^/^D/D/ZKKE/E'&KZ>/DWZh'ŽŶǌĄůĞƐdƌƵũŝůůŽ͕ĂƌůŽƐhƌŝĂƌƚĞĞƌƌşŽƐ͕ZŽĐşŽ

DW^WZWZdDdZKWK>/dE>/D^K/>DW'K>K'/>DW

^K/>W/dE^WdDW^K/>W/dE^WdDW/ŶĐůƵĚŝŶŐ^ŽŝůůĂƐƐŝĨŝĐĂƚŝŽŶ

^K/>W/dE^WdŚŽƌƌŝůůŽƐ͗ϭϬϭĞƉƚŚ͗Ϯ͘ϱϬtĂƚĞƌdĂďůĞ͗ϭ͘ϯϬŵ>ŝŵĂĞŶƚĞƌ

>ĂDŽůŝŶĂ͗ĐůŽƐĞƚŽϵϳŚŽƌƌŝůůŽƐ͗^WdͲϮϮĞƉƚŚ͗ϯ͘ϲϬŵtĂƚĞƌdĂďůĞ͗Ϭ͘ϵϬŵ^K/>W/dE^Wdd>
dd>

η^WddKd>сϭϮϴ

η^K/>ͲW/ddKd>сϭϮϬϰ

D/ZKdZDKZDW

D/ZKdZDKZDW/ŶĐůƵĚŝŶŐ'ĞŽůŽŐŝĐĂůůĂƐƐŝĨŝĐĂƚŝŽŶ

'K>K'/>DWʹ s/>>>^>sKZ

^dZ'D;^dZ'>K>/'/d>>sd/KEDK>Ϳ
Η^dZ'DŝƐĂƉƌŽĚƵĐƚŽĨDd/;DŝŶŝƐƚƌǇŽĨĐŽŶŽŵǇ͕dƌĂĚĞĂŶĚ/ŶĚƵƐƚƌǇŽĨ:ĂƉĂŶ ͿĂŶĚE^Η&ŝůĞEĂŵĞ;ǆĂŵƉůĞŽĨ^ϭϮΕϭϯ͕tϬϳϳΕϬϳϴͿ
^d'dDͺ^ϭϮtϬϳϳ͘ǌŝƉo DĨŝůĞ^d'dDͺ^ϭϮtϬϳϳͺĚĞŵ͘ƚŝĨo YĨŝůĞ^d'dDͺ^ϭϮtϬϳϳͺŶƵŵ͘ƚŝĨYƉůĂŶĞĨŝůĞDĨŝůĞϭϮ^ϳϳtϳϴt ϭϮ^ϳϳtϯϲϬϭƉŝǆĞůƐϯϲϬϭƉŝǆĞůƐϭϯ^ϭϯ^ϯϲϬϭƉŝǆĞůƐϳϴtϯϲϬϭƉŝǆĞůƐĂĐŚ'DƚŝůĞĐŽŶƚĂŝŶĞƌĂĐĐŽŵŵŽĚĂƚĞƐƚǁŽǌŝƉͲĐŽŵƉƌĞƐƐĞĚĨŝůĞƐ͕ĂDĨŝůĞĂŶĚĂƋƵĂůŝƚǇĂƐƐĞƐƐŵĞŶƚ;YͿĨŝůĞ͘ŽƚŚĨŝůĞƐŚĂǀĞĚŝŵĞŶƐŝŽŶƐŽĨϯϲϬϭƐĂŵƉůĞƐďǇϯϲϬϭůŝŶĞƐ͕ĐŽƌƌĞƐƉŽŶĚŝŶŐƚŽƚŚĞϭ㫦ͲďǇͲϭ㫦 ĚĂƚĂĂƌĞĂ͘

,KtK^Z'/^>h>dd,^>KW͍Ğůů^ŝǌĞсϯϬ͘ϳϮϮϵϯϱůĞǀĂƚŝŽŶDĂƉ^ůŽƉĞDĂƉi) − (a + 2d + g ))(Dz Dx) = ((c + 2(8f *+cellsize X )§¨ Dz ·¸ = (( g + 2h + i) − (a + 2b + c))© Dy ¹(8 * cell size Y )^>KW͗
ǌͬǆ͗^ůŽƉĞŝŶĂƐƚͲtĞƐƚǌͬǇ͗^ůŽƉĞŝŶEŽƌƚŚͲ^ŽƵƚŚarctan =2(Dz Dx ) + §¨© Dz Dy ·¸¹ * 57.595782DdZKWK>/dE>/DDW

ůŽĐŬƐ'ƌŽƵƉŽĨŚŽƵƐĞƐƐƵƌƌŽƵŶĚĞĚďǇƐƚƌĞĞƚƐ&/ͺhE/

>sd/KEDW^>KWDW^>KWDWŐƌĞĂƚĞƌƚŚĂŶϮϬ㫦㫦ϱϯϬϰůŽĐŬƐ

>K<^t/d,^>KWхсϮϬ°°^>KWDWǁŝƚŚŐƌĞĂƚĞƌƚŚĂŶϯϬ㫦㫦ϰϲϴůŽĐŬƐ

zED/,ZdZ/^d/^K&d,^K/>

Dd,K^ K&/EsZ^/KE K&/^WZ^/KE hZs^&ZKD ^hZ& ts^'EZ>/EsZ^/KEWZKhZ/EsZ^/KEDd,K^• ůĂƐƐŝĐDĞƚŚŽĚ͘• 'ĞŶĞƚŝĐůŐŽƌŝƚŚŵ͘• EĞŝŐŚďŽƌŚŽŽĚ
ůŐŽƌŝƚŚŵ͘>^^/Dd,K

&>Kt/'ZDŝƐƉĞƌƐŝŽŶƵƌǀĞ/ŶŝƚŝĂůŵŽĚĞů&ŽƌǁĂƌĚŵŽĚĞůŝŶŐKďƐĞƌǀĞĚĂŶĚĐĂůĐƵůĂƚĞĚĚĂƚĂDŽĚŝĨŝĞĚŵŽĚĞůDŽĚŝĨŝĞĚǀĞĐƚŽƌ/dZd/KEŽŵƉĂƌŝƐŽŶDĂƚƌŝǆŝŶǀĞƌƐŝŽŶ
:ĂĐŽďŝĂŶŵĂƚƌŝǆEŽZĞƐŝĚƵĂůŽŶǀĞƌŐĞWĂƌƚŝĂůĚŝĨĨĞƌĞŶƚŝĂůzĞƐŶĂůǇƐŝƐƌĞƐƵůƚZĞƐŝĚƵĂůǀĞĐƚŽƌŝƐ͗^ͲsĞůŽĐŝƚǇ/ŶŝƚŝĂůDŽĚĞů

x = (VS1 , VS 2 ,...VSn )T0§ f 1 obs − f 1 cal ( x 0 ) ·¸
¨ obs
¨ f 2 − f 2cal ( x 0 ) ¸∆y = ¨¸...
¸¨¨ f obs − f cal ( x ) ¸m
0 ¹
© m

Ŷ ĂƉƉƌŽĂĐŚ ďĂƐĞĚ ŽŶ ƚŚĞ :ĂĐŽďŝĂŶ DĂƚƌŝǆŝƐ ƵƐĞĚ ƚŽ ůŝŶĞĂƌŝǌĞ ƚŚŝƐ ƉƌŽďůĞŵ ŝŶ ƐĞǀĞƌĂůŝƚĞƌĂƚŝŽŶƐ͘§ ∂f1¨¨ ∂VS 1¨ ∂f 2a = ¨ ∂VS 1¨¨ .
¨ ∂f m¨ ∂V© S1

∂f1
∂VS 2
∂f 2
∂VS 2.
∂f m∂VS 2...
...
...
...

∂f1 ·¸∂VSn ¸∂f 2 ¸∂VSn ¸¸. ¸∂f m ¸∂VSn ¸¹ŽƌƌĞĐƚŝŽŶsĞĐƚŽƌѐǆ͗

(a T .a + εI )∆x = a T .∆yEĞǁDŽĚĞůƐƚŝŵĂƚŝŽŶ͗x l +1 = x l + ∆x

To perform this Classical Method (Root Mean Square), we refered toSeisImager Software that works with the Dispersion Curve for theFundamental Mode, and from its analysis obtain the Vs-profile.

Fig.3. Fundamental and Higher Modes of Dispersion Curves.

In this case, we introduce the information of the dispersion curve directly
to the program to obtain first, a Initial Model and then, the Inverted
Model.

d, WZK>D K& d,
>^^/ Dd,K /^d,d KE>z d<^ /EdKKhEdd,
&hEDEd> DKdK WZ&KZD d,
/EsZ^/KE͘'Ed/
>'KZ/d,D;'͘͘ͿsK>hd/KE/E/K>K'z

sK>hd/KE/E/K>K'z• KƌŐĂŶŝƐŵƉƌŽĚƵĐĞĂŶƵŵďĞƌŽĨŽĨĨƐƉƌŝŶŐƐŝŵŝůĂƌƚŽƚŚĞŵƐĞůǀĞƐďƵƚĐĂŶŚĂǀĞǀĂƌŝĂƚŝŽŶƐ ĚƵĞƚŽ͗Ͳ DƵƚĂƚŝŽŶƐ ;ƌĂŶĚŽŵĐŚĂŶŐĞƐͿͲ ^ĞǆƵĂůƌĞƉƌŽĚƵĐƚŝŽŶ ;ŽĨĨƐƉƌŝŶŐŚĂǀĞĐŽŵďŝŶĂƚŝŽŶƐŽĨĨĞĂƚƵƌĞƐŝŶŚĞƌŝƚĞĚĨƌŽŵĞĂĐŚƉĂƌĞŶƚͿнsK>hd/KE/E/K>K'z• ^ŽŵĞƐƉƌŝŶŐƐƐƵƌǀŝǀĞ͕ĂŶĚƉƌŽĚƵĐĞŶĞǆƚŐĞŶĞƌĂƚŝŽŶƐ͕ĂŶĚƐŽŵĞĚŽŶŽƚ͗Ͳ dŚĞŽƌŐĂŶŝƐŵƐĂĚĂƉƚĞĚ ƚŽƚŚĞĞŶǀŝƌŽŶŵĞŶƚ ŚĂǀĞŚŝŐŚĞƌĐŚĂŶĐĞƐƚŽƐƵƌǀŝǀĞ͘Ͳ KǀĞƌƚŝŵĞ͕ƚŚĞŐĞŶĞƌĂƚŝŽŶƐďĞĐŽŵĞŵŽƌĞĂŶĚŵŽƌĞĂĚĂƉƚĞĚďĞĐĂƵƐĞƚŚĞĨŝƚƚĞƐƚŽƌŐĂŶŝƐŵƐƐƵƌǀŝǀĞ͘/ŶŝƚŝĂůŝǌĞ ƚŚĞ ƉŽƉƵůĂƚŝŽŶ ;ƌĂŶĚŽŵůǇͿ^ŽůƵƚŝŽŶZĞƉƌĞƐĞŶƚĂƚŝŽŶ͗ŽŶǀĞƌƐŝŽŶƚŽĂ͞ŵĂĐŚŝŶĞ͟ǀĂůƵĞƐ;ďŝŶĂƌǇŽƌƌĞĂůͿǀĂůƵĂƚŝŽŶŽĨĨŝƚŶĞƐƐĨƵŶĐƚŝŽŶ^ĞůĞĐƚŝŽŶƌŽƐƐŽǀĞƌ

&>Kt/'ZDDƵƚĂƚŝŽŶ
EĞǁ 'ĞŶĞƌĂƚŝŽŶ
ǀĂůƵĂƚĞĐƌŝƚĞƌŝĂ ŽĨĞŶĚŝŶŐ ƚŚĞ'͘͘EĞǁ'ĞŶĞƌĂƚŝŽŶ

/E/s/h>^E^Z,^WϬǆϭϮŶĚ'ĞŶǆϮsϭ,

͘͘
sŶ>

͘͘
sŶ,ǆŶͲϭ

Śϭ>
ŚϮ>
͘͘

Śϭ,
Śϭ,
͘͘͘ǆŶϬϬǆϯyсŶͲƚŚ'ĞŶϬsϭ>͘͘͘/ŶĚŝǀŝĚƵĂů;ƌŽŵŽƐŽŵĞͿϱϬϬϭϬϬϬϭϱϬϬϮϬϬϬϮϱϬϬͲϭϬϬͲϮϬϬͲϯϬϬĞƉƚŚ;ŵͿϭƐƚ'ĞŶdŚĞďĞƐƚŝŶĚŝǀŝĚƵĂůŚĂƐƚŽďĞŝŶƚŚĞƐĞĂƌĐŚƐƉĂĐĞ͘ͲϰϬϬͲϱϬϬͲϲϬϬͲϳϬϬͲϴϬϬ^ͲǁĂǀĞsĞůŽǀŝƚǇ;ŵͬƐͿϯϬϬϬϯϱϬϬ

&/dE^^E^>d/KE&hEd/KE/ŶĚŝǀŝĚƵĂůůĞŶŐƚŚ͞ŵ͟ŝŶĚŝǀŝĚƵĂůƐǆϭϭ ǆϭϮ ͘ ͘ ͘ǆϮϭ ǆϮϮ ͘ ͘ ͘͘ ͘͘ ͘͘ ͘ǆŵϭ ǆŵϮ ͘ ͘ ͘ǆϭŶǆϮŶ͘͘͘ǆŵŶǀĂůϭǀĂůϮ͘͘͘ǀĂůŵsĂůƵĞŽĨƚŚĞĨŝƚŶĞƐƐĨƵŶĐƚŝŽŶŝŶ;ĂͿdŚĞ ƐĞůĞĐƚŝŽŶ ĨƵŶĐƚŝŽŶ ĚĞƚĞƌŵŝŶĞƐ ǁŚŝĐŚ ŽĨƚŚĞ ŝŶĚŝǀŝĚƵĂůƐ ǁŝůůƐ ƐƵƌǀŝǀĞ ĂŶĚ ĐŽŶƚŝŶƵĞ ƚŽƚŚĞ ŶĞǆƚ ŐĞŶĞƌĂƚŝŽŶ͘

1

val =

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