”ˆ‘”–Š‡‹˜‡”•‡‘†‡ŽŽ‹‰Ǥ–Š‡•‡…‘†…ƒ•‡ǡ™‡Šƒ†Ž‡–Š‡—…‡”–ƒ‹–›„›
—•‹‰ ƒ•‘Ǧ…ƒŽŽ‡† ’”‘š‹‹–›„ƒ•‡† ‹’Ž‡‡–ƒ–‹‘ ‘ˆ–Š‡‹˜‡”•‹‘•–”ƒ–‡‰›Ǥ‡”‡ǡ–Š‡‹•‘Ǧ
•—”ˆƒ…‡• ƒ”‡ ƒ†‡ —’ ‘ˆ †‡•‡Ž› •ƒ’Ž‡† ’‘‹–•Ǥ –‡”•‡…–‹‘• ƒ”‡ ‹†‡–‹ˆ‹‡† ™Š‡ –Š‡
’‘‹–• ‘ ‘‡ •—”ˆƒ…‡ ƒ”‡ ™‹–Š‹ ƒ ƒš‹— †‹•–ƒ…‡ δ ˆ”‘ ’‘‹–• ‘ ƒ‘–Š‡” •—”ˆƒ…‡Ǥ
Figure 2 Bulk modulus constraint cube in the porosity,
lithology, fluid space (PLF). The vertical axis is water
saturation. The lithology axis varies from pure quartz
(zero) to pure clay (one).
Figure 3 Three observations (Vp, Vs and density isosurfaces) intersecting in the PLF space. Solutions exist
at the two indicated points.
ͳͳͷ
Š‹• ƒš‹— †‹•–ƒ…‡ ”‡’”‡•‡–• ƒ
ƒ„•‘Ž—–‡–‘Ž‡”ƒ…‡‹–‡”˜ƒŽˆ‘”–Š‡‘†‡ŽǦ
Ž‡† φǡƒ†Ǥ•‡•‹–‹˜‹–›ƒƒŽ›•‹•‘ˆ–Š‡
ƒ’’Ž‹‡†‘†‡Ž•–‘–Š‡—…‡”–ƒ‹–‹‡•‹–Š‡
‡ƒ•—”‡†”‘…’”‘’‡”–‹‡•…ƒ„‡ƒ†‡–‘
†‡”‹˜‡ ƒ •—‹–ƒ„Ž‡ –‘Ž‡”ƒ…‡ ‹–‡”˜ƒŽ ˆ‘” ƒ
‰‹˜‡ †ƒ–ƒ•‡–Ǥ Š‡•‡ ’‘‹– •‘Ž—–‹‘• ƒ”‡
‡š’ƒ†‡†–‘•’Š‡”‹…ƒŽ’‘‹–…Ž‘—†•™‹–Šƒ
”ƒ†‹—• δ/2Ǥ‡šƒ’Ž‡‘ˆ–Š‡‹˜‡”•‹‘‹
‹‰—”‡͵—•‹‰–Š‡’”‘š‹‹–›„ƒ•‡†‹’Ž‡Ǧ
‡–ƒ–‹‘ ƒ† ƒ δαͲǤͲʹǡ ‹• •Š‘™ ‹
‹‰—”‡ͶǤ
Figure 4 Three observations (Vp, Vs and density) intersecting in the PLF space. Uncertainty is implicitly handled
by the proximity based implementation of the inverse
modelling, providing a cloud of solutions as opposed to
points as in Figure 3.
Š‡…ƒŽ‹„”ƒ–‹‘’”‘…‡†—”‡
–Š‡“—ƒ–‹–ƒ–‹˜‡…ƒŽ‹„”ƒ–‹‘‘ˆ”‘…Ǧ’Š›•‹…•‘†‡Ž•™‡…‘’ƒ”‡’”‡†‹…–‡†”‡•‡”˜‘‹”
’”‘’‡”–‹‡•ǡ‹Ǥ‡Ǥƒš‹•”‡ƒ†‹‰•ƒ––Š‡‹–‡”•‡…–‹‰’‘‹–•ǡ–‘‡ƒ•—”‡‡–•‘ˆ–Š‡•‡’”‘’‡”–‹‡•
ˆ”‘Žƒ„‘”ƒ–‘”›‘”™‡ŽŽǦŽ‘‰†ƒ–ƒǤŠ”‘—‰Š–Š‹•ƒƒŽ›•‹•‹–Š‡•’ƒ…‡ǡ™‡‡˜ƒŽ—ƒ–‡Š‘™
ƒ……—”ƒ–‡ƒ‘†‡Ž’”‡†‹…–•”‡•‡”˜‘‹”’”‘’‡”–‹‡•ˆ”‘•‡‹•‹…†ƒ–ƒǤƒ††‹–‹‘ǡ™‡…‘’ƒ”‡
–Š‡’”‡†‹…–‹‘•‘ˆ”‡•‡”˜‘‹”’”‘’‡”–‹‡•ˆ”‘†‹ˆˆ‡”‡–‘†‡Ž•ƒ††‹•…ƒ”†–Š‘•‡‘†‡Ž•–Šƒ–
’”‘˜‹†‡Ž‡••ƒ……—”ƒ–‡’”‡†‹…–‹‘•Ǥ—”‹‰–Š‡…ƒŽ‹„”ƒ–‹‘’”‘…‡••™‡…ƒƒŽ•‘ƒš‹‹œ‡–Š‡
–‘Ž‡”ƒ…‡‹–Š‡‹–‡”•‡…–‹‘•ƒ† “—‹…Ž›–‡•– –Š‡ ’‡”ˆ‘”ƒ…‡‘ˆ•‡˜‡”ƒŽ‘†‡Ž•ǡ†‹•…ƒ”†
–Š‡ Ž‡•• ‡ˆˆ‡…–‹˜‡ ‘‡•ǡ ƒ† …‘–‹—‡ ™‹–Š –Š‡ ‘•– ’”‘‹•‹‰ ‘‡•Ǥ • –Š‡ —„‡” ‘ˆ
‘†‡Ž•‹•”‡†—…‡†–‘–Š”‡‡‘”ˆ‘—”ǡ–Š‡—…‡”–ƒ‹–›‹–Š‡‘„•‡”˜ƒ–‹‘•…ƒ„‡…‘•–”ƒ‹‡†
–‘ ’‡”ˆ‘” ƒ ‘”‡ ”‹‰‘”‘—• ƒƒŽ›•‹•Ǥ ‹ƒŽŽ›ǡ ™Š‡ –Š‡ ‘•– •—‹–ƒ„Ž‡ ‘†‡Ž Šƒ• „‡‡
‹†‡–‹ˆ‹‡†ǡ–Š‡•ƒ‡‡–Š‘†‘Ž‘‰›…ƒ„‡”‡’‡ƒ–‡†ˆ‘”˜ƒ”‹‘—•˜ƒŽ—‡•‘ˆ‘†‡Ž’ƒ”ƒ‡–‡”•
ȋƒ•’‡…–”ƒ–‹‘ǡ’”‡••—”‡ǡ‡–…ǤȌ–‘‘’–‹‹œ‡–Š‡…ƒŽ‹„”ƒ–‹‘ƒ†‹’”‘˜‡’”‡†‹…–‹‘”‡•—Ž–•Ǥ‡
ƒ’’Ž‹‡†–Š‹•‡–Š‘†‘Ž‘‰›–‘“—ƒ–‹ˆ›–Š‡…ƒŽ‹„”ƒ–‹‘‘ˆ˜ƒ”‹‘—•”‘…Ǧ’Š›•‹…•‘†‡Ž•–‘–™‘
†ƒ–ƒ•‡–•‘ˆ…Žƒ›Ǧ”‹…Š•ƒ†•–‘‡•Ǥ
ͳǣ
Ǧ
‡ƒ’’Ž‹‡†–Š‡‡–Š‘†‘Ž‘‰›–‘ƒŽƒ„‘”ƒ–‘”›†ƒ–ƒ•‡–‘ˆ…Žƒ›Ǧ•ƒ†…‘’‘•‹–‡•’”‡’ƒ”‡†
„› ‹ ȋͳͻͻʹȌǤ Š‡ •ƒ’Ž‡• …‘•‹•– ‘ˆ ‹š–—”‡• ‘ˆ ’—”‡ ƒ‘Ž‹‹–‡ ƒ† ––ƒ™ƒ •ƒ† ™‹–Š ƒ
‰”ƒ‹ •‹œ‡ ”ƒ–‹‘ ‘ˆ ͳȀʹͲǡ ’”‘˜‹†‹‰ ƒ ‹†‡ƒŽ „‹ƒ”› ‹š–—”‡Ǥ ‘” Ž‘™ “—ƒ–‹–‹‡• ‘ˆ …Žƒ›ǡ –Š‡
•ƒŽŽ…Žƒ›’ƒ”–‹…Ž‡•Ž‹‡Ž›‘……—’›’ƒ”–‘ˆ–Š‡’‘”‡•’ƒ…‡‘ˆ–Š‡Žƒ”‰‡”•ƒ†’ƒ”–‹…Ž‡•ȋƒ’‘”‡Ǧ
ͳͳ͸
ˆ‹ŽŽ‹‰…Žƒ›ȌǤŠ‹••’ƒ–‹ƒŽ†‹•–”‹„—–‹‘Šƒ•ƒ‹‹ƒŽ‡ˆˆ‡…–‘–Š‡•–”—…–—”‡‘ˆ–Š‡…‘’‘•‹–‡Ǥ
Š‡ †ƒ–ƒ•‡– ˆ‘” ͷͲ ƒ ‘ˆ ‡ˆˆ‡…–‹˜‡ ’”‡••—”‡ ‹• •Š‘™ ‹ ‹‰—”‡ ͷ ™Š‡”‡ ƒ ”‡†—…–‹‘ ‹
’‘”‘•‹–›ƒ†‹…”‡ƒ•‡‹˜‡Ž‘…‹–›ƒ”‡‘„•‡”˜‡†ˆ‘”‹…”‡ƒ•‹‰…Žƒ›…‘–‡–Ǥ‘˜‡”–—”‡†Ǧ
•Šƒ’‡ –”‡† ’”‘†—…‡† „› –Š‡ –”ƒ•‹–‹‘ „‡–™‡‡ •ƒ† ƒ† •ŠƒŽ‡ Šƒ• „‡‡ ‘–‡† ‹ –Š‡
Ž‹–‡”ƒ–—”‡ƒ•ƒ‹†‹…ƒ–‘”‘ˆ†‹•’‡”•‡†…Žƒ›–‘’‘Ž‘‰›ȋƒ”‹‘‡–ƒŽǤͳͻͻʹȌǤ–Š‡…‘–‡š–‘ˆ
”‘…Ǧ’Š›•‹…•‘†‡ŽŽ‹‰ǡ™‡†‡‘–‡•ŠƒŽ‡ƒ•ƒˆ‹‡Ǧ‰”ƒ‹‡†”‘…ȋ…Žƒ›Ǧ•‹œ‡†ƒ†•‹Ž–Ǧ•‹œ‡†Ȍ‹
™Š‹…Š…Žƒ›‹‡”ƒŽ•ƒ”‡–Š‡Ž‘ƒ†Ǧ„‡ƒ”‹‰’Šƒ•‡Ǥ‡…ƒŽ‹„”ƒ–‡†ƒ‘†‡Žˆ‘”†‹•’‡”•‡†…Žƒ›ǡ
ƒ†ƒ‘†‡Ž–Šƒ–‹••—‹–ƒ„Ž‡ˆ‘”„‘–Š•–”—…–—”ƒŽƒ†Žƒ‹ƒ–‡†…Žƒ›–‘–Š‡†ƒ–ƒ•‡–Ǥ
Š‡ ‘†‡Ž ˆ‘” †‹•’‡”•‡† …Žƒ› ȋ˜‘”‹ Ƭ —–‹‡””‡œ ʹͲͲͳȌ ‹• ƒ ˜‡Ž‘…‹–›Ǧ’‘”‘•‹–›
”‡Žƒ–‹‘•Š‹’–Šƒ–—•‡•–Š‡ƒ•Š‹ǦŠ–”‹ƒȋȌŽ‘™‡”„‘—†ȋƒ•Š‹ƬŠ–”‹ƒͳͻ͸͵Ȍ
ƒ• ƒ ‹š‹‰ Žƒ™ „‡–™‡‡ –™‘ ‡† ‡„‡”•Ǥ Š‡ Š‹‰ŠǦ’‘”‘•‹–› ‡† ‡„‡” ‹• …Ž‡ƒ •ƒ†
™Š‘•‡ ˜‡Ž‘…‹–› ‹• …‘’—–‡† „› …‘–ƒ…– –Š‡‘”› ȋ‹†Ž‹ ͳͻͶͻȌǤ Š‡ Ž‘™Ǧ’‘”‘•‹–› ‡†
‡„‡” ”‡’”‡•‡–• –Š‡ •ƒ‡ •ƒ† ™‹–Š ‹–• ’‘”‡ •’ƒ…‡ …‘’Ž‡–‡Ž› ˆ‹ŽŽ‡† „› …Žƒ›Ǥ Š‡
’‘”‘•‹–› ƒ– –Š‹• ’‘‹– ‹• ‘– œ‡”‘ „‡…ƒ—•‡ …Žƒ› ’ƒ”–‹…Ž‡• Šƒ˜‡ ‹–”‹•‹… ’‘”‘•‹–›Ǥ Š‹• ‹•
•‘‡–‹‡• ”‡ˆ‡””‡† –‘ ƒ• •ƒ† ƒ– …”‹–‹…ƒŽ …Žƒ› …‘–‡– ȋ‹ ͳͻͻʹȌǤ ˜‘”‹ Ƭ —–‹‡””‡œ
ȋʹͲͲͳȌ…‘’—–‡†–Š‹•‹–‡”‡†‹ƒ–‡‡„‡”„›ƒ††‹‰•‹Ž–’ƒ”–‹…Ž‡•ȋ“—ƒ”–œȌ–‘ƒ’—”‡•ŠƒŽ‡
ƒŽ•‘—•‹‰–Š‡Ž‘™‡”„‘—†ǤŠ‡‘†‡Ž…‘•‹•–•‘ˆ–™‘†‘ƒ‹•Ǥ–Š‡ˆ‹”•–†‘ƒ‹ǡ…Žƒ›
‹• –Š‡ Ž‘ƒ†Ǧ„‡ƒ”‹‰ ’Šƒ•‡ ȋ•ƒ†›Ǧ•ŠƒŽ‡Ȍǡ ™Š‡”‡ƒ• ‹ –Š‡ •‡…‘† †‘ƒ‹ǡ –Š‡ •ƒ† ’ƒ… ‹•
Ž‘ƒ†„‡ƒ”‹‰ȋ•ŠƒŽ‡›Ǧ•ƒ†Ȍǡƒ•‹‹‰—”‡͸Ǥ
‘—”‘†‡ŽŽ‹‰™‡ˆ‘…—•‡†‘–Š‡•ŠƒŽ‡›Ǧ•ƒ†•‡…–‹‘‹™Š‹…Š…Žƒ›’ƒ”–‹…Ž‡•ˆ‹ŽŽ–Š‡
’‘”‡ •’ƒ…‡ ‘ˆ –Š‡ …Ž‡ƒ •ƒ† ™‹–Š‘—– •‹‰‹ˆ‹…ƒ–Ž› ƒˆˆ‡…–‹‰ ‹–• •–‹ˆˆ‡••Ǥ Š‡”‡ˆ‘”‡ǡ –Š‡
Figure 5 P-wave velocity versus porosity trend of
clay-sand composites at constant pressure prepared by Yin (1992). Dashed arrows indicate
increasing clay content. The V-shaped trend of
increasing clay content, producing an increase of
velocity (and a decrease in porosity) until clay
content equals sand porosity, has been attributed
to a pore filling clay topology.
Figure 6 Dispersed clay model (Dvorkin-Gutierrez)
calibrated to Yin’s data. Note porosity is modelled well, but
velocity is in general over-estimated. The model predicts that
clay mineral becomes load-bearing (porosity minimum and
velocity maximum) at about 30 % clay content.
ͳͳ͹
’”‘’‡”–‹‡•‘ˆ–Š‡‹š–—”‡…ƒ„‡…‘’—–‡†ˆ”‘–Š‡Ž‘™‡”„‘—†•‘ˆ–Š‡…Ž‡ƒ•ƒ†ƒ†
–Š‡ •ƒ† ƒ– …”‹–‹…ƒŽ …Žƒ› …‘–‡–Ǥ Š‡ ‡Žƒ•–‹… ‘†—Ž‹ ‘ˆ ƒ •ŠƒŽ‡›Ǧ•ƒ† ™‹–Š ‹…”‡ƒ•‹‰ …Žƒ›
…‘–‡–ȋȌƒ”‡‡š’”‡••‡†ƒ•ǣ
−1
K MIX
1 − C φ ss
C φ ss
4
=
+
− μ ss , 3
K ss + (4 / 3) μ ss K cc + (4 / 3) μ ss ȋͳȌ
−1
1 − C φ ss
C φ ss +
μ MIX = − Z ss , μ ss + Z ss μ cc + Z ss Z ss =
μ ss 9 K ss + 8μ ss
6 K ss + 2μ ss
, ȋʹȌ
ȋ͵Ȍ
™Š‡”‡ǡ Kcc ƒ† μ cc ƒ”‡…‘’—–‡†ˆ”‘–Š‡•ƒ†›Ǧ•ŠƒŽ‡‘†‡Žƒ–…”‹–‹…ƒŽ…Žƒ›…‘–‡–Ǥ••ǡɊ••
ƒ† φss ƒ”‡–Š‡‡ˆˆ‡…–‹˜‡‘†—Ž‹ƒ†’‘”‘•‹–›‘ˆ–Š‡…Ž‡ƒ•ƒ†•–‘‡Ǥ
…‘–”ƒ•–ǡ–Š‡…‘•–ƒ–…Žƒ›‘†‡Žƒ••—‡•–Š‡…Žƒ›’ƒ”–‹…Ž‡•ƒ”‡Ž‘…ƒ–‡†‹–Š‡ˆ”ƒ‡
‘ˆ–Š‡”‘…ǡ”‡†—…‹‰‹–•‘˜‡”ƒŽŽ•–‹ˆˆ‡••ǤŠ‡‘†‡Ž—•‡•…‘–ƒ…––Š‡‘”›ƒ†–Š‡Ž‘™‡”
„‘—† –‘ ‘†‡Ž •ƒ†• ™‹–Š ƒ …‘•–ƒ– …Žƒ›Ǧ“—ƒ”–œ ”ƒ–‹‘ ‹ –Š‡ ˜‡Ž‘…‹–›Ǧ’‘”‘•‹–› •’ƒ…‡
ȋ˜•‡–Š‡–ƒŽǤʹͲͲͷȌǤŠ‹•‹••—‹–ƒ„Ž‡ ˆ‘”•ƒ†•™‹–Š„‘–Š•–”—…–—”ƒŽƒ†Žƒ‹ƒ–‡†…Žƒ›Ǥ•
‹ǯ• †ƒ–ƒ•‡– ‹• …‘’‘•‡† ‘ˆ •›–Š‡–‹… …Žƒ›Ǧ•ƒ† ƒ‰‰”‡‰ƒ–‡• ™‡ †‘ ‘– ‡š’‡…– ƒ›
Žƒ‹ƒ–‹‘• –‘ „‡ ’”‡•‡– ƒ† ™‡ ”‡ˆ‡” –‘ –Š‹• ƒ• –Š‡ ‘†‡Ž ˆ‘” •–”—…–—”ƒŽ …Žƒ›Ǥ – ‹•
ƒƒŽ‘‰‘—• –‘ –Š‡ —…‘•‘Ž‹†ƒ–‡† •ƒ† ‘†‡Ž ȋ˜‘”‹ Ƭ —” ͳͻͻ͸Ȍ „—– ™‹–Š ƒ ”‡†—…‡†
…”‹–‹…ƒŽ’‘”‘•‹–›„‡…ƒ—•‡ƒ…Žƒ›”‹…Š•ƒ†Šƒ•Ž‘™‡”…”‹–‹…ƒŽ’‘”‘•‹–›–Šƒƒ…Ž‡ƒ•ƒ†ǤŠ‡
‹‡”ƒŽ’‘‹–‹•…‘’—–‡†„›‹ŽŽǯ•ȋͳͻͷʹȌƒ˜‡”ƒ‰‡‘ˆ“—ƒ”–œƒ†…Žƒ›‹‡”ƒŽ‘†—Ž‹Ǥ
‘˜‡–‹‘ƒŽ…ƒŽ‹„”ƒ–‹‘
…‘˜‡–‹‘ƒŽ…ƒŽ‹„”ƒ–‹‘…‘•‹•–•‘ˆƒ“—ƒŽ‹–ƒ–‹˜‡ˆ‹–‘ˆ‘†‡ŽŽ‡†…—”˜‡•ˆ‘”ƒ‰‹˜‡
…”‘••Ǧ’Ž‘–†‘ƒ‹Ǥ‡…ƒŽ‹„”ƒ–‡†„‘–Š‘†‡Ž•–‘–Š‡†ƒ–ƒ•‡–‹–Š‡˜‡Ž‘…‹–›Ǧ’‘”‘•‹–›•’ƒ…‡
ȋ‹‰—”‡ ͹ȌǤ Š‡ †‹•’‡”•‡† …Žƒ› ‘†‡Ž ƒ–…Š‡• ™‡ŽŽ –Š‡ …Ž‡ƒ •ƒ† ƒ† ’—”‡ …Žƒ› ‡†
‡„‡”•ǡ„—–‹–‹••‡•–Š‡‹–‡”‡†‹ƒ–‡˜ƒŽ—‡•‘ˆ…Žƒ›…‘–‡–Ǥ Š‡•–”—…–—”ƒŽ…Žƒ›‘†‡Ž
”‡’”‘†—…‡• –Š‡ ˜ƒ”‹ƒ„‹Ž‹–› ‘ˆ –Š‡ Ǧ™ƒ˜‡ ˜‡Ž‘…‹–› †ƒ–ƒǡ „—– ‹–• ƒ……—”ƒ…› ‹• †‹ˆˆ‹…—Ž– –‘
‡˜ƒŽ—ƒ–‡Ǥ‘–‡–Šƒ––Š‡•Š‡ƒ”˜‡Ž‘…‹–›†ƒ–ƒ•Š‘™‘•‡•‹–‹˜‹–›–‘…Žƒ›…‘–‡–Ǥ
 ‹‰—”‡ ͸ǡ –Š‡ †‹•’‡”•‡† …Žƒ› ‘†‡Ž ”‡’”‘†—…‡• –Š‡ †‡…”‡ƒ•‡ ‘ˆ ’‘”‘•‹–› ˆ‘”
‹…”‡ƒ•‹‰…Žƒ›…‘–‡–•Š‘™„›–Š‡†ƒ–ƒǡƒ†’”‡†‹…–•ƒ…Šƒ‰‡‹–Š‡Ž‘ƒ†Ǧ„‡ƒ”‹‰’Šƒ•‡ǡ
ˆ”‘‰”ƒ‹–‘ƒ–”‹š•—’’‘”–‡†ǡˆ‘”ƒ…Žƒ›˜‘Ž—‡‘ˆƒ’’”‘š‹ƒ–‡Ž›͵ʹΨǤ‘–Š‘†‡Ž•…ƒ
„‡—•‡†–‘‡š’Žƒ‹–Š‡†ƒ–ƒƒ†–‘‹ˆ‡”–Š‡‹–‡”ƒŽ‘”‰ƒ‹œƒ–‹‘‘ˆ–Š‡…Žƒ›’ƒ”–‹…Ž‡•‹–Š‡
ͳͳͺ
•ƒ’Ž‡•Ǥ ‘™‡˜‡”ǡ ™‡ …ƒ‘– †‡–‡”‹‡ ™Š‹…Š ‘†‡Ž ‡š’Žƒ‹• –Š‡ †ƒ–ƒ „‡––‡”ǡ ‘”ǡ ˆ”‘
–Š‡•‡”‡•—Ž–•ǡ…ƒ™‡“—ƒ–‹ˆ›Š‘™•—……‡••ˆ—ŽŽ›‡‹–Š‡”‘†‡Ž”‡’”‡•‡–•–Š‡†ƒ–ƒǤ
—ƒ–‹–ƒ–‹˜‡ƒƒŽ›•‹•‹–Š‡•’ƒ…‡
‘” –Š‡ “—ƒ–‹–ƒ–‹˜‡ ƒƒŽ›•‹•ǡ ™‡ —•‡† •‡˜‡ •ƒ’Ž‡• ‡ƒ…Š ™‹–Š …Žƒ› …‘–‡– δ͵ͲΨǤ
Š‡…‘•‹†‡”‹‰–Š‡‹–‡”•‡…–‹‘•„‡–™‡‡–Š”‡‡‹•‘Ǧ•—”ˆƒ…‡•ˆ‘”†‡•‹–›ǡǦƒ†Ǧ™ƒ˜‡
˜‡Ž‘…‹–‹‡•ǡ ™‡ ‘„–ƒ‹‡† ƒ •‘Ž—–‹‘ ˆ‘” ‘Ž› –Š‡ ’—”‡ •ƒ† •ƒ’Ž‡ǡ ™Š‹…Š …‘•–‹–—–‡• ƒ
…ƒŽ‹„”ƒ–‹‘’‘‹–ǤŠ‹•‹•†—‡–‘–Š‡ƒ‘ƒŽ‘—•„‡Šƒ˜‹‘—”‘ˆ•Š‡ƒ”˜‡Ž‘…‹–‹‡•–Šƒ–‘‡‘ˆ–Š‡
‘†‡Ž•…‘—Ž†•ƒ–‹•ˆƒ…–‘”‹Ž›†‡•…”‹„‡ȋ‹‰—”‡͹ȌǤŠ‡”‡ˆ‘”‡ǡ™‡…‘–‹—‡†—•‹‰‘Ž›Ǧ™ƒ˜‡
˜‡Ž‘…‹–›ƒ††‡•‹–›ǡ ‹‰‘”‹‰ Ǧ™ƒ˜‡˜‡Ž‘…‹–› ‡ƒ•—”‡‡–•Ǥ …‘’ƒ”‹•‘ ‘ˆ–Š‡ ”‡•—Ž–•
…ƒ„‡•‡‡‹‹‰—”‡ͺǡ™Š‡”‡–Š‡•–”—…–—”ƒŽ…Žƒ›‘†‡Ž’”‘†—…‡†•‘Ž—–‹‘•ˆ‘”–Š‡•‡˜‡
•ƒ’Ž‡•ǡ ‰‘‘† ‡•–‹ƒ–‡• ‘ˆ –Š‡ ’‘”‘•‹–› ƒ† Ž‡•• ƒ……—”ƒ–‡ ‡•–‹ƒ–‡• ˆ‘” Ž‹–Š‘Ž‘‰›Ǥ  –Š‡
…‘–”ƒ”›ǡ –Š‡ †‹•’‡”•‡† ‘†‡Ž ˆ‘—† •‘Ž—–‹‘• ˆ‘” ‘Ž› ˆ‘—” •ƒ’Ž‡•Ǣ –Š”‡‡ ƒ……—”ƒ–‡ ‹
’‘”‘•‹–›ƒ†–™‘‹Ž‹–Š‘Ž‘‰›Ǥ
ˆ™‡‹…Ž—†‡ΪȀǦͷ’‡”…‡–—…‡”–ƒ‹–›‹–Š‡Ǧ™ƒ˜‡˜‡Ž‘…‹–›ǡ–Š‡‹˜‡”•‡‘†‡ŽŽ‹‰
’”‘˜‹†‡•‘”‡•‘Ž—–‹‘•ȋ•‡‡‹‰—”‡ͻȌǤ–Š‹•…ƒ•‡–Š‡†‹•’‡”•‡†Ǧ…Žƒ›‘†‡Ž‹’”‘˜‡•‹–•
’‡”ˆ‘”ƒ…‡ ƒ† ’”‘†—…‡• •‘Ž—–‹‘• ˆ‘” ƒŽŽ •‡˜‡ •ƒ’Ž‡• ™‹–Š ˜ƒ”›‹‰ ƒ……—”ƒ…›Ǥ Š‡
•–”—…–—”ƒŽ…Žƒ›‘†‡Ž ƒŽ•‘ ’”‘˜‹†‡•ƒ‹…”‡ƒ•‡† —„‡” ‘ˆ•‘Ž—–‹‘• ƒ† •Š‘™•ƒ ”‘„—•–
•‡– ‘ˆ ’‘”‘•‹–› ƒ† Ž‹–Š‘Ž‘‰› ’”‡†‹…–‹‘•Ǥ “—ƒ–‹–ƒ–‹˜‡ …‘’ƒ”‹•‘ ‘ˆ –Š‡ ‘†‡ŽŽ‹‰ ‹•
Figure 7 Conventional calibration of two shaley-sands
models; structural clay (a) and dispersed clay (b) models.
Both models have some success, but the accuracy of each
is difficult to estimate.
ͳͳͻ
Figure 8 Quantitative calibration of dispersed clay (left) and structural clay (right) models. Vertical axis is
sample number, empty circles are lab measurements and filled circles model predictions. Only 7 samples with
clay content below 0.3 were used. Of the two models, the structural clay model produced more solutions.
Figure 9 Quantitative calibration of the dispersed clay model (left) and structural clay model (right), using 5%
uncertainty in Vp. Vertical axis is sample number, empty circles are lab measurements and filled circles model
predictions. More solutions were found relative to the results (Fig. 8) in which uncertainty was not included.
Figure 10 Quantitative calibration of dispersed clay (grey) and structural clay (black) models, using a 5 % of
uncertainty in Vp. Vertical axis is percentage of predictions matching the data, versus various tolerance ranges
in porosity and lithology predictions (+/−
− 0.01, 0.02, 0.03, 0.04, 0.05) in the horizontal axis.
ͳʹͲ
•Š‘™‹‹‰—”‡ͳͲǡ™‹–Š–Š‡’‡”…‡–ƒ‰‡‘ˆ…‘””‡…–’”‡†‹…–‹‘•ƒŽ‘‰–Š‡˜‡”–‹…ƒŽƒš‹•ǡƒ†
˜ƒ”‹‘—• –‘Ž‡”ƒ…‡ ”ƒ‰‡• „‡–™‡‡ ‘„•‡”˜‡† ƒ† ‘†‡ŽŽ‡† ’‘”‘•‹–‹‡• ƒ† Ž‹–Š‘Ž‘‰‹‡•
ȋΪȀ−ͲǤͲͳǡ ͲǤͲʹǡ ͲǤͲ͵ǡ ͲǤͲͶǡ ͲǤͲͷȌ ƒŽ‘‰ –Š‡ Š‘”‹œ‘–ƒŽ ƒš‹•Ǥ ‹‰—”‡ ͳͲ •Š‘™• –Šƒ– –Š‡ –™‘
‘†‡Ž• ’”‡†‹…– •‹‹Žƒ”Ž› ™‡ŽŽ –Š‡ Ž‹–Š‘Ž‘‰›ǡ ™Š‡”‡ƒ• –Š‡ ’‘”‘•‹–› ‹• ‘”‡ ’”‡…‹•‡Ž›
‡•–‹ƒ–‡†„›–Š‡†‹•’‡”•‡†…Žƒ›‘†‡ŽǤ‘™‡˜‡”ǡ‹‰—”‡•ͺƒ†ͻ•Š‘™–Šƒ––Š‡†‹•’‡”•‡†
…Žƒ›‘†‡Ž‹•‘”‡•‡•‹–‹˜‡–‘–Š‡—…‡”–ƒ‹–›‘ˆ–Š‡Ǧ™ƒ˜‡˜‡Ž‘…‹–›Ǥ
ʹǣ
ǦǦ
–Š‹•…ƒ•‡™‡ƒ••‡••‡†–Š‡…ƒŽ‹„”ƒ–‹‘‘ˆ˜ƒ”‹‘—•‘†‡Ž•–‘ƒŽƒ”‰‡”†ƒ–ƒ•‡–„ƒ•‡†‘
ͺͲ•ƒ†•–‘‡•ƒ’Ž‡•™‹–Š™‹†‡”ƒ‰‡•‘ˆ’‘”‘•‹–›ǡƒ‰‡ƒ†…Žƒ›…‘–‡–ȋƒ‡–ƒŽǤͳͻͺ͸ȌǤ
‡ •–ƒ”–‡† „› ‡š’Ž‘”‹‰ –Š”‡‡ ‘†‡Ž•Ǥ ‡ ‹• ƒ ‰”ƒ—Žƒ” ‘†‡Ž „ƒ•‡† ‘ …‘–ƒ…– –Š‡‘”›
…‘„‹‡†™‹–Š„‘—†•ƒ†–Š‡‘–Š‡”–™‘ƒ”‡‹…Ž—•‹‘‘†‡Ž•Ǥ
Š‡ˆ‹”•–‘†‡Ž‹•”‡ˆ‡””‡†–‘ƒ•–Š‡‘†‹ˆ‹‡†ƒ•Š‹ǦŠ–”‹ƒ—’’‡”„‘—†ȋȌ
ƒ†—•‡•‡”–œǦ‹†Ž‹ȋ‹†Ž‹ͳͻͶͻȌ–Š‡‘”›–‘…‘’—–‡ƒ…Ž‡ƒǡŠ‹‰ŠǦ’‘”‘•‹–›•ƒ†ƒ†
ƒ—’’‡”„‘—†–‘‡•–‹ƒ–‡Ž‘™‡”’‘”‘•‹–‹‡•–‘™ƒ”†•–Š‡‹‡”ƒŽ’‘‹–ǤŠ‹•‘†‡ŽŠƒ•
„‡‡ —•‡† –‘ †‡•…”‹„‡ ƒ ‹š–—”‡ ‘ˆ •‡†‹‡– †‡’‘•‹–‡† ƒ– …”‹–‹…ƒŽ ’‘”‘•‹–› ™‹–Š •‘‡
ƒ††‹–‹‘ƒŽ ‹‡”ƒŽǤ – ‹‹…• –Š‡ •–‡‡’ †‹ƒ‰‡‡–‹… –”‡† ‘ˆ …Ž‡ƒ •ƒ†• ‹ –Š‡ ˜‡Ž‘…‹–›Ǧ
’‘”‘•‹–›•’ƒ…‡ȋ˜•‡–Š‡–ƒŽǤʹͲͲͷȌǤ‘”…Žƒ›Ǧ”‹…Š†ƒ–ƒǡ‹–…‘‡…–•ƒŽ‘™‡”…”‹–‹…ƒŽ’‘”‘•‹–›
‡„‡”™‹–Š•‘ˆ–‡”‡ˆˆ‡…–‹˜‡‹‡”ƒŽ‘†—Ž‹Ǥ ‡—•‡†“—ƒ”–œ‹‡”ƒŽ’”‘’‡”–‹‡•ǡ“α͵͹
ƒǡɊ“ αͶͶ
ƒˆ‘”„—Žƒ†•Š‡ƒ”‘†—Ž‹ǡƒ†…Žƒ›’”‘’‡”–‹‡•…‘’—–‡†ˆ‘”–Š‹•†ƒ–ƒ•‡–
…αʹͷ
ƒƒ†Ɋ… αͻ
ƒȋƒ‡–ƒŽǤͳͻͺ͸ȌǤˆˆ‡…–‹˜‡’”‡••—”‡™ƒ•ͶͲƒǡ‹‡…‘–ƒ…–
’‘‹–• ’‡” ‰”ƒ‹ ‘ ƒ˜‡”ƒ‰‡ ȋ…‘‘”†‹ƒ–‹‘ —„‡”Ȍǡ ƒ† ™‡ ƒ••—‡† …”‹–‹…ƒŽ ’‘”‘•‹–› –‘
†‡…”‡ƒ•‡Ž‹‡ƒ”Ž›„‡–™‡‡ͲǤͶˆ‘”…Ž‡ƒ•ƒ†ƒ†ͲǤʹ™Š‡…Žƒ›…‘–‡–‹•ͳǤ
Š‡ǡ ™‡ ƒ’’Ž‹‡† –Š‡ ‘†‡Ž ‘ˆ — Ƭ Š‹–‡ ȋͳͻͻͷȌ ˆ‘” …Žƒ›Ǧ•ƒ† ‹š–—”‡•ǡ ™Š‹…Š
†‹˜‹†‡• –Š‡ ’‘”‡ •’ƒ…‡ ‹–‘ •ƒ† ”‡Žƒ–‡† ’‘”‡• ȋ•–‹ˆˆȌ ƒ† …Žƒ› ”‡Žƒ–‡† ’‘”‡• ȋ…‘’Ž‹ƒ–Ȍǡ
ƒ••‹‰‹‰ †‹ˆˆ‡”‡– ƒ•’‡…– ”ƒ–‹‘• –‘ –Š‡Ǥ ‘” ‹’Ž‡‡–ƒ–‹‘ ™‡ —•‡† ƒ ‘Ǧ‹–‡”ƒ…–‹‘
ƒ’’”‘š‹ƒ–‹‘ ȋ—†•‘ Ƭ ‘’‘ˆˆ ͳͻͺͻǢ ‘”„› ‡– ƒŽǤ ͳͻͻͶȌ –‘ …‘’—–‡ –Š‡ ‡ˆˆ‡…–‹˜‡
…‘’Ž‹ƒ…‡–‡•‘”ȗˆ”‘–Š‘•‡‘ˆ–Š‡Š‘•–”‘…Ͳƒ†–Š‡’‘”‡•’ƒ…‡ƒ•ǣ
N
(
)
S* = S 0 − vn S 0 C n − I K n , n =1
[ (
(
K n = C0 I + G n Cn − C0
))]
−1
.
ȋͶȌ
ȋͷȌ
‡“—ƒ–‹‘•Ͷƒ†ͷǡȗ‹•–Š‡‡ˆˆ‡…–‹˜‡…‘’Ž‹ƒ…‡–‡•‘”ǢͲ–Š‡…‘’Ž‹ƒ…‡–‡•‘”‘ˆ
–Š‡‹•‘–”‘’‹…Š‘•–”‘…Ǣ˜‹•–Š‡˜‘Ž—‡…‘…‡–”ƒ–‹‘‘ˆ–Š‡–Š’Šƒ•‡Ǣƒ†‹•–Š‡‹†‡–‹–›
ͳʹͳ
–‡•‘”ǤŠ‡ˆƒ…–‘”
‹•ƒˆ‘—”–ŠǦ”ƒ–‡•‘”–Šƒ–†‡’‡†•‘–Š‡•–‹ˆˆ‡••–‡•‘”‘ˆ–Š‡Š‘•–
”‘…ȋͲȌƒ†–Š‡•Šƒ’‡Ȁ‘”‹‡–ƒ–‹‘ ‘ˆ –Š‡ –Š‹…Ž—•‹‘–›’‡–Šƒ–…Šƒ”ƒ…–‡”‹œ‡•–Š‡‡Žƒ•–‹…
‡ˆˆ‡…– ‘ˆ ‹†‹˜‹†—ƒŽ ‹…Ž—•‹‘•Ǥ Š‡ ‡š…‡•• …‘’Ž‹ƒ…‡ †—‡ –‘ –Š‡ ’‘”‡ •’ƒ…‡ ‹…Ž—†‡•
…‘–”‹„—–‹‘• ‘ˆ •ƒ† ”‡Žƒ–‡† ’‘”‡• ȋȽ•–‹ˆˆȌ ƒ† …Žƒ› ”‡Žƒ–‡† ’‘”‡• ȋȽ•‘ˆ–ȌǤ •’‡…– ”ƒ–‹‘• ‘ˆ
Ƚ•–‹ˆˆαͲǤͳˆ‘”•ƒ†ƒ†Ƚ•‘ˆ–αͲǤͲͷˆ‘”…Žƒ›”‡Žƒ–‡†’‘”‡•™‡”‡‹‹–‹ƒŽŽ›ƒ’’Ž‹‡†ǤŠ‡‡ˆˆ‡…–‹˜‡
•–‹ˆˆ‡••–‡•‘”‹•–Š‡‘„–ƒ‹‡†„›‹˜‡”–‹‰–Š‡‡ˆˆ‡…–‹˜‡…‘’Ž‹ƒ…‡–‡•‘”ǤŠ‡‡ˆˆ‡…–‘ˆ
–Š‡ ˆŽ—‹† ‹• …‘’—–‡† —•‹‰ ƒ••ƒǯ• ȋͳͻͷͳȌ ‡“—ƒ–‹‘•Ǥ …”‡ƒ•‹‰ …Žƒ› …‘–‡– ‡ƒ•
‹…”‡ƒ•‹‰—„‡”‘ˆ…‘’Ž‹ƒ–’‘”‡•ƒ†”‡•—Ž–•‹ƒ•‘ˆ–‡‹‰‘ˆ–Š‡‡ˆˆ‡…–‹˜‡’”‘’‡”–‹‡•
‘ˆ–Š‡”‘…Ǥ
Š‡–Š‹”†‘†‡Ž—•‡††‹ˆˆ‡”‡–‹ƒŽ‡ˆˆ‡…–‹˜‡‡†‹—ȋȌ–Š‡‘”›ȋ‡””›ƒͳͻͻʹȌ–‘
‹–”‘†—…‡‡’–›‹•‘Žƒ–‡†’‘”‡•™‹–Šƒ…‘•–ƒ–ƒ•’‡…–”ƒ–‹‘ȋȽαͲǤʹͷȌ‹–‘ƒ‹‡”ƒŽŠ‘•–
‡†‹—ǤŠ‹•”‡“—‹”‡••‘Ž˜‹‰ƒ…‘—’Ž‡†•›•–‡‘ˆ‘”†‹ƒ”›†‹ˆˆ‡”‡–‹ƒŽ‡“—ƒ–‹‘•ǣ
(1 − y ) d
dy
[K ( y )] = (K
*
2
)
− K * P (*2 ) ( y ) , (1 − y ) d [μ * ( y )] = (μ 2 − μ * )Q (*2 ) ( y ) , dy
ȋ͸Ȍ
ȋ͹Ȍ
™Š‡”‡ȗƒ†Ɋȗƒ”‡–Š‡‡ˆˆ‡…–‹˜‡„—Žƒ†•Š‡ƒ”‘†—Ž‹ǡȗȋͲȌαͳƒ†ɊȗȋͲȌαɊͳƒ”‡–Š‡
‡ˆˆ‡…–‹˜‡ ‡Žƒ•–‹… ‘†—Ž‹ ƒ– ‹‹–‹ƒŽ …‘†‹–‹‘• ȋ‹‹–‹ƒŽ Š‘•– ƒ–‡”‹ƒŽȌǡ ʹǡ Ɋʹ ƒ† › †‡‘–‡ –Š‡
‘†—Ž‹ ƒ† …‘…‡–”ƒ–‹‘ ‘ˆ –Š‡ ƒ††‡† ‹…Ž—•‹‘•Ǥ Š‡ –‡”• ȗ ƒ† ȗ ƒ”‡ ‰‡‘‡–”‹…ƒŽ
ˆƒ…–‘”• ƒ••‘…‹ƒ–‡†™‹–Š–Š‡‹…Ž—•‹‘ƒ–‡”‹ƒŽǤŠ‡ˆŽ—‹†‡ˆˆ‡…–™ƒ•ƒ‰ƒ‹‹–”‘†—…‡†—•‹‰
ƒ••ƒǯ•‡“—ƒ–‹‘•ȋ
ƒ••ƒͳͻͷͳȌǤ
ŽŽ–Š”‡‡‘†‡Ž•’”‘˜‹†‡†ƒ•ƒ–‹•ˆƒ…–‘”›…ƒŽ‹„”ƒ–‹‘‹–Š‡˜‡Ž‘…‹–›Ǧ’‘”‘•‹–›•’ƒ…‡ˆ‘”
Ǧ ƒ† Ǧ˜‡Ž‘…‹–‹‡• ȋ‹‰—”‡ ͳͳȌǡ „—– ƒ “—ƒ–‹–ƒ–‹˜‡ ƒƒŽ›•‹• ‹• ”‡“—‹”‡† –‘ ‡˜ƒŽ—ƒ–‡ ƒ†
…‘’ƒ”‡–Š‡‹”•—……‡••‡•ˆ—”–Š‡”Ǥ
Š‡ “—ƒ–‹–ƒ–‹˜‡ ƒƒŽ›•‹• ‹ –Š‡ •’ƒ…‡ ˆ‘” –Š‡ –Š”‡‡ ‘†‡Ž• ‹• •—ƒ”‹œ‡† ‹
‹‰—”‡ͳʹǤŽŽ–Š”‡‡‘†‡Ž••Š‘™•‹‹Žƒ”’‘”‘•‹–›’”‡†‹…–‹‘•ǡ„—–Ž‹–Š‘Ž‘‰›‡•–‹ƒ–‹‘•„›
–Š‡…‘•‹•–‡–Ž›—†‡”Ǧ’‡”ˆ‘”•Ǥ‡…‡ǡ™‡†‹•…ƒ”†‡†–Š‡‘†‡Žƒ†ˆ‘…—•‡†–Š‡
“—ƒ–‹–ƒ–‹˜‡ƒƒŽ›•‹•‘–Š‡‘–Š‡”–™‘‘†‡Ž•ȋƒ†ȌǤ…‘’ƒ”‹•‘„‡–™‡‡–Š‡‹”
”‡•—Ž–•ˆ”‘–Š‡‹–‡”•‡…–‹‘•‘ˆ’ǡ•ƒ††‡•‹–›‹•‘Ǧ•—”ˆƒ…‡•‹••Š‘™‹‹‰—”‡ͳ͵ǤŠ‡
‡’–›…‹”…Ž‡•”‡’”‡•‡–ȋŽƒ„‘”ƒ–‘”›Ȍ‡ƒ•—”‡‡–•ǡƒ†–Š‡ˆ‹ŽŽ‡†…‹”…Ž‡•ƒ”‡‘—”‘†‡ŽŽ‹‰
”‡•—Ž–•ǤŠ‡”‡‹•‘”‡–Šƒ‘‡’”‡†‹…–‹‘ˆ‘”‡ƒ…Š•ƒ’Ž‡ȋ˜‡”–‹…ƒŽƒš‹•ȌǤ—”–Š‡”‘”‡ǡˆ‘”
‡˜‡”› ’‘”‘•‹–› ’”‡†‹…–‹‘ǡ ƒ …‘””‡•’‘†‹‰ Ž‹–Š‘Ž‘‰› ’”‡†‹…–‹‘ ‡š‹•–•ǡ ‹†‹…ƒ–‡† ‹ –Š‡
ˆ‹‰—”‡ „› –Š‡ •‹œ‡ ‘ˆ –Š‡ ˆ‹ŽŽ‡† …‹”…Ž‡•Ǥ Š‡ ”ƒ†‹—• ‘ˆ –Š‡ ˆ‹ŽŽ‡† …‹”…Ž‡• ‹…”‡ƒ•‡• ™‹–Š
ͳʹʹ
†‡…”‡ƒ•‹‰ …Žƒ› …‘–‡–Ǥ  ‹•’‡…–‹‘ ‘ˆ ‹‰—”‡• ͳʹ ƒ† ͳ͵ •Š‘™• –Šƒ– „‘–Š ‘†‡Ž
’”‡†‹…–‹‘•ƒ”‡•‹‹Žƒ”‹—„‡”ƒ†ƒ……—”ƒ…›ǡ™‹–Šƒ•Ž‹‰Š–ƒ†˜ƒ–ƒ‰‡ˆ‘”–Š‡‘†‡ŽǤ
Š‡”‡ˆ‘”‡ǡ™‡’‡”ˆ‘”‡†ƒ•‡•‹–‹˜‹–›ƒƒŽ›•‹•‘‘‡‡›’ƒ”ƒ‡–‡”ˆ‘”‡ƒ…Š‘ˆ–Š‡‘†‡Ž•Ǥ
‡ –‡•–‡† …‘‘”†‹ƒ–‹‘ —„‡”• „‡–™‡‡ ͺ ƒ† ͳͲ ˆ‘” –Š‡ ‘†‡Ž ƒ† ˜ƒ”‹‘—•
…‘„‹ƒ–‹‘• ‘ˆ ƒ•’‡…– ”ƒ–‹‘• ‹ –Š‡ ‘†‡ŽǤ Š‡ ‘†‡Ž •Š‘™• •–ƒ„Ž‡ ”‡•—Ž–• ‹
–‡”•‘ˆ…‘‘”†‹ƒ–‹‘—„‡”ȋȌǡ„—–•Ž‹‰Š–Ž›ˆƒ˜‘—”‹‰αͺ‘˜‡”–Š‡‘–Š‡”ȋ‹‰—”‡ͳͶȌǤ
‘ƒƒŽ›œ‡–Š‡‘†‡Ž™‡—•‡†ˆ‹˜‡†‹ˆˆ‡”‡–‘†‡Ž•ȋͳ–‘ͷȌ™‹–Šƒ•’‡…–”ƒ–‹‘•‘ˆ•ƒ†
ƒ† …Žƒ› ’‘”‡• ȋȽ•ƒ† ǡ Ƚ…Žƒ› Ȍ ƒ• ˆ‘ŽŽ‘™•ǣ ͳ α ȋͲǤͳǡ ͲǤͲ͵ͷȌǢ ʹ α ȋͲǤͳǡ ͲǤͲ͸ȌǢ ͵ α ȋͲǤͳʹǡ
ͲǤͲ͵ͷȌǢͶαȋͲǤͳʹǡͲǤͲͷȌǢͷαȋͲǤͳʹǡͲǤͲ͸Ȍǣ•‡‡‹‰—”‡ͳͷǤ‘”‘•‹–›’”‡†‹…–‹‘•‘ˆ–Š‡
‘†‡Ž™‡”‡Š‹‰ŠŽ›†‡’‡†‡–‘–Š‡ƒ•’‡…–”ƒ–‹‘•‘ˆ•ƒ†ƒ†…Žƒ›’‘”‡•ǡ™Š‡”‡ƒ•Ž‹–Š‘Ž‘‰›
‡•–‹ƒ–‹‘•™‡”‡Ž‡•••‡•‹–‹˜‡ǤŠ‹•ƒƒŽ›•‹•†‡‘•–”ƒ–‡†–Šƒ––Š‡Ž‹–Š‘Ž‘‰›”‡•—Ž–•™‡”‡
‹’”‘˜‡† ™Š‡ —•‹‰ ƒ•’‡…– ”ƒ–‹‘• ‘ˆ Ƚ•ƒ† α ͲǤͳʹ ƒ† Ƚ…Žƒ› α ͲǤͲ͵ͷ ȋ‘†‡Ž ͵ȌǤ ‘™‡˜‡”ǡ
„‡––‡”’‘”‘•‹–›‡•–‹ƒ–‹‘•™‡”‡ƒ…Š‹‡˜‡†™‹–Š•Ž‹‰Š–Ž›•–‹ˆˆ‡”…Žƒ›’‘”‡•ȋ‘†‡Ž•ͶȋȽ…Žƒ›α
ͲǤͲͷȌƒ†ͷȋȽ…Žƒ›αͲǤͲ͸Ȍ‹‹‰—”‡ͳͷȌǤ
Figure 11 Conventional calibration of the modified
HS upper bound (MHS) model (top left); Xu and
White (XW) model (top right) and Differential
effective model (DEM) (bottom right), for P and S
velocities on Han’s dataset. Note that the three
models seem to provide satisfactory calibrations,
particularly for the P-wave data.
ͳʹ͵
Figure 12 Results of the quantitative calibration of the modified Hashin-Shtrikman (MHS), Xu and White (XW) and
differential effective modelling (DEM) models on Han’s data set. Vertical axis is percentage of predictions matching
the data, versus various tolerance ranges in porosity and lithology predictions (+/- 0.01, 0.02, 0.03, 0.04, 0.05) in the
horizontal axis. Note the poor performance of the DEM model in terms of lithology.
Figure 13. Quantitative calibration of the modified HS upper bound (MHS) on the left; Xu and White model (XW)
on the right panel. Vertical axis is sample number, empty circles are lab measurements and filled circles model
predictions. Note that both models provide a large number of accurate predictions.
ͳʹͶ
Figure 14 Improved calibration of the modified Hashin-Shtrikman model (MHS), on Han’s data set for various
coordination numbers (C). Vertical axis is percentage of predictions matching the data, versus various tolerance
ranges in porosity and lithology (+/- 0.01, 0.02, 0.03, 0.04, 0.05) in the horizontal axis. Results are stable, and the
calibration is not significantly dependent on coordination number.
Figure 15 Improved calibration of the Xu and White model (XW), on Han’s data set for various combinations of
aspect ratios. Models 1 to 5 have aspect ratios (sand-pores, clay-pores) as follow: M1 = (0.1, 0.035); M2 = (0.1,
0.06); M3 = (0.12, 0.035); M4 = (0.12, 0.05); M5 = (0.12, 0.06). Vertical axis is percentage of predictions matching
the data, versus various tolerance ranges in porosity and lithology (+/- 0.01, 0.02, 0.03, 0.04, 0.05) in the horizontal
axis. Note that porosity predictions were optimized by using different aspect ratios whereas lithology maintains
relatively stable.
ͳʹͷ
Š‡ …‘’ƒ”‹•‘ „‡–™‡‡ –™‘ ‘†‡Ž• ‹ –Š‡ •’ƒ…‡ ”‡“—‹”‡• ƒ …‘˜‡–‹‘ƒŽ
…ƒŽ‹„”ƒ–‹‘‘ˆ–Š‡‘†‡Ž•‹ƒ…”‘••Ǧ’Ž‘–†‘ƒ‹ǡ•—…Šƒ•˜‡Ž‘…‹–›Ǧ’‘”‘•‹–›•’ƒ…‡ǤŠ‹•‹‹–‹ƒŽ
…ƒŽ‹„”ƒ–‹‘•–‡’ǡŠ‘™‡˜‡”ǡ…ƒ‹ˆŽ—‡…‡–Š‡ˆ‹”•–“—ƒ–‹–ƒ–‹˜‡”‡•—Ž–•‹–Š‡•’ƒ…‡ǤŠ‹•
ƒ„‹‰—‹–› …ƒ „‡ ƒ••‡••‡† „› ’‡”ˆ‘”‹‰ ƒ ȋ“—ƒ–‹–ƒ–‹˜‡Ȍ •‡•‹–‹˜‹–› ƒƒŽ›•‹• ȋ‹ –Š‡ •’ƒ…‡Ȍˆ‘”‡›’ƒ”ƒ‡–‡”•‘ˆ‡ƒ…Š‘†‡Žȋ‡Ǥ‰Ǥǡƒ•’‡…–”ƒ–‹‘•ǡ’”‡••—”‡ǡƒ†‡ˆˆ‡…–‹˜‡‹‡”ƒŽ
’”‘’‡”–‹‡•Ȍǡƒ†•‡Ž‡…–‹‰–Š‡…‘„‹ƒ–‹‘‘ˆ’ƒ”ƒ‡–‡”•–Šƒ–’”‘˜‹†‡•–Š‡Š‹‰Š‡”—„‡”
‘ˆ •‘Ž—–‹‘• ˆ‘” –Š‡ †ƒ–ƒ•‡– —†‡” ‡šƒ‹ƒ–‹‘Ǥ ˆ–‡” –Š‡ ‘’–‹ƒŽ ’ƒ”ƒ‡–‡”• Šƒ˜‡ „‡‡
ˆ‘—†ǡˆ—”–Š‡”…‘’ƒ”‹•‘™‹–Š‘–Š‡”‘†‡Ž•…ƒ„‡ƒ†‡Ǥ
Š‡†ƒ–ƒ•‡–—•‡†‹–Š‡ˆ‹”•–…ƒ•‡Šƒ•„‡‡”‡ˆ‡”‡…‡†‹–Š‡Ž‹–‡”ƒ–—”‡–‘‹ŽŽ—•–”ƒ–‡–Š‡
‡ˆˆ‡…–‘ˆ’‘”‡Ǧˆ‹ŽŽ‹‰…Žƒ›‘’‘”‘•‹–›ƒ†˜‡Ž‘…‹–‹‡•‘ˆ…Žƒ›Ǧ•ƒ†‹š–—”‡•Ǥ–•„‹‘†ƒŽ‰”ƒ‹Ǧ
•‹œ‡†‹•–”‹„—–‹‘ƒ†‰”ƒ‹•‹œ‡”ƒ–‹‘ȋͳȀʹͲȌ•—‰‰‡•–ƒ‹†‡ƒŽ…‘†‹–‹‘ˆ‘”ƒ†‹•’‡”•‡†Ǧ…Žƒ›
‹…”‘•–”—…–—”‡Ǥ‘™‡˜‡”ǡ–Š‡’”‡†‹…–‹‘•ˆ‘”–Š‡†‹•’‡”•‡†…Žƒ›‘†‡Ž™‡”‡˜‡”›•‡•‹–‹˜‡
–‘–Š‡—…‡”–ƒ‹–›‘ˆ–Š‡†ƒ–ƒǤ˜‡”ƒŽŽǡ–Š‡•–”—…–—”ƒŽǦ…Žƒ›‘†‡Ž’”‘†—…‡†ƒ‘”‡”‘„—•–•‡–
‘ˆ’”‡†‹…–‹‘•ˆ‘”„‘–ŠŽ‹–Š‘Ž‘‰›ƒ†’‘”‘•‹–›ǤŠ‹•…ƒ„‡‡š’Žƒ‹‡†ˆ”‘‹‰—”‡͸ǤŠ‡”‡
…Žƒ› ‡š…‡‡†• ͳͲ Ψ „› ˜‘Ž—‡ǡ –Š‡ †‹•’‡”•‡† ‘†‡Ž ‘˜‡”Ǧ’”‡†‹…–• Ǧ˜‡Ž‘…‹–› „‡…ƒ—•‡
•–”—…–—”ƒŽ …Žƒ› „‡…‘‡• ‹’‘”–ƒ– ‹ ”‡†—…‹‰ –Š‡ •–‹ˆˆ‡•• ‘ˆ –Š‡ •ƒ’Ž‡•Ǥ Š‹• •—‰‰‡•–•
–Šƒ––Š‡‡ˆˆ‡…–‘ˆ…Žƒ›‘–Š‡‡Žƒ•–‹…‹–›‹•’”‡†‘‹ƒ–Ž›‹–‡”Ǧ‰”ƒ—Žƒ”‘”•–”—…–—”ƒŽǡ‡š…‡’–
ˆ‘”–Š‘•‡™‹–Š…Žƒ›˜‘Ž—‡•„‡Ž‘™ͳͲΨƒ–™Š‹…Š„‘–Š†‹•’‡”•‡†ƒ†•–”—…–—”ƒŽ…Žƒ›Šƒ˜‡
•‹‹Žƒ”‹’ƒ…–•ǤŠ‹•‹•Ž‹‡Ž›”‡Žƒ–‡†–‘–Š‡•ƒ’Ž‡’”‡’ƒ”ƒ–‹‘’”‘…‡†—”‡•ǡƒ†‹–‹•‘–ƒ
‰‡‡”ƒŽ…‘†‹–‹‘‘ˆ…Žƒ›Ǧ”‹…Š•ƒ†•–‘‡•ǤŠ‡“—ƒ–‹–ƒ–‹˜‡ƒƒŽ›•‹•”‡˜‡ƒŽ‡†–Š‹•…‘†‹–‹‘
‡˜‡–Š‘—‰Š‹–™ƒ•‘–‡˜‹†‡–ˆ”‘–Š‡…‘˜‡–‹‘ƒŽ…ƒŽ‹„”ƒ–‹‘’”‘…‡••Ǥ
–Š‡•‡…‘†…ƒ•‡™‡—•‡†–Š‡“—ƒ–‹–ƒ–‹˜‡…ƒŽ‹„”ƒ–‹‘ƒ’’”‘ƒ…Š–‘•‡Ž‡…–‘”†‹•…ƒ”†
–Š‡ ‘•– •—‹–ƒ„Ž‡ ”‘…Ǧ’Š›•‹…• ‘†‡Ž• –‘ ”‡’”‘†—…‡ ƒ †ƒ–ƒ•‡–Ǥ ‡ …‘’ƒ”‡† –Š‡ ‘˜‡”ƒŽŽ
”‡•—Ž–• ‘ˆ –Š”‡‡ ‘†‡Ž• ȋǡ ƒ† Ȍ ƒ† ™‡”‡ “—‹…Ž› ƒ„Ž‡ –‘ †‹•…ƒ”† –Š‡ Ž‡ƒ•–
ƒ……—”ƒ–‡‘†‡ŽȋȌǤŠ”‘—‰Šƒ•‡•‹–‹˜‹–›ƒƒŽ›•‹•‘ˆ–Š‡”‡ƒ‹‹‰‘†‡Ž•ǡ™‡‡š’Ž‘”‡†
–Š‡’‘–‡–‹ƒŽˆ‘”‘’–‹‹œ‹‰–Š‡…ƒŽ‹„”ƒ–‹‘‹‘”†‡”–‘‹†‡–‹ˆ›–Š‡‘†‡Ž–Šƒ–’”‘˜‹†‡•–Š‡
‘•– •–ƒ„Ž‡ ƒ† ”‘„—•– ’”‡†‹…–‹‘•Ǥ ‘™‡˜‡”ǡ ‹ …ƒ•‡• ™‹–Š Š‹‰Š —…‡”–ƒ‹–›ǡ ™Š‡”‡ ™‹†‡
”ƒ‰‡• ‘ˆ ’‘”‘•‹–‹‡• ƒ† Ž‹–Š‘Ž‘‰‹‡• ƒ”‡ ‡š’‡…–‡†ǡ –Š‡ ‘†‡Ž ’”‘†—…‹‰ ƒ ™‹†‡” ”ƒ‰‡ ‘ˆ
”‡•—Ž–•™‘—Ž†„‡’”‡ˆ‡””‡†ǤŠ‡†ƒ–ƒ•‡–—•‡†‹…ƒ•‡ʹȋƒǯ•†ƒ–ƒȌ…‘–ƒ‹••ƒ’Ž‡•ˆ”‘
˜ƒ”‹‘—• ‘”‹‰‹• ȋ“—ƒ””‹‡•ǡ ™‡ŽŽ …‘”‡•Ȍ ™‹–Š ƒ ™‹†‡ ”ƒ‰‡ ‘ˆ ’‘”‘•‹–‹‡• ƒ† …Žƒ› …‘–‡–•ǡ
ˆ”‘…Ž‡ƒ–‹‰Š–•ƒ†•–‘Š‹‰Š’‘”‘•‹–›…Žƒ›Ǧ”‹…Š•ƒ†•–‘‡•ǤŠ‡”‡ˆ‘”‡ǡ†‹˜‹†‹‰–Š‡†ƒ–ƒ•‡–
‹–‘ ‘”‡ Š‘‘‰‡‡‘—• •—„•‡–•ǡ ˆ‘” ‡šƒ’Ž‡ ‹ –‡”• ‘ˆ ‘”‹‰‹ǡ †‡‰”‡‡ ‘ˆ …‘•‘Ž‹†ƒ–‹‘ǡ
’‘”‘•‹–› ‘” …Žƒ› …‘–‡–ǡ …ƒ ‹’”‘˜‡ –Š‡ …ƒŽ‹„”ƒ–‹‘ ƒ† ™‘—Ž† ƒŽŽ‘™ ‹ˆ‡”‡…‡ ‘ˆ ”‘…
‹…”‘•–”—…–—”‡†‡–ƒ‹Ž•ˆ”‘–Š‡‘†‡Žǯ••—……‡••Ǥ
„‘–Š‡šƒ’Ž‡•’‘”‘•‹–›’”‡†‹…–‹‘•™‡”‡‘”‡ƒ……—”ƒ–‡–ŠƒŽ‹–Š‘Ž‘‰›’”‡†‹…–‹‘•Ǥ
‘•– ‘„•‡”˜ƒ–‹‘• ‘ˆ ƒ–—”ƒŽ ”‘…• ‹†‹…ƒ–‡ –Šƒ– ‡Žƒ•–‹… ’”‘’‡”–‹‡• ƒ”‡ ‘”‡ •‡•‹–‹˜‡ –‘
ͳʹ͸
’‘”‘•‹–›–Šƒ–‘Ž‹–Š‘Ž‘‰›˜ƒ”‹ƒ–‹‘•Ǥ‡…‡ǡŠ‹‰Š‡”…‘””‡Žƒ–‹‘•‡š‹•–„‡–™‡‡˜‡Ž‘…‹–›ƒ†
’‘”‘•‹–› –Šƒ „‡–™‡‡ ˜‡Ž‘…‹–› ƒ† …Žƒ› …‘–‡–Ǥ ƒ”‹ƒ–‹‘• ‘ˆ ‡Žƒ•–‹… ‘†—Ž‹ ƒ”‡ ‘”‡
’”‘‘—…‡† ƒŽ‘‰ ’‘”‘•‹–› –Šƒ Ž‹–Š‘Ž‘‰› ƒš‡•ǡ ™Š‹…Š ‹ –—” ’”‘†—…‡ Ž‡•• ƒ……—”ƒ–‡
’”‡†‹…–‹‘•‘ˆŽ‹–Š‘Ž‘‰›–Šƒ’‘”‘•‹–›Ǥ
—” ‹˜‡•–‹‰ƒ–‹‘ ‹ –Š‡ •’ƒ…‡ ‹…Ž—†‡† •‘Ž—–‹‘• ™‹–Š Š‹‰Š ™ƒ–‡” •ƒ–—”ƒ–‹‘
ȋεͻͲΨȌ–‘•‹’Ž‹ˆ›–Š‡ƒƒŽ›•‹•Ǥ”‡ƒŽ…ƒ•‡•ǡŠ‘™‡˜‡”ǡ—…‡”–ƒ‹–›‹ˆŽ—‹†•ƒ–—”ƒ–‹‘…‘—Ž†
Ž‡ƒ†–‘Ž‡••ƒ……—”ƒ–‡’‘”‘•‹–›ƒ†Ž‹–Š‘Ž‘‰›’”‡†‹…–‹‘•Ǥ
 ‘”†‡” –‘ …‘’ƒ”‡ –Š‡ ’”‡†‹…–‹‘• ‘ˆ –Š‡ †‹ˆˆ‡”‡– ”‘…Ǧ’Š›•‹…• ‘†‡Ž•ǡ ‹ ‘—”
‡šƒ’Ž‡•™‡—•‡† ‘Ž›—Ž–”ƒ•‘‹…Žƒ„‘”ƒ–‘”› †ƒ–ƒǡƒ ’”‘…‡†—”‡ ™Š‹…Š’”‘˜‹†‡•ƒš‹—
…‘–”‘Ž‘ˆ–Š‡Ž‹–Š‘Ž‘‰›ǡ’‘”‘•‹–›ƒ†•ƒ–—”ƒ–‹‘Ǥ—–‹ƒ”‡•‡”˜‘‹”…Šƒ”ƒ…–‡”‹œƒ–‹‘…‘–‡š–
™Š‡”‡ ’”‡†‹…–‹‘• ƒ”‡ ‡˜ƒŽ—ƒ–‡† ‹ –Š‡ •…ƒŽ‡ ‘ˆ –Š‡ ˆ‹‡Ž†ǡ ƒ •‹‹Žƒ” ‡–Š‘†‘Ž‘‰› …‘—Ž† „‡
—•‡†ǡ…ƒŽ‹„”ƒ–‹‰–Š‡”‘…Ǧ’Š›•‹…•‘†‡Ž•–‘Ž‘‰†ƒ–ƒ—’Ǧ•…ƒŽ‡†–‘•‡‹•‹…ˆ”‡“—‡…‹‡•Ǥ
‡ ƒ’’Ž‹‡† ƒ ‹˜‡”•‡ ‘†‡ŽŽ‹‰ •–”ƒ–‡‰› –Šƒ– ƒ••‡••‡• –Š‡ ƒ„‹Ž‹–› ‘ˆ ƒ ”‘…Ǧ’Š›•‹…•
‘†‡Ž –‘ ’”‡†‹…– ’‘”‘•‹–›ǡ Ž‹–Š‘Ž‘‰› ƒ† •ƒ–—”ƒ–‹‘ ȋ ’ƒ”ƒ‡–‡”•Ȍ ˆ”‘ •‡‹•‹…
’ƒ”ƒ‡–‡”•Ǥ›ƒƒŽ›œ‹‰–Š‡’‡”ˆ‘”ƒ…‡‘ˆ–Š‡‘†‡Ž•‹–Š‡†‘ƒ‹ǡ™‡™‡”‡ƒ„Ž‡
–‘ •‡Ž‡…– –Š‡ ‘†‡Ž –Šƒ– ’”‘˜‹†‡† –Š‡ ‘•– ”‘„—•– ‡•–‹ƒ–‹‘• ‘ˆ ”‡•‡”˜‘‹” ’”‘’‡”–‹‡•Ǥ
††‹–‹‘ƒŽŽ›ǡ‹–Š‡ˆ‹”•–…ƒ•‡™‡ƒŽ•‘†‹ƒ‰‘•‡†–Š‡†‘‹ƒ–ˆƒ…–‘”–Šƒ–ƒˆˆ‡…–‡†‡Žƒ•–‹…‹–›
‘ˆ–Š‡•ƒ’Ž‡•Ǥ
‡ƒŽ•‘‹ŽŽ—•–”ƒ–‡†Š‘™–Š‹•“—ƒ–‹–ƒ–‹˜‡ƒ’’”‘ƒ…Š…ƒ„‡—•‡†‹ƒ™‘”ˆŽ‘™–‘ˆ‹†ƒ
‘†‡Žˆ‘”ƒŽƒ”‰‡ƒ†Š‡–‡”‘‰‡‡‘—•†ƒ–ƒ•‡–ǡ…‘•‹†‡”‹‰ƒ™‹†‡”ƒ‰‡‘ˆ‘’–‹‘•ǡ“—‹…Ž›
†‹•…ƒ”†‹‰ –Š‡ Ž‡•• ‡ˆˆ‡…–‹˜‡ ‘†‡Ž• ƒ† ˆ‘…—•‹‰ ‘ –Š‡ ‘•– ’”‘‹•‹‰ ‘‡•Ǥ Š‡ǡ „›
–‡•–‹‰ •‡˜‡”ƒŽ ‘†‡Ž ’ƒ”ƒ‡–‡”•ǡ ™‡ ƒ••‡••‡† –Š‡ •‡•‹–‹˜‹–› ‘ˆ –Š‡ •‡Ž‡…–‡† ‘†‡Ž• ‹
–‡”• ‘ˆ ’”‡†‹…–‹‘• ‘ˆ ”‡•‡”˜‘‹” ’”‘’‡”–‹‡•Ǥ Š‹• •—‰‰‡•–• –Šƒ– …ƒŽ‹„”ƒ–‹‰ ƒ ”‘…Ǧ’Š›•‹…•
‘†‡Ž ‘Ž› „› „‡•– ˆ‹––‹‰ ‹ ƒ …”‘•• ’Ž‘– †‘ƒ‹ǡ –‘ ”‡Žƒ–‡ ‹˜‡”–‡† •‡‹•‹… †ƒ–ƒ ƒ†
”‡•‡”˜‘‹” ’ƒ”ƒ‡–‡”•ǡ …ƒ Ž‡ƒ† –‘ ‹ƒ……—”ƒ–‡ ’”‡†‹…–‹‘• ‘ˆ ’‘”‘•‹–› ƒ† Ž‹–Š‘Ž‘‰›Ǥ
ƒŽ›œ‹‰–Š‡‘†‡Ž•‹–Š‡†‘ƒ‹Šƒ•–Š‡ƒ†˜ƒ–ƒ‰‡‘ˆ‡˜ƒŽ—ƒ–‹‰—’–‘–Š”‡‡•‡‹•‹…
‘„•‡”˜ƒ„Ž‡• •‹—Ž–ƒ‡‘—•Ž› ƒ† …ƒ ’‘‹– –‘ ‹…‘•‹•–‡…‹‡• ‹ –Š‡ ‘†‡Ž ’”‡†‹…–‹‘•
„‡–™‡‡„—Žƒ†•Š‡ƒ”‘†—Ž‹Ǥ…‘…Ž—•‹‘ǡ–Š‹•‹•ƒ‹–‡‰”ƒ–‡†ƒ†”‘„—•–ƒ’’”‘ƒ…Š–‘
–Š‡ ‹˜‡”•‹‘ ’”‘„Ž‡ ‘ˆ ˆ‹†‹‰ –Š‡ ‘•– ƒ’’”‘’”‹ƒ–‡ ”‘… ’Š›•‹…• ‘†‡Ž –‘ ‡š’Žƒ‹
‡ƒ•—”‡††ƒ–ƒǤ
ͳʹ͹
Š‡ ƒ—–Š‘”• ƒ…‘™Ž‡†‰‡ –Š‡ ‘”™‡‰‹ƒ ”‡•‡ƒ”…Š …‘—…‹Ž ȋȌ ˆ‘” ˆ‹ƒ…‹ƒŽ
•—’’‘”––Š”‘—‰Š–Š‡‡–”‘ƒ•’”‘‰”ƒƒ†‡š–‡”ƒŽ•’‘•‘”•ȋ–ƒ–‘‹Žǡ‘–ƒŽǡ‘…•‘—”…‡ȌǤ
‘›ƒ‘ƒŽ•‘™‘—Ž†Ž‹‡–‘–Šƒ–ƒ–‘‹Žˆ‘”‰”ƒ–‹‰ƒŽ‡ƒ˜‡–‘’—”•—‡†‘…–‘”ƒŽ•–—†‹‡•Ǥ
˜•‡–ŠǡǤǡ—‡”Œ‹ǡǤǡƒ˜‘ǡ
ǤƬ˜‘”‹ǡǤʹͲͳͲǤ‘…Ǧ’Š›•‹…•†‹ƒ‰‘•–‹…•‘ˆ†‡’‘•‹–‹‘ƒŽ
–‡š–—”‡ǡ†‹ƒ‰‡‡–‹…ƒŽ–‡”ƒ–‹‘•ǡƒ†”‡•‡”˜‘‹”Š‡–‡”‘‰‡‡‹–›‹Š‹‰ŠǦ’‘”‘•‹–›•‹Ž‹…‹…Žƒ•–‹…
•‡†‹‡–•ƒ†”‘…•Ǧ”‡˜‹‡™‘ˆ•‡Ž‡…–‡†‘†‡Ž•ƒ†•—‰‰‡•–‡†™‘”ˆŽ‘™•Ǥ
‡‘’Š›•‹…•͹ͷǡ
͵ͳǦͶ͹Ǥ
˜•‡–ŠǡǤǡ—‡”Œ‹ǡǤƬƒ˜‘ǡ
ǤʹͲͲͷǤ—ƒ–‹–ƒ–‹˜‡•‡‹•‹…‹–‡”’”‡–ƒ–‹‘ǣ’’Ž›‹‰”‘…’Š›•‹…•
–‘‘Ž•–‘”‡†—…‡‹–‡”’”‡–ƒ–‹‘”‹•Ǥƒ„”‹†‰‡‹˜‡”•‹–›”‡••Ǥ
‡”‰‡ǡǤǤǡ‡””›ƒǡǤ
ǤǡƬ‘‡”ǡǤǤͳͻͻ͵ǤˆŽ—‡…‡‘ˆ‹…”‘•–”—…–—”‡‘”‘…‡Žƒ•–‹…
’”‘’‡”–‹‡•Ǥ
‡‘’Š›•‹…ƒŽ‡•‡ƒ”…Š‡––‡”•ʹͲǡʹ͸ͳͻǦʹ͸ʹʹǤ
‡””›ƒǡǤ
ǤͳͻͺͲǤ‘‰Ǧ™ƒ˜‡Ž‡‰–Š’”‘’ƒ‰ƒ–‹‘‹…‘’‘•‹–‡‡Žƒ•–‹…‡†‹ƒǤ’Š‡”‹…ƒŽ
‹…Ž—•‹‘•Ǥ‘—”ƒŽ‘ˆ–Š‡…‘—•–‹…ƒŽ‘…‹‡–›‘ˆ‡”‹…ƒ͸ͺǡͳͺͲͻǦͳͺͳͻǤ
‡””›ƒǡǤ
ǤͳͻͻʹǤ‹‰Ž‡Ǧ•…ƒ––‡”‹‰ƒ’’”‘š‹ƒ–‹‘•ˆ‘”…‘‡ˆˆ‹…‹‡–•‹‹‘–‡“—ƒ–‹‘•‘ˆ
’‘”‘‡Žƒ•–‹…‹–›Ǥ‘—”ƒŽ‘ˆ–Š‡…‘—•–‹…ƒŽ‘…‹‡–›‘ˆ‡”‹…ƒͻͳǡͷͷͳǦͷ͹ͳǤ
‡””›ƒǡǤ
ǤͳͻͻͷǤ‹š–—”‡–Š‡‘”‹‡•ˆ‘””‘…’”‘’‡”–‹‡•Ǥǣ‘…Š›•‹…•ƒ†Šƒ•‡‡Žƒ–‹‘•ǡ
‡ˆ‡”‡…‡Š‡Žˆ͹ǡ
ǡƒ•Š‹‰–‘ǡǡ͸ͶͻǦ͸͸;ȋ‡†Ǥ†ǤǤǤŠ”‡•Ȍǡ‡”‹…ƒ
‡‘’Š›•‹…ƒŽ
‹‘Ǥ
‹‰„›ǡǤǤͳͻͺͳǤŠ‡‡ˆˆ‡…–‹˜‡‡Žƒ•–‹…Ǧ‘†—Ž‹‘ˆ’‘”‘—•‰”ƒ—Žƒ””‘…•Ǥ‘—”ƒŽ‘ˆ’’Ž‹‡†‡…Šƒ‹…•Ǧ
”ƒ•ƒ…–‹‘•‘ˆ–Š‡•‡ͶͺǡͺͲ͵ǦͺͲͺǤ
”ƒ‡‰‡ǡǤǡƒ‘„•‡ǡǤƬ‘Šƒ•‡ǡǤǤʹͲͲ͸Ǥ‘…’Š›•‹…•‘†‡ŽŽ‹‰‘ˆ•ŠƒŽ‡†‹ƒ‰‡‡•‹•Ǥ
‡–”‘Ž‡—
‡‘•…‹‡…‡ͳʹǡͶͻǦͷ͹Ǥ
˜‘”‹ǡǤƬ—”ǡǤͳͻͻ͸ǤŽƒ•–‹…‹–›‘ˆŠ‹‰ŠǦ’‘”‘•‹–›•ƒ†•–‘‡•ǣŠ‡‘”›ˆ‘”–™‘‘”–Š‡ƒ†ƒ–ƒ
•‡–•Ǥ
‡‘’Š›•‹…•͸ͳǡͳ͵͸͵Ǧͳ͵͹ͲǤ
˜‘”‹ǡǤƬ
—–‹‡””‡œǡǤǤʹͲͲͳǤ‡š–—”ƒŽ•‘”–‹‰‡ˆˆ‡…–‘‡Žƒ•–‹…˜‡Ž‘…‹–‹‡•ǡ’ƒ”–ǣŽƒ•–‹…‹–›‘ˆƒ
„‹‘†ƒŽ‰”ƒ‹‹š–—”‡Ǥ
‡…Š‹…ƒŽ”‘‰”ƒš’ƒ†‡†„•–”ƒ…–•ʹͲǡͳ͹͸ͶǦͳ͹͸͹Ǥ
ƒ••ƒǡǤͳͻͷͳǤŽƒ•–‹…™ƒ˜‡•–Š”‘—‰Šƒ’ƒ…‹‰‘ˆ•’Š‡”‡•Ǥ
‡‘’Š›•‹…•ͳ͸ǡ͸͹͵Ǧ͸ͺͷǤ
ƒǡǤǡ—”ǡǤƬ‘”‰ƒǡǤͳͻͺ͸Ǥˆˆ‡…–•‘ˆ’‘”‘•‹–›ƒ†…Žƒ›…‘–‡–‘™ƒ˜‡˜‡Ž‘…‹–‹‡•‹
•ƒ†•–‘‡•Ǥ
‡‘’Š›•‹…•ͷͳǡʹͲͻ͵ǦʹͳͲ͹Ǥ
ƒ•Š‹ǡǤƬŠ–”‹ƒǡǤͳͻ͸͵Ǥ˜ƒ”‹ƒ–‹‘ƒŽƒ’’”‘ƒ…Š–‘–Š‡–Š‡‘”›‘ˆ–Š‡‡Žƒ•–‹…„‡Šƒ˜‹‘—”‘ˆ
—Ž–‹’Šƒ•‡ƒ–‡”‹ƒŽ•Ǥ‘—”ƒŽ‘ˆ–Š‡‡…Šƒ‹…•ƒ†Š›•‹…•‘ˆ‘Ž‹†•ͳͳǡͳʹ͹ǦͳͶͲǤ
‹ŽŽǡǤͳͻͷʹǤŠ‡‡Žƒ•–‹…„‡Šƒ˜‹‘—”‘ˆƒ…”›•–ƒŽŽ‹‡ƒ‰‰”‡‰ƒ–‡Ǥ”‘…‡‡†‹‰•‘ˆ–Š‡Š›•‹…ƒŽ‘…‹‡–›‘ˆ
‘†‘‡…–‹‘͸ͷǡ͵ͶͻǦ͵ͷͷǤ
ͳʹͺ
‘”„›ǡǤǤǡ…Š™ƒ”–œǡǤǤƬ—†•‘ǡǤǤͳͻͻͶǤ‹•‘–”‘’‹…‡ˆˆ‡…–‹˜‡Ǧ‡†‹—‘†‡Ž‹‰‘ˆ–Š‡
‡Žƒ•–‹…’”‘’‡”–‹‡•‘ˆ•ŠƒŽ‡•Ǥ
‡‘’Š›•‹…•ͷͻǡͳͷ͹ͲǦͳͷͺ͵Ǥ
—†•‘ǡǤǤƬ‘’‘ˆˆǡǤͳͻͺͻǤ”‡†‹…–‹‰–Š‡‘˜‡”ƒŽŽ’”‘’‡”–‹‡•‘ˆ…‘’‘•‹–‡Ǧƒ–‡”‹ƒŽ•™‹–Š•ƒŽŽǦ
•…ƒŽ‡‹…Ž—•‹‘•‘”…”ƒ…•Ǥ—”‡ƒ†’’Ž‹‡†
‡‘’Š›•‹…•ͳ͵ͳǡͷͷͳǦͷ͹͸Ǥ
ƒ‘„•‡ǡǤǡ—†•‘ǡǤǤƬ‘Šƒ•‡ǡǤǤʹͲͲ͵ǤǦƒ–”‹šƒ’’”‘ƒ…Š–‘•ŠƒŽ‡ƒ…‘—•–‹…•Ǥ
‡‘’Š›•‹…ƒŽ
‘—”ƒŽ–‡”ƒ–‹‘ƒŽͳͷͶǡͷ͵͵ǦͷͷͺǤ
‘Šƒ•‡ǡǤǤǡ——†ǡǤǤƬƒ‘„•‡ǡǤʹͲͲͶƒǤˆˆ‡…–‘ˆ‰”ƒ‹•…ƒŽ‡ƒŽ‹‰‡–‘•‡‹•‹…
ƒ‹•‘–”‘’›ƒ†”‡ˆŽ‡…–‹˜‹–›‘ˆ•ŠƒŽ‡•Ǥ
‡‘’Š›•‹…ƒŽ”‘•’‡…–‹‰ͷʹǡͳ͵͵ǦͳͶͻǤ
‘Šƒ•‡ǡǤǤǡ’‹‡•ǡǤƬ˜‘”‹ǡǤʹͲͲͶ„Ǥ–”ƒ–‡‰›ˆ‘”‡•–‹ƒ–‹‘‘ˆŽ‹–Š‘Ž‘‰›ƒ†”‡•‡”˜‘‹”
’”‘’‡”–‹‡•ˆ”‘•‡‹•‹…˜‡Ž‘…‹–‹‡•ƒ††‡•‹–›Ǥ
‡…Š‹…ƒŽ”‘‰”ƒš’ƒ†‡†„•–”ƒ…–•ʹ͵ǡ
ͳ͹ʹ͸Ǧͳ͹ʹͻǤ
—•–‡”ǡ
ǤǤƬ‘•‘œǡǤǤͳͻ͹ͶǤ‡Ž‘…‹–›ƒ†ƒ––‡—ƒ–‹‘‘ˆ•‡‹•‹…Ǧ™ƒ˜‡•‹ʹǦ’Šƒ•‡‡†‹ƒǤ
Š‡‘”‡–‹…ƒŽ‘”—Žƒ–‹‘•Ǥ
‡‘’Š›•‹…•͵ͻǡͷͺ͹Ǧ͸Ͳ͸Ǥ
ƒ”‹‘ǡǤǡ—”ǡǤǡ‹ǡǤƬƒǡǤͳͻͻʹǤ‘’”‡••‹‘ƒŽ˜‡Ž‘…‹–›ƒ†’‘”‘•‹–›‹•ƒ†Ǧ…Žƒ›
‹š–—”‡•Ǥ
‡‘’Š›•‹…•ͷ͹ǡͷͷͶǦͷ͸͵Ǥ
‹†Ž‹ǡǤǤͳͻͶͻǤ‘’Ž‹ƒ…‡‘ˆ‡Žƒ•–‹…„‘†‹‡•‹…‘–ƒ…–Ǥ‘—”ƒŽ‘ˆ’’Ž‹‡†‡…Šƒ‹…•Ǧ
”ƒ•ƒ…–‹‘•‘ˆ–Š‡•‡ͳ͸ǡʹͷͻǦʹ͸ͺǤ
ǯ‘‡ŽŽǡǤǤƬ—†‹ƒ•›ǡǤͳͻ͹ͶǤ‡‹•‹…˜‡Ž‘…‹–‹‡•‹†”›ƒ†•ƒ–—”ƒ–‡†…”ƒ…‡†•‘Ž‹†•Ǥ‘—”ƒŽ
‘ˆ
‡‘’Š›•‹…ƒŽ‡•‡ƒ”…Š͹ͻǡͷͶͳʹǦͷͶʹ͸Ǥ
Š‡‰ǡǤͳͻͻͲǤˆˆ‡…–‹˜‡Ǧ‡†‹—–Š‡‘”›‘ˆ•‡†‹‡–ƒ”›Ǧ”‘…•ǤŠ›•‹…ƒŽ‡˜‹‡™ͶͳǡͶͷͲ͹ǦͶͷͳʹǤ
ƒŽ–‘ǡǤͳͻͺ͹ǤŠ‡‡ˆˆ‡…–‹˜‡‡Žƒ•–‹…Ǧ‘†—Ž‹‘ˆƒ”ƒ†‘’ƒ…‹‰‘ˆ•’Š‡”‡•Ǥ‘—”ƒŽ‘ˆ–Š‡
‡…Šƒ‹…•ƒ†Š›•‹…•‘ˆ‘Ž‹†•͵ͷǡʹͳ͵Ǧʹʹ͸Ǥ
—ǡǤǤƬŠ‹–‡ǡǤǤͳͻͻͷǤ‡™˜‡Ž‘…‹–›‘†‡Žˆ‘”…Žƒ›Ǧ•ƒ†‹š–—”‡•Ǥ
‡‘’Š›•‹…ƒŽ”‘•’‡…–‹‰Ͷ͵ǡ
ͻͳǦͳͳͺǤ
‹ǡǤͳͻͻʹǤ…‘—•–‹…˜‡Ž‘…‹–‹›ƒ†ƒ––‡—ƒ–‹‘‘ˆ”‘…•ǡ‹•‘–”‘’›ǡ‹–”‹•‹…ƒ‹•‘–”‘’›ǡƒ†•–”‡••
‹†—…‡†ƒ‹•‘–”‘’›ǤŠǤǤ†‹••‡”–ƒ–‹‘ǡ–ƒˆ‘”†‹˜‡”•‹–›Ǥ