depth - sabbagh.com · al 0 depth & ° & @ ¯

23

Upload: lecong

Post on 13-May-2019

232 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

��������������� ���������������������������� �!�"����#��$�&%'���()�����*�+� �,� -��.). %�/��0)�������1�2�3�546��.����#���7.��"�8��9

:<;>=@?BADC)E�F*GH;>IJIK;>LBM�NJOPADQD;SRT:�FUGH;>IJIV;>LBM�NJW6FJX6QZY\[�]^=@_KMa`b�QDcedf?S=<gih3cjMJk^?BAl?SLBQlh3R3NVmimon�N^prq�sr?ut1vSv+wBxyNVs8Al?y?BY QDk^LSdf?Bk�N^z|{�}~v�}Bwavu��vSv+wBx���GHE�S?BMJk�{�`Sh3kJMy]JQDR3NHpP]^=@CJ]Jh���kJQl�Sh=jR�Qld�`SN^��h3R�d<mi;>��;3`ShdfdfhSN*z|{�}~v>�>wavu�@�3�S�S���"GHE

g�M^h�k^?BkKC^h3Rfdf=@]Jced�QD�Sh�h�+;SAZ]J;>d�Ql?Bk���{���Or�*?S�^MJQDLBM�dfh3Y�_*h=@;>d�]^=�h�ce?B;>d�QZk^LBR�QZR*?Bk^h�?S�yd�M^hPQZY�_*?S=�d�;Skad���;Scedf?S=@R�QDk;Sc@MJQDh�yQDkJL<;�MKQlLBM6Alh�Sh3A~?S�JRfdf=@]Jced�]J=@;SAaQDk~dfhLS=@Qld�`6QDk�;SCJ�+;SkJceh3C�LB;SR�d�]^=�IKQDkJh3RF�z|k6d�MJQDRi_K;>_*h=3N+�PhrC^h3Y�?BkJRfdf=j;>dfhd�MJ;>dTRf?S_KMJQZRfd�QDc;>dfh3C�h3CJC^`�c]J=�=�h3k~drdfh3cjMJkJQD�y]^h3R8c;Sk�I*h�]Jd�QDADQl�h3C�df? Y�h3;SR�]^=@h<d�M^h�d�MJQZc��Hk^h3R�RT;SkJC�=�h3Y ;SQZkJQDk^LADQl��h�?S�JMJQlLBM�dfh3Y�_*h=@;>d�]^=�hrce?B;>d�QDk^LBRF�Gy?BY h�=�h3Rfh3;>=jc@M!MJ;SR�IUhh3k&ce?BkJCJ]Kcedfh3C�df?�;>_J_KAl`"R�]Kc@M�dfh3c@MJkJQZ�~]^h3R�df?�d�M^h_J=�h3Rfh=@�yQDceh6c;SR�hSNK��?S=���MJQZc@M�d�M^h�ce?B;>d�QZk^L�MJ;SR�?Bk^h�kJQDceh3AD`�C^h KkJh3C�AD;3`Sh=�;SkJC�k^?Sd�MKQDk^L�?S�¡ce?BkJRfh3�y]^h3kJceh�MK;SRCJQ£¢�]JRfh3C�QDkadf?!d�M^h�IK;SRfh"Y�hd�;SA*d�MK;>dr�r?B]JADC�ce=�h3;>dfh6;SCJCKQld�Ql?BkJ;SAVAD;3`Sh=@R8?S��;Sk^?BY ;SAl?B]KRrY�;>dfh=@QD;SA¤Fo��h6CJQDR@c]JR�Rd�M^h�Y&]Jc@M¥Y�?S=�h&CJQl¦�c]JADd8QZkJRfh=��HQDceh"c;SRfhSN*QDk)��MJQZc@M)d�M^h�d�QDY�h6dfh3Y�_*h=@;>d�]J=�h6hetH_U?BR@]^=�h"?S�od�M^h�ce?BY�IK]JRfd�QD?Bkd�]^=�IKQZk^h�IKAZ;SC^h)MJ;SR�ce=�h3;>dfh3C§;¨��?B]^=�AD;u`Sh=�h3C©Rf`HRfdfh3Y)NrQDkª;SCJCJQld�Ql?Bk$df?�d�M^h)IV;SRfh�Y�hd�;SA¤Fªg�M^h�_K;>=�d�QZc]JAD;>=ce?B;>d�QDk^LBR�d�MJ;>d6�rh�CJQDR�c]KR�R�;>=�h�Y ;SC^h ]J_�?S�8{�Q«nr?~n8=@E<Al¬­��Qld�M�;)df?S_$;SAD]JY QZkJQDC^h&ce?B;>d�QDk^L^No®"g�¯S¯B°&N�;SkKC��Qld�M^?B]Jdrd�MJh6df?S_¥;SAD]KY QDkJQDCJh<ce?B;>d�QDk^L^NVp��¨E��S�SxyF

±¤²J³µ´|¶¤´�·3¸µ´|¹�º@¸�¸µ»+´P¼f½@¸µ»<¾!¿j³µÀÁ¹"ÂU¿j·�ÃÄ´�³µ´|·+Å�´¡¿Æ·�Ç�¿Æ·>¹u´|¶�¸¤³µÈ+Å�¸µÉÁÊÆ´¡Ëy´|¶�¸µÉÌ·+ÍuÎBÏ�¿j·3¸¤³µ´|ºjÀlÎSÐ�³µÉÁ¹�ºfÑÎ�ÒjÓeÔ�ÕK²KÒjÖ�×

Page 2: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

��¥����� .)01�&���+���

E�C^�+;SkKceh3C d�]^=�IKQZk^h3RN�R�]Kc@M§;SR d�M^h1®�O��^=@;SY�h�v��yE��>���HE�N8;>=�h�]JR�h3C©QDk ;>_J_KAZQDc;>d�Ql?BkJR!=@;SkJLBQDk^L¨�«=@?BY;>h=�?BRf_K;ScehPdf?�AD;SkJC^�µIK;SRfh3C�_*?u�rh=�LSh3k^h=@;>df?S=jRF�g�M^h3Rfh¡d�]^=�IVQDk^h3R�;>=�h¡ J=@h3C";>diMJQlLBM^h=�dfh3Y _Uh=j;>d�]^=�h3R��|�3�S�>w�����3�S�>w � ���jN�;SkJC$]^d�QDADQl�h�?S_Jd�QDY&]JY ce?y?BADQDk^L�?S��M^?Sd�R�h3ced�Ql?Bkªce?BY�_*?Bk^h3kad�R3F¥srh3c;S]JRfh�?S��d�M^h�MJQlLBM^h=�?S_Uh=j;>d|�QDk^L)dfh3Y�_*h=@;>d�]J=�hSN�d�MJh _*h=��«?S=jY ;SkJceh�;SkJC CJ]^=@;>IKQZADQld�`¥?S�8d�M^h  J=@R�d�Rfd�;>LSh�IVAD;SC^h3R6MJ;SR�I*h3ce?BY�h�?Bk^h�?S�Td�M^h_J=@QDY h8AZQl�«he��AZQDY Qld�QDkJL���;Scedf?S=@RF¡z|kJCJQl�HQDCJ]J;SA~IKAD;SCJh3R�;>=�h�kJQZc��Sh3A£�µIK;SR�h3C�®�g��!�S�S��;SADAl?�`yRNad�MJ;>dP;>=�h�_J=�?Sdfh3cedfh3C�I~`R�;Sce=@Ql VcQD;SA�Y hd�;SADADQDc�ce?B;>d�QDk^LBR"df?�hetHdfh3kJC�Rfh=��HQDceh!ADQl��hSF�g�M^h� K=@Rfd|��Rfd�;>LSh!IKAD;SCJh3R�;>=@h&h3R�_Uh3cQZ;SADAl`)QDY�_*?S=�d�;Sk~dN;SkJC1Qld�QZR�C^h3R�QD=@;>IKAlh6df?)C^h�Sh3AD?S_¨;Sk ��������������{<��O Rf`HRfdfh3Y df?�Y�?BkJQldf?S=3NUh�>;SAD]J;>dfhSN�;SkJC¥_J=�h3CJQZced�=�h3Y ;SQZkJQDk^Lce?B;>d�QDk^L&ADQl��hSF�g�MJh�ce?B;>d�QDk^LBRr]JRfh3C�?Bk�d�M^h�d�]^=�IVQDk^hTIKAD;SCJh3R�QDkJcAD]KC^hTn8?~nr=@E�A£¬ ;SkKC�{�Q«nr?~nr=@E�A£¬!N>��Qld�M ;�df?S_;SAD]JY QZkJQDC^h�ce?B;>d�QDkJL��µ®�g��S�B°&NV®�g<¯S¯B°&N^=�h3Rf_*h3ced�Ql�Sh3Al`J�jNH;SkJC�;&{�Q«nr?~n8=@E<Al¬�ce?B;>d�QDk^L^NJc;SADAlh3C�p��1E5�S�Sx��£���µFb�QDcedf?S=&g�h3c@MKk^?BAl?SLBQlh3R&MJ;SR6I*hh3k _Uh=@�«?S=@Y�QDk^L)=�h3Rfh3;>=jc@M$QDkadf?¥d�M^h�kJ?BkJC^h3Rfdf=@]Kced�Ql�Sh�c@MK;>=@;Scedfh=@Ql�3;>d�Ql?Bk$?S�

QDkH��Rfh=@�yQDceh<MJQlLBMH�µdfh3Y�_*h=@;>d�]J=�h<Y�hd�;SAZADQDc���R�]Kc@M�;SRr[¨nr=@E�A£¬��od�M^h=jY ;SAKIV;>=�=@Qlh=rce?B;>d�QDk^LBR"��g�s�n���;>_J_KADQlh3C I~`�+;Sc]K]JY _KAD;SR�Y�;�Rf_K=@;3`�?Bk){<Q£�µIV;SRfh3C)R�]^_*h=@;SADAD?u`�d�]^=�IVQDk^h�IKAD;SC^h3RFoz|k�d�MJQDR8=�h_*?S=�dr�Ph6CJh3R�ce=@QlI*h�?B]^=8he¢U?S=�d�RQDk);>_J_KAD`yQDkJL ()�+�6/��K.��� df?�d�M^h"_J=�?SIKADh3Y ?S�ocjMJ;>=@;Scedfh=@QD�3QDk^L d�M^h�®"g�¯S¯B° CJ]J_KAlhet�ce?B;>d�QDkJL^F

���¥�\)� �!�#" .)0)46�P�%$ � �!�"����#

g�M^h)®�g�¯S¯B° CJ]^_KADhet�ce?B;>d�QZk^L1MK;SR�d��P?�AD;u`Sh=@R&?S��I*hd�;¥;SAD]KY QDkJQDCJhSNi;Sk$h3Rf_*h3cQD;SADAl`1=@QDcjM ?Bk^hSN�c;SAZAlh3C'&o°&NMJ;3�HQDk^L�;)ce?BkKCJ]Jced�Ql�HQld�`1?S�8;>IU?B]Jd ��(Á�*)$�w,+�G-�+Y)Ni;SkJC#;/.ÁkJ?S=@Y ;SA10�?Bk^hSN�c;SADAlh3C2&�N���Qld�M�;�ce?BkKCJ]Jced�Ql�HQld�`?S�";>IU?B]Jd��3( }/) �w,41G-�+Y)Nr;SR�QDkªd�M^h1p��¨E��S�Sx ce?B;>d�QDk^L^F z|k©;SCJCJQld�QD?Bk�N�d�M^h=@h¥QDR�d�MJh�]JR�]J;SAT;SAZ]JY QDky]JY?3t^QDC^h�AD;u`Sh=���E<A653q%7u��d�MJ;>d"QDR�d�M^h�;Sced�]J;SAod�MJh=@Y ;SA�IK;>=�=@QDh=�;>I*?��Sh8&�°&N�;SkJC�;Sk¨QDk~dfh=f��CJQ£¢�]JR�Ql?Bk��?Bk^h���z:9����Qld�M�;�k^?BY QZkJ;SAVce?BkKCJ]Jced�Ql�HQld�`�?S��¯3(Á�;)¨�w 4 G��+Y I*hd��rhh3k�&#;SkJC�d�M^h�®�g��&�S�S��R�]^IKRfdf=j;>dfhSF���h6MJ;3�Sh�k^?SdRfd�]JCJQDh3C d�M^h<z<9�QDk d�MKQDR�=�h_*?S=�dNyI*h3c;S]JRfh�QldPQDRrR�Y ;SAZA���;SR8QDk d�MJh<c;SRfh�?S��d�M^h�p��¨E��S�SxB�P;SkJC�Alh3R�RrQDY�_*?S=�d�;Sk~dQDk$C^hdfh=@Y QDkKQDk^L)d�M^h�=�h3Y ;SQZkJQDk^L�AZQl�«h�?S��d�M^h�ce?B;>d�QDk^L^F�g�M^h�®�g��!�S�S��R�]^IKR�df=@;>dfh�QZR�QDCJh3kad�QDc;SAPdf?1d�M^h�?Bk^hRfd�]JCJQDh3C�h3;>=@ADQlh=3N^;SkJC�MJ;SR�; k^?BY�QDkJ;SA*ce?BkJCJ]Jced�QD�yQld�`�?S��v=(Á�8) �w,4uG��+Y)F�oQlLB]^=�h��&R�M^?u�<R<d�MJh>.Ìh3ADh3cedf=@QDc;SA�_J=�?S KADh,0K?S��d�M^h�®�g<¯S¯B° ce?B;>d�QDk^L^F6g�M^h� JLB]^=�h!R�]^LSLSh3R�d�R�d�MJ;>d�d�M^h &o°

;SkJC?& AD;u`Sh=@R�Y�;3`#MJ;u�Sh�CJQ£¢*h=�h3k~d6d�MJQDc@�ykJh3R�Rfh3RN�IK]^d�Y hd�;SADAD]^=�LBQZc;SA�Y�h3;SR�]^=@h3Y�h3kad�R�?Bk#�>;>=@Ql?B]KR�R�;SY�_VAlh3RR�]^LSLSh3Rfd�d�MJ;>d6d�M^h�d��P?�AZ;3`Sh=@R�MJ;3�Sh�ce?BY _K;>=@;>IKAlh�d�MKQDc��Hk^h3R�Rfh3R3N���MJQDcjM¨�Ph�d�;>�Sh df?�I*h��wSw�@�Y)F g�=�`yQZk^L�df?;SR�Rfh3R�R&d�M^h�d�MJQDc@�yk^h3R@R�?S��d�MJh�z:9©AD;u`Sh=�QDk#d�M^h���;Sceh�?S��d�MJh�AD;>=@LSh�ce?BY�IKQDk^h3C d�MJQDc@�yk^h3R@R�?S�Td�M^h�;SAD]JY�QDkJQDC^hAD;3`Sh=jR�Rfhh3Y�h3C�]Jka�<QDRfhSNJ;SkJC�d�MJ;>d<QDRT?Bk^h"=�h3;SR�?Bk���?S=�QlLBk^?S=@QZk^L!d�M^h6_J=�h3R�h3kJceh"?S��z:9¨QDk�?B]J=�Rfd�]JCJQDh3RFg�My]JRNy?B]^=TQDk~�Sh=@R�Ql?Bk�_J=�?SIKADh3Y­I*h3ce?BY�h3Rr?Bk^h�?S�iC^hdfh=jY QDkJQDkJL6d�M^h�d�MJQDc@�yk^h3R@RP?S�id�M^h"E<A653q%7<AD;3`Sh=��A9��B�jN

��MJQDcjM©MJ;SR ; �ykJ?u��k©ce?BkKCJ]Jced�Ql�HQld�`ª?S�"w G��+Y�N8;SkKC©C^hdfh=@Y QZkJQDk^L¨d�M^h1ce?BkJCJ]Jced�Ql�HQld�` ?S��d�M^hB&o° ;SkJCC&AD;3`Sh=jRN*h3;Sc@M¨?S����MKQDc@M¥QDR��wSw�@�Y d�MJQZc��UF<��h�R�M^?B]KADC�Y�h3k~d�Ql?Bk1d�MJ;>d�Qld<QDR�;�IKQld�CJQZR�ce?BkJceh=�d�QDkJL�df?�QDC^h3k~d�Ql�«`;)AD;3`Sh=�I~`¨;� ^tHh3C�c@M^h3Y�QDc;SAD�+Y�hd�;SADAZ]^=�LBQDc;SA¡kJ;SY hSN�R�]JcjM�;SR�&�° ?S=E&©��M^h3k�Qld�R6h3Alh3cedf=@QDc;SA�ce?BkKCJ]Jced�Ql�HQld�`Y ;3` cjMJ;Sk^LShSF¡z�dPRfhh3Y�R�df?�]KR¡d�MJ;>d�d�MJh�h3Alh3cedf=@QZc;SAK;SkJC cjM^h3Y QDc;SA��+Y�hd�;SADAD]^=@LBQDc;SA^_J=�?S_*h=�d�QDh3R�R�M^?B]JAZC!IUhTd�QDh3Cdf?SLShd�M^h=3N¡Rf?¥d�MJ;>d�Ql�rd�M^h�h3Alh3cedf=@QDc;SAPce?BkJCJ]Jced�Ql�HQld�`1cjMJ;Sk^LSh3RNod�M^h3k Rf?¥R�MJ?B]JADC¨d�M^h�c@M^h3Y QZc;SA�kJ;SY�h�?S�Td�M^hAD;3`Sh=uF���h ��QDADA�;SCJ;>_Jd"d�MJh ce?Bka�Sh3k~d�Ql?Bk�N�M^?u�rh�Sh=3N�d�MJ;>d"d�M^h�d��r?�AD;u`Sh=@R6=@hd�;SQDk¨d�M^h3Ql=6R�;SY h kJ;SY�h3RN�h�Sh3kQl�8d�M^h3Ql=!ce?BkJCJ]Jced�QD�yQld�QDh3R�R�M^?B]KADC cjMJ;Sk^LShSN�;SkJC h�Sh3k Ql�8d�M^h�ce?BkJCJ]Jced�Ql�HQld�`�?S�Td�M^h>& AD;u`Sh=�R�M^?B]JADC I*h3ce?BY�hMJQlLBM^h=Td�MK;Sk)d�M^hF&�° AD;3`Sh=HGE�ADA^ce?B;>d�QDk^LBR¡��?S=@Y ;�d�MKQDk&_J=�?Sdfh3ced�Ql�Sh�;SCKM^h=�h3k~d�AD;3`Sh=P?S�UE�A653q%7�� ���µNI� ¯��µF¡E�R¡d�M^hT_J=�?Sdfh3ced�QD�Sh�?3t^QDC^h�Rf_V;SADADR

?>¢ CJ]^=jQDk^L Rfh=��HQDcehSNU;SAD]JY QDky]JY\QZk�d�M^h&ce?B;>d�QDk^L�CJQ£¢�]JRfh3R�?B]Jd�df?�=�he�µ�«?S=jY2d�M^h�_J=�?Sdfh3ced�Ql�Sh!?utHQDCJh�AD;u`Sh=3NU;SkKC;SADRf? CJQl¢*]JR�h3RTQDkadf?�d�MJh�R�]^IKR�df=@;>dfh6;SkJC�c;S]JR�h3R�d�M^h6QDk~dfh=@CJQl¢*]JR@Ql?Bk��?BkJh�df?�QDkKce=�h3;SRfh6QDk�d�MJQZc��Hk^h3R�RF�oQlLB]^=�h��)QDADAD]KRfdf=@;>dfh3R";�Y QZce=�?SLS=@;>_KM�?S�T;¥®"g�¯S¯B°\ce?B;>d�QZk^L^F�E8d�d�M^h df?S_$QDR6;�{�QDE�Ao?u�Sh=@AZ;3` ce?B;>d�QDkJL^N

�«?BAZAl?u�rh3C)Iy`�d�M^h6{�Q«nr?~n8=@E<Al¬�I*?BkJC)ce?B;>d<;SkKC�d�M^h�QDk~dfh=f��CJQ£¢�]JR�QD?Bk�AD;u`Sh=3FPg�M^h�®�g��!�S�S��R�]JIKRfdf=@;>dfh6QDR�d�M^hADQlLBM~d|��ce?BAl?S=�h3C)=@hLBQl?Bk�;>d�d�M^h�IU?Sdfdf?BY�F

Page 3: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

Al 2 O3 IZ GTD111β+ β0

3.32

7.8

8.4

12.0

Conductivity / 105

Depth

�oQlLB]^=�h�����g�M^h�h3ADh3cedf=@QDc;SA�_J=�?S KAlh�?S��d�M^h!®"g�¯S¯B°7ce?B;>d�QDk^L^F�z�k�d�M^h�=@h3ce?BkJRfdf=@]Jced�QD?BkJR��rh!;SR�R�]JY�h�d�MJ;>d�d�M^hd�MJQDc@�yk^h3R@R�?S�<d�MJh�&�° ;SkJC &�AZ;3`Sh=@R�;>=�h)h3;Sc@M h3�~]K;SA8df?§�wSw�@�Y)F©g�M^h¥®"g��!�S�S��R�]^IVRfdf=@;>dfhSN�?S��ce?B]^=@R�hSNhetydfh3kKCJRTdf?�QDkJ KkJQld�`SF

¯

Page 4: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

�oQlLB]^=�h�� ��[�QZce=�?SLS=@;>_KM!?S�*;"R�;SY�_KADhr?S��®�g�¯S¯B° CJ]^_KADhet�ce?B;>d�QDk^L^Nyce?BY�_J=@QDR@QDk^L<;6df?S_�{<QZE<Ay?u�Sh=jAD;3` ce?B;>d�QDkJL^N�«?BAZAl?u�rh3C)Iy`�d�M^h6{�Q«nr?~n8=@E<Al¬�I*?BkJC)ce?B;>d<;SkKC�d�M^h�QDk~dfh=f��CJQ£¢�]JR�QD?Bk�AD;u`Sh=3FPg�M^h�®�g��!�S�S��R�]JIKRfdf=@;>dfh6QDR�d�M^hADQlLBM~d|��ce?BAl?S=�h3C)=@hLBQl?Bk�;>d�d�M^h�IU?Sdfdf?BY F

}

Page 5: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

g�M^h�_J=jQDY ;>=�` ?SI��|h3ced�Ql�Sh6QZRPdf?�h3Rfd�QDY ;>dfh"d�M^h�h3�y]JQl�>;SAlh3k~d8ce?BkKCJ]Jced�Ql�HQld�`�?S��d�MJh�?��Sh=@AD;u`�;SkKC�IU?BkKC�ce?B;>d|�QDk^LBRN�;SR�R@]JY QDk^L�;� ^tyh3C¥d�MJQDc@�ykJh3R�R�?S��h3;Sc@M ce?B;>d�QDk^L�?S��=�?B]JLBMJAl`#�wSw�@¡F�g�MJQDR�QZk^�«?S=jY ;>d�Ql?Bk1QDR�h3R�Rfh3k~d�QD;SA�df?Y ;SQDk~d�;SQDkJQDkJL�d�MJh�QDk~dfhLS=@Qld�`1?S�8IKAD;SC^h3R3N�I*h3c;S]JRfh�Qld6;SAZAl?u��R6d�M^h d�QDY�h3AD`¥=�h_V;SQl="?S=�=�h��]^=�IVQDR�MJY�h3k~d�?S�8ce?B;>d|�QDk^LBR"df?¥hetydfh3kKC d�M^h�Rfh=��HQDcehe��ADQl��h ?S�8?S_*h=@;>d�QDk^L�IVAD;SC^h3RF*�J]^=�d�MJh=3N�Qld�QDR�C^h3R@Ql=@;>IKAlh!df?¥?SIJd�;SQDk#d�MJh &��µ_KMK;SRfhC^h_KAlhdfh3C1�?Bk^h��¨��E�A65uq%73��d�MJQDc@�yk^h3R@RN�R�QDkJceh&d�MJQDR�QDkJ�«?S=@Y�;>d�Ql?Bk¨QDkJCJQDc;>dfh3R�d�M^h�Alh�Sh3Ao?S�PIKAD;SC^h&hetH_U?BR@]^=�h&df?Rfh=��HQDceh�dfh3Y�_*h=@;>d�]J=�hSF¡g�M^h�?��Sh=@;SADAJ=@h3Y ;SQDkJQDkJL�ce?B;>d�QZk^L�d�MJQZc��Hk^h3R�R�QZkJCJQDc;>dfh3R¡d�MJh�=�h3CJ]Jced�QD?Bk�?S��d�M^h�ce?B;>d�QDkJLd�MJQDc@�yk^h3R@R�c;S]JRfh3C)Iy`�d�M^h"?3t^QDCJ;>d�QD?BkH��QDkJCJ]Kceh3C�CJhLS=@;SCJ;>d�Ql?Bk�?S��d�M^h�df?S_�I*hd�;+�µ_KMJ;SRfh�CJh_KAlhdfh3C�AD;u`Sh=;�£���µF��h"MJ;3�Sh"_*h=���?S=@Y�h3C�;!k~]JY�I*h=P?S��Y�?yCJh3AVc;SADc]KAD;>d�Ql?BkJRP?S�id�M^h�g�s�n§_J=�?SIKADh3Y)N~]JR@QDk^L�?B]J=P_J=@?S_J=@Qlhd�;>=�`

h3CJC^`~��c]^=�=�h3k~d�{���O ce?yCJhSN (��+��/��J. �� ;SkJC MJ;u�Sh¨CJhdfh=@Y QDk^h3C QDY�_*?S=�d�;Sk~d�Rf`HRfdfh3Y �«h3;>d�]J=�h3RN�R�]Kc@M ;SR?S_*h=@;>d�QDk^L¨��=�h3�~]Jh3kJce`SNPce?BQDATcjMJ;>=@;Scedfh=@QZRfd�QDcRNrh3Alh3cedf=�?BkJQZc�dfh3Rfd�h3�~]KQl_KY�h3k~d�ce?BkJR�QDC^h=j;>d�Ql?BkJRN�;SkKC Y�h3;SkJR�?S�;Scceh3Alh=@;>d�QDkJL�d�M^h&ce?BY�_K]^d�;>d�Ql?BkKRFTE<R<; =�h3R�]KAldNJ�rh�MJ;u�Sh�ce?BkJcAD]KC^h3C�d�MJ;>d<d�M^h6?S_Jd�QZY�]JY2�«=@h3�~]^h3kKce`�=j;Sk^LSh�«?S=�_Uh=@�«?S=@Y�QDk^L d�MJh QDk~�Sh=@R�Ql?BkJR�=�h3�y]JQl=@h3C ?S�&d�M^h g�sTn _K=�?SIKAlh3Y,QDR�� [¥:<�#df?§�>w§[¥:��SF GH]Kcceh3R�Rf��]JAQDk~�Sh=@R�Ql?BkJR�QDk d�MJQDR =@;Sk^LSh���QZADAT;SADAl?�� ]JR�df?$;Sc@MJQDh�Sh¥d�M^h¥C^h3R�Ql=�h3C©=�h3Rf?BAD]^d�QD?Bkª�«?S=�d�M^h3Rfh�hetHdf=�h3Y�h3AD`$d�MKQDkce?B;>d�QDk^LBRFsrh3c;S]JRfh d�M^h=�h#;>=�h kJ?©ce?BY Y�h=@cQD;SAZAl` ;u�+;SQDAZ;>IKAlh¨h3CJC^`~��c]^=�=�h3k~d�QDkJR�df=@]JY�h3k~d�R�d�MJ;>d)?S_*h=@;>dfh QDk d�MKQDR

�«=@h3�~]^h3kKce`¥=@;SkJLShSN��rh�]JR�h3C�d�M^h�:<h��Alhdfd|��po;Sc@�+;>=@Cª:�p5¯S�BvSv+E2{�hd��P?S=��#E�kJ;SAl`y�h=3N�d�MJ;>d�QDR�C^h3R�QlLBk^h3C#df??S_*h=@;>dfh¨?u�Sh=)d�M^h1�«=@h3�~]^h3kKce`©=@;Sk^LSh1?S���>:<�1df?©�>wSwB[¥:��SF g�MJQDR�QDkJRfdf=@]KY�h3kad�Y�h3;SR�]^=�h3R�d�M^h1=�h��Jh3ced�QD?Bkce?~h¦�cQlh3kad"?S�8;�?Bk^he�µ_*?S=�d"k^hd��P?S=��©��kJ;SY h3Al`SN�d�M^h�Al?B;SC^h3C�ce?BQZA«�jN���=�?BY ��MJQDcjM1d�M^h QDY�_*h3CJ;SkJceh!CJ;>d�;HN�d�MK;>d;>=�h6d�M^h6QZk^_K]^d8df? d�M^h6QZka�Sh=@R@Ql?Bk);SAlLS?S=@Qld�MKY)NJ;>=�h�C^hdfh=jY QDk^h3C�Fg�M^h=@h!;>=@h�Rfh�Sh=@;SA�R�dfh_KR"df?)I*h c;>=�=@Qlh3C¨?B]Jd6CJ]^=@QDkJL�d�M^h dfh3R�d�QDk^L^F8�oQl=@Rfd���QDAZAiI*h�df?�c@MK;>=@;Scedfh=@Ql�h�d�M^h

_J=�?SI*h�QDk��«=�hhe��R�_K;ScehSNVd�MJh3k�df?�ce?BADAlh3ced�d�MJh�QDY�_*h3CJ;SkKceh6CJ;>d�;HNU;SkKC� KkJ;SAZAl`�df?�QDk~�Sh=�d�d�M^h3R�h�CJ;>d�;�]JR�QDk^L�?B]J=. ����AD;3`Sh=�;SAlLS?S=@QDd�MJY)F 0

.��"�8� � � �P�r���&���+� �

�oQlLB]^=�h"¯�QDADAD]JR�df=@;>dfh3R�;Sk�;Sced�]J;SAUd�]^=�IVQDk^h�IKAZ;SC^hSF¡g�M^h�R�]Jced�Ql?Bk�R�QDC^h<��;Sceh3R8d�MJh<�HQlh�rh=3N~�<Qld�M�d�MJh�Alh3;SCKQDk^Lh3C^LSh df?�d�MJh�=@QlLBM~dF g�M^h c@MJ?S=@C#Alh3k^LSd�M�QZR"Y�h3;SR�]^=�h3C ;SAl?Bk^L)d�M^h�R@]Jced�Ql?Bk�R�QDCJh&��=�?BY d�MJh Alh3;SCJQDk^L�h3C^LSh�df?d�M^h6df=@;SQZADQDk^L&h3C^LShSFg�M^hrR�;SY�_KADh3Ri]JRfh3C&QDk�d�M^hPp��1E��S�Sx<_J=�?��fh3ced��rh=�h��K;>d�ce?B]J_U?BkKRN+R�?<d�M^hP��;Sced�d�MJ;>d�d�M^h8ce?BQDA~QZR�h3Y�IUh3CKC^h3C

QDkª;�AD;>=�LSh�;Sce=�`HADQDc�I*?3tª�8;SR ]JkJQDY _U?S=@d�;SkadF g�M^h�_J=�h3Rfh3k~d R�;SY�_KADh3RN�M^?��Ph�Sh=3N8�rh=�h�Rfh3ced�Ql?BkKR�?S��;Sced�]K;SAd�]^=�IKQZk^h�IKAZ;SC^h3RNU��MJQDcjM1Y h3;SkJR�d�MJ;>d�d�M^h3Ql=;.Á;Sced�Ql�Sh,0�;>=�h3;SR"?S�PQDkadfh=@h3Rfd";>=�h�c]^=��Sh3C�N�MJ;u�yQDkJL�;�R�]Kced�Ql?Bk¥;SkKC_J=�h3R�R@]^=�h�R@QDC^hSF"��h!�Ph=@h!;>IVAlh!df?�QZkJRf_*h3ced�d�M^h�R�;SY _KAlh!;>d�?BkKAl`�?Bk^h!_*?BQDk~d�?Bk¨d�M^h!R�]Jced�Ql?Bk¨R�QZC^hSN*IUh3c;S]KRfhd�MJ;>d�QDR�d�MJh�?BkJAl`)_*?BQDk~d�?S��d�;SkJLSh3kJce`�?S�¡d�M^h&IKAD;SCJh6?u�Sh="d�M^h!ce?BQDA¤F���h&_*?BR�QDd�Ql?Bk^h3C�d�MJh�IKAD;SCJh�Rf?�d�MJ;>d�d�M^h_*?BQDkado?S�*d�;Sk^LSh3kJce`�AD;u`�?Bk d�M^h�Y QDCJ_KAD;Sk^hr?S�Vd�MJh�R�]Jced�Ql?Bk�R@QDC^hSNa;SkJC!d�MK;>d�QDR¡��MJh=�h8d�M^h�Y�h3;SR�]J=�h3Y�h3k~d�R¡�Ph=@hd�;>�Sh3k�F8GHhhF��QDLB]^=�h"}^Fg�M^h�dfh3Rfd�_*?BR�QDd�Ql?BkJR"=�h3AZ;>d�Ql�Sh df?1d�M^h�cjM^?S=@C ADh3k^LSd�M#��=�?BY d�M^h�Alh3;SCKQDk^L)h3C^LSh�?Bk d�M^h�R�]Jced�Ql?Bk R�QDC^h ;>=@h

R�M^?���k�QDk)g�;>IKAlh �>FGH;SY�_KAlh E s Ogih3Rfd<Rf_*?SdT�«=�?BY2Alh3;SCJQDk^L!h3C^LSh���QDkV� }^FÁ� ¯yFÁ� ¯yFÌwgi?Sd�;SA�c@M^?S=@C�Alh3k^LSd�M)��=�?BY\Alh3;SCKQDk^L!h3C^LSh���QDkU� v~FÁ� xyFÁ� �yF v>�p�h=jceh3kad<?S��dfh3Rfd<Rf_*?SdTdf?�c@MJ?S=@C�Alh3k^LSd�M x>w �+} �S�

g�;>IKAlh ���rW�h3AD;>d�QD�Sh"dfh3Rfd�_*?BR�Qld�QD?BkJRr?Bk)d�M^h�R�;SY _KAlh3RF

��R�QDk^L d�MJh�:<p k^hd��P?S=@��;SkJ;SAl`y�h=�;SkJC�d�M^h;9Uhdfh3c&ce?BQDA¤NK�Ph&Y�h3;SR�]^=�h3C�d�M^h�=@h��Jh3ced�Ql?Bk�ce?yh¦�cQlh3k~dN�� 9f9 N?S�*d�M^h<Al?B;SCJh3C ce?BQDA¤N~�«=�?BY­?Bk^h�df?� J�«d�`�Y�hLB;SM^h=�df�SN^QDk�?BkJhe��Y�hLB;SM^h=�df��Rfdfh_KRN~�«?S=Ph3;Sc@M�?S�*d�M^h�dfh3Rfd8R�;SY�_VAlh3RF

Page 6: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

�oQlLB]^=�h�¯ �PGHM^?u�<QDk^L�;&Rfh3ced�Ql?Bk�?S�i;Sk�;Sced�]J;SAUd�]^=@IKQDk^h�IVAD;SC^hSF¡g�M^h�R�]Jced�Ql?Bk�R�QDCJh���;Sceh3R8d�M^h<�HQlh�rh=3Ny��Qld�M�d�M^hAlh3;SCJQDkJL�h3CJLSh�df?�d�M^h�=@QlLBM~dF�g�M^h cjM^?S=@C#ADh3k^LSd�M QDR"Y h3;SR�]^=�h3C ;SAl?Bk^L)d�M^h�R@]Jced�Ql?Bk#R�QZC^h��«=@?BY d�M^h�Alh3;SCKQDk^Lh3C^LSh6df? d�MJh6df=@;SQDADQZk^L�h3CJLShSF

x

Page 7: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

Leading Edge

Coil

Blade Sample

SuctionSide

Acrylic Box

�oQlLB]^=�h"} �TGHM^?u�<QDk^L!d�M^h6_*?BR�Qld�QD?Bk�?S��d�M^h�IKAD;SC^h6R�;SY _KAlh"?Bk)d�M^h�;Sce=�`yAZQDc�I*?3t)?u�Sh=�d�M^h6ce?BQDA¤F8q�k^h"_*?BQDk~dT?Bkd�M^h�R�]Kced�Ql?Bk)R�QDC^hSN^?BkKAl`SN^�r;SR<]JRfh3C�F

v

Page 8: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

� 9f9 QZR�=�h3ce?S=@CJh3C¥;SR�;�Y�;>LBkJQld�]JC^h&;SkJC�_VMJ;SRfh���QZk¥C^hLS=@hh3Rj�jF����¨NVd�MJh�c@MK;Sk^LSh&QZk�k^?S=@Y�;SADQl�h3C�QZY�_*h3CJ;SkJcehCJ]^h¥df? d�M^h1�r?S=��~_VQlh3cehSN�QDR�d�M^h3k ce?BY�_K]^dfh3C �«=@?BY d�M^h¨R�c;>dfdfh=@QZk^L$ce?yh¦�cQlh3k~d�RF ��sr` .Ák^?S=@Y�;SADQl�h3C�N 08�rhY�h3;SkJRrd�MJ;>drd�M^h�df=@]^h<CK;>d�;&;>drh3;Sc@M���=�h3�y]^h3kJce` MJ;u�Sh�IUhh3k�CJQl�HQDC^h3C I~`�d�M^h�=�h3;Sced�;SkJceh"?S�id�M^h<_K=�?SI*h�ce?BQDAUQDk�«=@hh3Rf_K;ScehSN*;>d<d�MJ;>d���=�h3�~]Jh3kJce`SF ��g�M^h�=�h3;SAi;SkJC1QDY ;>LBQZkJ;>=�`�_K;>=�d�R<?S�¡d�M^h�k^?S=jY ;SADQl�h3C¥QDY�_*h3CJ;SkJceh3RT��?S=�d�M^h�«?B]J=�dfh3Rfd�R�;SY _KAlh3RT;>=�h�R@M^?u��k�QDk��oQlLB]^=�h3R������yF

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance

gtd111

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance

gtd111

�oQlLB]^=�h�� �!W�h3;SA���Alh�«dj�";SkJC QDY�;>LBQDkJ;>=�` ��=@QlLBM~dj��_K;>=�d�R�?S�8d�M^h�k^?S=@Y�;SADQl�h3C#QDY _Uh3CK;SkJceh3R��«?S=�d�M^h�®�g��&�S�S�R�]^IKR�df=@;>dfhSF

� � QDR�=�h3ce?S=jC^h3C!;SR¡;�cjMJ;Sk^LSh�QDk�=�h3R�QZRfd�;SkJceh6��=�h3;SAy_K;>=�dj�jNB;SkJC!;�c@MK;Sk^LSh�QDk�=�h3;Sced�;SkJceh���QDY�;>LBQDkJ;>=�`"_K;>=@dj�jFg�M^h"c@MK;Sk^LSh�QDk�=�h3;Sced�;SkKceh�QDRT;SAl�8;3`HR�k^hLB;>d�QD�Sh���CJ]^h�df?�mih3k^�,0JAD;3���jN^��M^h=�h3;SRTd�MJh6c@MJ;Sk^LSh�QDk�=�h3R�QDRfd�;SkKceh6QDR_*?BR�Qld�Ql�ShSFg�M^h QZY�_*h3CJ;SkJceh�CJ;>d�;)d�MJ;>d�;>=�h R�M^?���k#QDk �oQlLB]^=@h3R������);>=�h�Y&]JcjM#k^?BQDR�QDh=3N�?S=�;>d�Alh3;SR�dN�Alh3R�R�R�Y�?y?Sd�M

d�MJ;Sk d�MJh<CJ;>d�;�d�MJ;>dP�rh�df?y?S����?S=�d�M^h�p��¨E��S�Sx�_J=�?��fh3cedNyh�Sh3k�d�M^?B]JLBM �rh<]JRfh3C�d�M^h<R@;SY�h<;SAlLS?S=jQld�MJY R�;SkKC�«=@h3�~]^h3kKce`�=@;SkJLSh6df? _J=�?HCJ]Jceh"d�MJh�CJ;>d�;HF�z|kJC^hh3C�N^�Ph6�rh=�h�]KkJ;>IKAlh�df?�h�Sh3k�=�h_J=�?HCJ]Jceh"d�MJh6QDY�_*h3CJ;SkJceh"?S�d�M^h�ce?BQDA�QZk��«=�hhe��R@;>_*ceh�d�MJ;>d��rh�MJ;SC�QDk�d�MJh"h3;>=@ADQlh=�_K=�?��|h3cedFg�M^h=@h�;>=�h"d��P? AZQl�Sh3Al`�=�h3;SRf?BkKR8�«?S=Td�MJQZRN~d�MJh� K=@RfdrIUh3QZk^L�d�MJ;>dTd�MJh�kJhd��r?S=���;SkK;SAl`~�h=8d�MJ;>dT�rh"]JRfh3C���?S=

d�M^h�®�g�¯S¯B°5Y�h3;SR@]^=�h3Y�h3k~d�R8�r;SRTkJ?SdPd�M^h"R�;SY h�;SR8��?S=8d�M^h"p��¨E��S�SxyNV;SkJC�NHQDk���;ScedNJY ;u`�MJ;u�Sh6Rf?BY�h�C^=@Ql��dQDk1QldF!����h�MJ;SC¥d�;>�Sh3k¨LS=�h3;>d"_K;SQZkJR�df?�=�h_*h3;>dfh3CJAl`�c;SAZQlIJ=@;>dfh&d�M^h!QDkJRfdf=@]KY�h3kad�?u�Sh="d�M^h!h3k~d�Ql=�h���=�h3�y]^h3kJce`=@;Sk^LShSF � g�M^h!Rfh3ce?BkJC#_U?BR@R�QlIKQDAZQld�`SNU��MJQDcjM1�Ph�d�MJQZk^��QDR�Y�?S=�h AZQl�Sh3Al`SN�QDR�d�MJ;>d"d�M^h�;Sce=�`HADQDc&I*?3t1d�MJ;>d6M^?B]JR�h3Rd�M^h ce?BQDAoY ;u`1MJ;u�Sh�;>LSh3C#QDk¨Rf?BY h Y ;SkJk^h=3N�R�?)d�MJ;>d6Qld";Sced�]J;SADAl`¥_J=�h3Rfh3k~d�R";)Al?B;SC¨?Bk¨d�M^h R�`yRfdfh3Y ;>d"d�M^h�«=@h3�~]^h3kKcQlh3R�?S�TQDkadfh=@h3RfdF�g�M^h���;Sced6d�MJ;>d�d�M^h�CJ;>d�;�;>=@h�k^?BQDRf`1MJ;SR6Rf?BY h he¢Uh3ced�?Bk�d�M^h�QZkadfh=�_K=�hd�;>d�Ql?Bk�?S�d�M^h�=�h3ce?BkJR�df=@]Jced�Ql?BkJR3N�IK]^d"k^?Sd6df?�d�M^h�hetydfh3k~d6d�MJ;>d��Ph ;>=�h�]JkJ;>IKAlh&df?�C^=j;3� =�h3;SR�?BkJ;>IKAlh ce?BkJcAZ]JR�Ql?BkJR3N�;SRd�M^h�k^hetHd�Rfh3ced�Ql?Bk¥R�M^?���RF

����� � ��������01�&���+� �#� 01�*��# �5�"���*0)����.'�3��4���.�������� .��"�8�

z�k�QDk~�Sh=�d�QDk^L�d�MJh8®�g�¯S¯B°§_J=@?SIKAlh3Y ��?S=oGH;SY _KAlh3RiE�N�s ;SkJC�O�N3�rhrCJQZCJk 0 d�]JRfh�d�M^hP{���AD;3`Sh=¡;SAlLS?S=jQld�MJY)N+��MJQDcjM��QDADA�I*h C^h3R�ce=@QDIUh3C¨R�MJ?S=�d�Al`SN�I*h3c;S]JRfh QDd��8;SR6h3;SR@Qlh=6df?�R�QDY _KAl`�]JR�h (��+��/��J. �� df?�LSh3k^h=@;>dfh�QZY�_*h3CJ;SkJceh

Page 9: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance

sampleA

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50R

eact

ance

Frequency (MHz)

Imaginary Part of Normalized Impedance

sampleA

�oQlLB]^=�h�x �PW�h3;SA���Alh��dj�8;SkJC�QDY ;>LBQDkJ;>=@`1��=@QlLBM~dj�r_K;>=@d�RT?S��d�MJh�k^?S=@Y ;SAZQl�h3C)QDY�_*h3CJ;SkJceh3R8��?S=�GH;SY _KAlh"E�F

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance

sampleB

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance

sampleB

�oQlLB]J=�h�v ��W�h3;SAP��Alh�«dj�T;SkJC�QDY ;>LBQZkJ;>=�`1��=jQlLBMadj�8_K;>=�d�RT?S��d�M^h�k^?S=jY ;SADQl�h3C)QDY _Uh3CK;SkJceh3R8�«?S=�GH;SY�_KAlh"s�F

Page 10: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance

sampleE

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ceFrequency (MHz)

Imaginary Part of Normalized Impedance

sampleE

��QDLB]^=�h�� ��W�h3;SAP��Alh��dj�r;SkJC�QDY�;>LBQDkJ;>=�`¨��=@QlLBM~dj�r_K;>=�d�RT?S��d�M^h�kJ?S=@Y ;SADQl�h3C)QZY�_*h3CJ;SkJceh3R8��?S=�GH;SY�_KADh�O�F

CJ;>d�;HF<g�M^h3Rfh�CK;>d�;��rh=�h�d�MJh3k¥ce?BY�_V;>=�h3C�df?�d�M^h!Y�h3;SR�]^=@h3C�CJ;>d�;�?S� �oQlLB]^=�h3R�x����yF�z|k¥;�Rfh3kJR�hSNK�rh&Rf?BAD�Sh3Cd�M^h�QDk~�Sh=@R�QD?Bk)_J=�?SIKADh3Y�.ÌI~`)MJ;SkJC�F 0�g�M^h"=�h3;SR�?Bk���?S=�d�MJQDR�QDRTd�MJ;>d�d�MJh=�h�;>=�h6?BkKAl`�d�MJ=�hh6_K;>=@;SY hdfh=@R�df?� JdQDk~df?�d�M^h�®�g<¯S¯B° Y�?yCJh3A¤NUkK;SY�h3Al` � 5 N�d�MJh�d�MJQZc��Hk^h3R�R�?S��d�M^h!E�A 5 q 7 AD;u`Sh=3N�;SkJC1d�M^h�ce?BkJCJ]Kced�Ql�yQDd�`)?S� &o°;SkJC &�F �K]^=�d�M^h=3N~�Ph<�r;Sk~dfh3C df?&Rfhh�het^;Sced�Al` M^?��§d�M^h�ce?BY�_K]^dfh3C �+Y�h3;SR�]^=�h3C�CJ;>d�;6 Jd�d�M^h<R�QZY�_KAlhTY�?HC^h3A^?S�d�M^h6®�g�¯S¯B°5ce?B;>d�QDk^L

kK;SY�h3Al`SN^?Bk^h"QDk���MJQDcjM��rh";SR�R�]JY�h3C�d�MJ;>drd�M^h%&�°�;SkJC &¨d�MJQDc@�yk^h3R@Rfh3Rr�Ph=�h� ^tHh3C�;>d�wSw�Y QDce=�?BkKRNy;SkKC��rh"QlLBk^?S=�h3C�z:9�Fy��h6;SADRf?&�r;Sk~dfh3C)df?�Rfhh"M^?u� d�MJh�MKQlLBMH�µ��=�h3�~]Jh3kJce` CJ;>d�;!ce?B]JADC�I*h�]KRfh3Cdf?&CJhdfh=@Y QDk^hTd�MJh�d�MJQDc@�ykJh3R�R�?S��d�MJh<E�A653q%7�AD;u`Sh=r;SkJC�d�M^h &o° ce?BkJCK]Jced�Ql�HQld�`SNy;SkJC�d�MJh<Al?��T�µ�«=@h3�~]^h3kKce`!CK;>d�;M^h3Al_�C^hdfh=jY QDk^h6d�MJh�ce?BkJCJ]Jced�QD�yQld�`�?S�od�M^hE& AD;u`Sh=3Frg�M^h=�h��?S=�hSNJ�rh�R�QDY _KAl` =@;Sk�;�ky]JY�I*h=T?S�odfh3Rfd�Y�?yCJh3ADR]JR�QDkJL ()�+�6/��K. �� ;SkKC)d�M^h3k�_KAl?Sdfdfh3C�d�M^h6I*h3RfdT Jd�R8��QDd�M�d�M^h�Y�h3;SR�]J=�h3C)CJ;>d�;�?��Sh=<d�M^h"h3k~d�Ql=�h"��=�h3�y]^h3kJce`=@;Sk^LShSF¨g�MJQDR�k^?Sd&?BkJAl`�LBQl�Sh3R!]JR�d�M^h�;SkJRf�rh=�df?¨d�M^h�ce?B;>d�QDk^L>�µd�MJQZc��Hk^h3R�R!�~]Jh3Rfd�Ql?Bk�NoIK]^d&;SADRf?¨QDk^��?S=@Y R�]JR;SR�df?�d�M^h&�y]J;SADQDd�`�?S��d�MJh& Kd<?��Sh=6d�M^h&��QDC^h��«=�h3�y]^h3kJce`�=@;Sk^LSh!d�MJ;>d��Ph�]JR�h3C�F"g�M^h&=�h3R�]JAld�R�;>=�h!R�M^?���k¨QDk�oQlLB]^=�h3R����@�3�yFz|k �oQlLB]J=�h6�yN^�Ph�_J=�h3R�h3kad8d�M^h�=�h3R�]KAld�Rr�«?S=Td�M^h�®�g��&�S�S�"R@]^IKRfdf=@;>dfhSFPg�M^h�AlhLSh3kJC�ce?S=�=�h3Rf_*?BkJCKRPdf?�d�MJ=�hh

df=@QD;SA��>;SAD]^h3R�?S�¡d�M^h�ce?BQDA�AZQl�«df?>¢#QDk�Y QDADRFPg�M^h6ce?BkJCJ]Kced�Ql�yQDd�`�?S�od�M^h�R�]^IVRfdf=@;>dfh�QDR<;SR�R�]JY h3C)df?�I*h�v=(Á� ) �w 4G��+Y)Ny;SR���?S=�d�M^h�p��¨E��S�Sx�ce?B;>d�QDk^L^F�g�MJh�_K]^=�_*?BRfh8?S��d�MJQZR�Rfd�]JC^`!QDR¡df?&C^hdfh=@Y QZk^h�d�M^h�he¢*h3ced�Ql�Sh�ce?BQDAKAZQl�«df?>¢oN��MJQDcjM¨QDR�k^h3ceh3R�R�;>=�`¥df?)�ykJ?u� QDk1?S=@C^h=�df?�C^hdfh=@Y�QDk^h&d�M^h!d�MJQDc��Hk^h3R�R�?S�Pd�M^h�E<AI5q�7�ce?B;>d�QDkJL)�«?S=�GH;SY�_VAlh3RE�N*s�;SkKC1O�F �K]^=�d�M^h=3N*Qld��+;SAZQDCJ;>dfh3R<?B]^=�;SR@R�]JY�_Jd�QD?Bk�d�MJ;>d�d�M^h!ce?BkJCJ]Jced�QD�yQld�`�?S��d�M^h!R�]^IVRfdf=@;>dfh�QZR<QDk¥��;Scedv=(Á� )��w,46G��+Y)Fo��h�Rfhh�d�MJ;>d�d�M^h�QDY ;>LBQZkJ;>=�`!CJ;>d�;� Kd�d�M^h�Y�?yCJh3AJ?u�Sh=8d�M^h<h3kad�QD=�h���=�h3�y]^h3kJce`!=@;Sk^LSh�I*hdfdfh=d�MJ;Sk)d�M^h�=�h3;SA¤F�g�MJQZR8?SIKRfh=��>;>d�Ql?Bk�M^?BAZCJRT;SADY�?BRfd�]KkJQl��?S=@Y Al`���?S=�d�M^h"?Sd�MJh=<R�;SY�_VAlh3RFz|k �oQlLB]^=�h��w��rh�_J=@h3Rfh3kad�=�h3R�]JAld�R��«?S="GH;SY�_KADh�E�FUg�M^h6d�MJ=�hh6df=@QD;SAi_K;>=@;SY�hdfh=jR<;>=�h�d�M^h�d�MKQDc��Hk^h3R�R&��QDk

Y QDce=�?BkKRj�¡?S� 9�����E<A653q%73�P;SkJC�d�M^h�ce?BkJCJ]Jced�QD�yQld�QDh3R�?S� &�°�;SkJC &�F�E�LB;SQZk�NH�Ph"Rfhh�d�MJ;>d8d�M^h�=�h3;Sced�;SkJceh6CK;>d�;ADQlh"Y�?S=�h�Rf`yR�dfh3Y ;>d�QDc;SADAl`�I*hd��rhh3k�d�M^h"d��P?�df=@QD;SA*=�h3R@]JAld�R8d�MJ;Sk)d�MJh6=�h3R�QDR�d�;SkJceh6CJ;>d�;HFGH;SY�_VAlh&s�=�h3R�]KAld�R�;>=�h�R�M^?u�<k�QDk �oQlLB]J=�h)�S�>F�g�M^h&df=@QD;SA�_K;>=j;SY�hdfh=@R6;>=�h!d�M^h�R�;SY h!;SR�QDk �oQlLB]J=�h)�wHN

IK]^dNy?S��ce?B]^=@Rfh�d�M^h3Ql=r�>;SAD]^h3R�;>=@h�CJQl¢Uh=�h3k~dFPn8Alh3;>=jAl`SNad�M^h�=�h3R�QZRfd�;SkJceh�I*h3MJ;u�Sh3R8Y�]JcjM�Y�?S=�h�h=�=@;>d�QDc;SADAD`&d�MK;Skd�M^h�=@h3;Sced�;SkJcehSN�;SkJC¥h3;Sc@M1LBQl�Sh3R�ce?Bk��KQDced�QZk^L =�h3R�]KAld�RF�g�MJh�MJQlLBMH�µ��=�h3�y]^h3kJce`�=�h3R�QZRfd�;SkJceh�dfh3kKCJR�df?�I*h�cAl?BR�h=df?)d�M^h ce?BY�IKQDkJ;>d�Ql?Bk2&o°

�v )$�w 4

&��>)ª�w 4 N���M^h=@h3;SR�d�M^h MJQlLBMH�µ��=�h3�y]^h3kJce`�=@h3;Sced�;SkJceh ��;3�S?S=@R�d�M^h

�w

Page 11: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance for gtd111

Measured6.5 mils6.8 mils7.0 mils

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance for gtd111

Measured6.5 mils6.8 mils7.0 mils

�oQlLB]^=@h�� ��W�h3R�]KAld�R8�«?S="®�g��!�S�S�>F�S�

Page 12: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance for SampleA

MeasuredZ2 = 55; beta+ = 8E5, beta = 6E5Z2 = 55; beta+ = 7E5, beta = 6E5

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance for SampleA

MeasuredZ2 = 55; beta+ = 8E5, beta = 6E5Z2 = 55; beta+ = 7E5, beta = 6E5

�oQlLB]^=@h �w �PW�h3R@]JAld�R8��?S=�GH;SY�_VAlh"E�F�3�

Page 13: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

ce?BY�IVQDkJ;>d�Ql?Bk*&�°�&

�� )��w 4 FPg�M^h�GH;SY�_KADh�O§=�h3R�]JADd�RT;>=�h6Y�?S=�h6ce?BkJR@QDRfdfh3k~dNK;SR�R�M^?���k�QDk*�oQlLB]^=@h �S�>F

g�M^h"df=@QZ;SA*_K;>=@;SY�hdfh=@R<;>=�h�QDCJh3kad�QDc;SA*df?�d�M^h"_J=�h�HQl?B]JR8d��P?¨��hetHceh_JdNU;>LB;SQDk�NJd�MJh"�+;SAD]Jh3R�;>=�h�CJQl¢Uh=�h3k~dj�jF

�3¯

Page 14: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance for SampleB

MeasuredZ2 = 15; beta+ = 5E5, beta = 5E5Z2 = 15; beta+ = 7E5, beta = 5E5Z2 = 15; beta+ = 7E5, beta = 7E5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance for SampleB

MeasuredZ2 = 15; beta+ = 5E5, beta = 5E5Z2 = 15; beta+ = 7E5, beta = 5E5Z2 = 15; beta+ = 7E5, beta = 7E5

��QDLB]^=�h �S���PW�h3R�]JAld�R8��?S=�GH;SY _KAlh6s�F

�e}

Page 15: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedance for SampleE

MeasuredZ2 = 30; beta+ = 1.0E6, beta = 8.4E5Z2 = 30; beta+ = 1.2E6, beta = 8.4E5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedance for SampleE

MeasuredZ2 = 30; beta+ = 1.0E6, beta = 8.4E5Z2 = 30; beta+ = 1.2E5, beta = 8.4E5

�oQlLB]^=�h �3� �PW�h3R�]JAZRfdT�«?S=�GH;SY�_KAlh"O�F

�3�

Page 16: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

���(������*�+� � ()�3� ���¥�7��/@�r��%)��� ������ ���3���1�

g�M^h&=�h3ce?BkJRfdf=j]Jced�Ql?Bk1?S��d�M^h ®�g�¯S¯B°7_K=�?SIKAlh3Y �r;SR";Scce?BY _KADQDR�MJh3C���QDd�M^?B]^d�;Ska`1Rf?S_KMJQDR�d�QDc;>dfh3C¥QZka�Sh=@R@Ql?Bk;SAlLS?S=@Qld�MKY R�IUh3c;S]KRfh8d�M^h=�h8�Ph=@hT?BkJAl`6d�M^=@hhT�+;>=@QZ;>IKAlh3R�?S�UQDk~dfh=�h3RfdF�®�h3k^h=j;SADAl`SNaM^?��Ph�Sh=uN~QDk~�Sh=@Rfh8_J=�?SIVAlh3Y Rce?Bkad�;SQZk�Y ;Ska`&�>;>=@QD;>IKAlh3R3N>;SkKC�c;SkJk^?SdoI*h8R�?BAl�Sh3C!I~`&MJ;SkJC�F���h�MJ;u�Sh�C^h�Sh3Al?S_*h3C!;��Sh=�`�=@?SIK]JRfd¡;SAlLS?S=@QDd�MJY)Nc;SADAlh3C d�M^h�{���AD;u`Sh=!;SADLS?S=@Qld�MJY)N�d�MJ;>d!;SADAl?���R�]KR6df?1h¦�cQlh3k~d�Al`#ce?BY�_K]^dfh�AD;u`Sh=�d�MJQZc��Hk^h3R�Rfh3R��«?S=&d�M^h=@Y�;SA£�IK;>=�=@QDh=�ce?B;>d�QZk^LBR���;SR"�rh3ADA¡;SR6Y�`y=@QD;SC¨?Sd�M^h=6_K=�?SIKAlh3Y RÆ�jF���h�MK;3�Sh�;>_J_VADQlh3C1d�MJQDR";SAlLS?S=jQld�MJY df?)d�M^h=@Y�;SA£�IK;>=�=@QDh=Pce?B;>d�QDk^LBR8]JR@QDk^L�h3QDLBMadrdf?�d��Ph3AD�Sh6AD;3`Sh=@R�� �oQlLB]J=�h��3¯&QDADAZ]JRfdf=@;>dfh3R¡d�MJh�ce?Bk^ KLB]^=@;>d�Ql?Bk���?S=Ph3QlLBM~d8AD;3`Sh=@R3Fz|ka�Sh=�d�QZk^L d�M^h1QDY�_*h3CJ;SkJceh¥CJ;>d�;#�HQD;#d�MJh1����AD;u`Sh=�;SADLS?S=@Qld�MJY�Y�h3;SkJR�;SR�R�QlLBkJQZk^L ;#�>;SAD]^h¥df?����>NTd�M^h

d�MJQDc@�yk^h3R@RT?S��d�MJh6df?S_¥AD;u`Sh=�?S� �oQlLB]^=�h �3¯yNU;SkJC);SR�R�QlLBkKQDk^L�ce?BkJCJ]Jced�QD�yQld�QDh3R8df? d�M^h6=�h3Y�;SQDkJQDk^L!Rfh�Sh3k¥AD;3`Sh=@R3Nh3;Sc@M1?S�o��MJQDcjM�MJ;SR<d�M^h�R�;SY h�d�MJQDc@�ykJh3R�RN���NKd�MJ;>d�C^h Kk^h3R�d�M^h6=�h3Rf?BAZ]^d�Ql?Bk)?S�¡d�M^h�=�h3ce?BkJRfdf=j]Jced�Ql?Bk�F8g�MJQDR�QDR

GTD 111 Substrate

Al L 0σ=0

σ 1

σ 2

σ 3

σ 4

σ 5

σ 6

σ 7

σ=7.8Ε5

L

L

L

L

L

L

L

2O3

�oQlLB]^=�h��3¯ ��g�MJh�����AD;u`Sh=<QDk~�Sh=@R�QD?Bk�;SADLS?S=@Qld�MJY)N^QDk���MJQZc@M��©QDR8d�M^h�LBQl�Sh3k�=@h3Rf?BAD]^d�Ql?Bk�NH;SkKC�d�MJh"?SI �|h3ced�QD�Sh6QDRdf?�C^hdfh=@Y�QDk^h�� � ;SkJC 9 d�M^=�?B]JLBM� �+F

C^?Bk^hTIy`&;6_J=�?Hceh3R�R¡?S�*k^?BkJADQDkJh3;>=oADh3;SRfd|��R��y]J;>=�h3RNyQDk!��MJQDcjM!d�M^h�h3QlLBM~d¡�>;>=@QD;>IKAlh3R¡;>=@h�c@M^?BR�h3k df?6LBQl�Sh�d�M^hTI*h3Rfd Jd8df?�d�M^h"QDY�_*h3CJ;SkJceh�CJ;>d�;HF�g�MJh�QZka�Sh=@R@Ql?Bk�QDR8C^?Bk^h�QDk�Rfh�Sh=@;SA�Rfdfh_VRN^Rfd�;>=�d�QDk^L!��QDd�M�d�MJh�ce?BY _K]^d�;>d�Ql?Bk�?S�; d�;>IKADh6?S��CJ;>d�;HNU�«=�?BY2��MJQDcjM)d�M^h6 VkJ;SAiRf?BAZ]^d�Ql?Bk�QDR�C^hdfh=@Y QDkJh3C)I~`�QZkadfh=�_*?BAD;>d�QD?Bk�FPg�MJh6_J=�?Hceh3R�R�QZR��~]KQldfh��;SR�dNK;SkJC�QDRT�y]JQldfh6ce?BkKRfh=��>;>d�Ql�Sh�QDk)ce?BY�_V]^d�;>d�Ql?BkJ;SA�=@h3Rf?B]^=@ceh3RF���������������������y/������ �� ��"!$#%�&�'!�()� )� �!�#" �*!��,+.-0/2123 ��h&��QDADA�;>_J_VAl`�d�MJh��3����AD;u`Sh=�;SADLS?S=@Qld�MJY2df?

�3x

Page 17: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

d�M^h�Y�?HC^h3Ao?S�8d�M^h�®"g�¯S¯B° R�]JIKRfdf=@;>dfh d�MK;>d�QDR"R�M^?���k#QDk'��QDLB]^=�h��>F � � Nid�M^h�ADh3k^LSd�M�?S�8d�M^h�E�A 5 q 7 AD;3`Sh=QDR�¯>w�Y�QDce=�?BkJRN�;SkJC�d�M^h�Alh3k^LSd�MJR"?S�8d�M^h &�° ;SkJC & AD;3`Sh=jR�;>=�h�h3;Sc@M �wSw�Y QDce=@?BkJRF g�M^h�QDkadfh=���CJQ£¢�]JR�Ql?Bk�?Bk^hSNJz:9�NJQDR8LBQl�Sh3k�;SR<�>w Y QZce=�?BkJRF¡O�;ScjM�?S��d�M^h6h3Alh�Sh3k�AD;3`Sh=@R���Qld�MJQZk�d�M^h�ce?B;>d�QDk^L�°��r?S=��y_KQlh3ceh�QDR8LBQD�Sh3k;SR��+}�Y QZce=�?BkJRNy��MJQDcjM)Y�h3;SkJRTd�MK;>dTd�M^h"_J=�?SIKADh3Y CJh_Jd�M�hetydfh3kKCJRTdf?��Sx+}�Y QZce=�?BkJRF�g�MJh�AZQl�«df?>¢1?S��d�MJh6ce?BQDAQDR�_K=�h3R�]JY�h3C�df?�I*h���Y QZA��

��S�yF }�Y�QDce=�?BkJRj�jNV��MJQDcjM�QDR<d�M^h&;Sced�]J;SAoC^h_Jd�M�?S��d�M^h&ce?BQZA���Qld�MKQDk)d�M^h!;Sce=�`HADQDc

I*?3t�d�MJ;>d��8;SR�]JRfh3C)QZk)d�M^h6p��¨E��S�Sx ;SkJC¥®"g�¯S¯B°�hetH_*h=@QDY�h3k~d�RFg�M^h�ky]JY�h=jQDc;SA8hety_*h=@QZY�h3kad QZR�=@]Jk ;>d d�MJh¥¯S¯¨��=�h3�~]Jh3kJcQlh3R���QDk [�:<��� �¥wHFÁxS�+}^N�wHFÁ�H�>N�wHFÁ�+}~v~N��>FÌwB�+}^N

�>FÁ�S�S�yN��>F }a�H�>N��>FÁxyN*�>F v>�yN��>FÁ�S�H�>NK�yFÁ�>wB�yNK�yF }a�+}^NJ�yFÁxS�SxyNK�yFÁ�S�S�yNK¯yFD�3�S¯yNJ¯yF }J�3�yNK¯yFÁxS�S¯yNK¯yFÁ�Bv>�yNH}^FÁ�Bv>�yN^}^FÁ�S�S�yN^}^FÁ�yN�yFÁ�S�S�yNV�yFÁ�SxBv~NU�yFÁ�H�uv~NUxyFÁ�Bv>�yNVxyFÁx+}a�yNUv~FÌwB¯yNUv~F }a�S�yN�v~FÁ�S�S�yNV�yFÁ�S¯S�yNV�yFÁxSxS¯yNV�yFÌwB�S�yN*�yFÁ�+}S}^NV�yFÁ�S�S�yFPg�MJh3Rfh";>=�h�d�M^h�«=@h3�~]^h3kKcQlh3RTd�MJ;>d"n8OrGyz8]JRfh3C�QDk)d�M^h�CJh3Y�?BkJRfdf=@;>d�QD?Bk�?S�od�M^h3Ql=�R�`yRfdfh3Y ;>d<OPp�W�z���n8MJ;>=jAl?Sdfdfh�QDk�[¥;3`��>wSwB�yF��h�C^?6k^?Sd��yk^?��©��M~`�d�MJQZR¡Rfh3�~]Jh3kJceh�?S�U�«=�h3�y]^h3kJcQDh3Ro�r;SR�cjM^?BRfh3k�N~IK]^d�Qld¡QDR���MJ;>d¡�rh�]JRfh3C�QDk!d�M^hThetHh=@cQDR�hSFg�M^h ()�+�6/��K. �� =j]Jk�_J=�?HCJ]Jceh3C�d�M^h��«?BADAD?u��QDkJL�=�h3R@]JAld�R �b�;>=@QD;>IVAlh6{�?^F � � ¯ } � x v � � �w �S� �3��� )��w 4 � �yFÁ�S� �3�yFÁ¯ �3�yFÁ� �S�>F v �wHFÁ¯ �yFÌwB¯ �yFÌwB� v~FÁ¯S¯ xyFÁ�S� xyF }~v xyFÁ�+} �+} ( },@

GHh3kJR�Qldu� )��w � � � }^F v�} �yFÁ�S� v~FÁ�Bv �yFÁ�S� �3�yF v �3xyFÁ¯ �>wHFÁx �S�yFÁ� ¯S�yFÁ� ¯S�yFÁ� }a�yFÁ¯ �>FÁ¯>wg�M^h" K=@Rfd�h3Alh�Sh3k��+;>=jQD;>IKAlh3RT;>=�h�d�M^h�ce?BkJCK]Jced�Ql�HQld�Qlh3R8?S�od�M^h6h3Alh�Sh3k1AD;u`Sh=@R�����=�?BY\df?S_¥df?�I*?Sdfdf?BY��jNK;SkKC

d�M^h�d��Ph3AD�«d�M �+;>=jQD;>IKAlh�QZR6d�M^h�d�MJQDc��Hk^h3R�R�?S�Td�M^h�;SAD]JY QDky]JY!�µ?utHQZC^h AD;3`Sh=uNoY h3;SR�]^=�h3C QDk Y QZce=�?BkJRN�_KAD]JR6d�M^hADQl��df?>¢ ?S��d�M^h¥ce?BQDA¤F©� M^h3k©�rh�R�]JIJdf=@;Sced d�M^h¥ADQl��df?>¢�NP�Ph�;>=@h¥Alh��d���Qld�M©;#�+;SAD]Jh)?S�"�S� Y QDce=�?BkKR!�«?S=�d�M^hd�MJQDc@�yk^h3R@R�?S��d�MJh<?utHQDCJh�ce?B;>d�QDkJL^F�g�M^h<d�MJQl=@C�=�?u� ADQDR�d�R�d�M^h .ÁRfh3kJR@Qld�Ql�HQld�`�ce?yh¦�cQlh3k~d�R 0H?S��d�M^h�Rf?BAD]^d�Ql?Bk�Fog�MJQDR��QDADAyI*h�C^h Vk^h3C�QDk�d�M^h<CJQDR�c]JR@R�Ql?Bk&?S��k^?BkJADQDkJh3;>=¡_K;>=@;SY�hdfh=rh3Rfd�QDY ;>d�QD?Bk�d�MJ;>dPQZR¡LBQl�Sh3k�QZk!d�M^h�k^hetHd�Rfh3ced�Ql?Bk�FGH]^¦�ceh)Qld�df?#R@;3`ªd�MJ;>d�d�M^h�R�Y�;SADAlh=�d�M^h�ky]JY�IUh=!d�M^h�Y ?S=�h�Rfh3kJR�QDd�Ql�Sh�d�M^h�Rf?BAD]^d�QD?Bkªdf?�d�MJ;>d _K;>=�d�QZc]JAD;>=�+;>=jQD;>IKAlhSF�:<h3kJcehSNo�rh�Rfhh�d�MK;>d�d�M^h�R�?BAD]^d�Ql?Bk�QDR�Y�?BRfd�R�h3kJR�Qld�Ql�Sh�df?¥d�M^h d�MJQZc��Hk^h3R�R"?S�Td�M^h�?3t^QDC^h�ce?B;>d�QDkJL^N��Qld�M#CJh3ce=�h3;SR�QDk^L¥Rfh3kJR�Qld�QD�yQld�QDh3R�df?¥d�M^h�C^hh_*h=�AD;u`Sh=@RN¡;SR��rh��r?B]JADC#hety_*h3ced�QZk#;�?Bk^he��CKQDY�h3kJR�QD?BkJ;SA¡AD;3`Sh=_J=�?SIKADh3Y ?S��d�MJQZRTd�`y_*h"��Qld�M�het^cQld�;>d�Ql?Bk�;SkKC�C^hdfh3ced�Ql?Bk�?ycc]^=jQDk^L!?BkJAl`�;>I*?u�Sh6d�M^h��P?S=��y_KQlh3cehz|k�?S=@C^h=�df?�C^hdfh=@Y QDkJh6d�M^h�ce?BkKCJ]Jced�Ql�HQld�Qlh3R�?S�¡d�M^hE&�°­;SkJC &ªAZ;3`Sh=@RNU�rh�;3�Sh=j;>LSh�d�M^h�=�h3R@]JAld�R�?��Sh=��

�wSw+��Y QDce=�?Bk�R�AZ;>IKRNyd�M^h� J=jRfd�I*h3QDk^L�d�M^h &o°�AZ;3`Sh=3N^;SkJC�d�M^h�Rfh3ce?BkJC�d�M^h &1AD;u`Sh=3F�W�h3Y�h3Y�I*h=@QZk^L6d�MJ;>d8h3;Sc@M��Y ;>d�M^h3Y ;>d�QZc;SA«�8AD;u`Sh=�?S�od�M^h6QDk~�Sh=@R�Ql?Bk);SADLS?S=@Qld�MJY\QZR��+}�Y QDce=@?BkJRNH�Ph�MJ;3�Sh

�+} ) �¤�3(Á�S�<° �3�3(Á¯<° �3�3(Á��° �S��( vS�i°$}>)��w (Á¯�

�S�3x>w (Áx�

�wSw )�&�°�>w ) �w (Á¯<° �+} ) �¤�3(ÌwB¯<° �3(ÌwB��°©v=(Á¯S¯B�i° � )�x3(Á�S�

��+}ax3( }

��wSw )�& �|�u�

�^=�?BY d�MKQDRr�Ph6ce?BkJcAZ]JC^h�d�MJ;>dTd�M^h"ce?BkJCJ]Kced�Ql�yQDd�`�?S��d�M^h�&�°5AD;u`Sh=�QDR��S��(ÁxH�F)1�w 4 G��+Y ;SkJC�?S��d�M^h�&#AD;3`Sh=�3( }ax )#�w 4 G-�+Y)F�oQDkJ;SADAD`SN>QZk�?S=jC^h=¡df?6c;SADc]JAD;>dfh8d�M^hTd�MKQDc��Hk^h3R�R�?S�Ud�M^hTQDkadfh=���CJQ£¢�]JR�Ql?Bk��?Bk^hSNa�rhT;3�Sh=@;>LSh<?u�Sh=�d�MJh8AZ;SRfd�x+}

Y QDce=�?BkKR8?S��d�MJh"_J=�?SIKAlh3Y LS=jQDC�NH��MJQDcjM��Ph��yk^?���Y&]JRfd�ce?Bk~d�;SQDk)I*?Sd�M)d�M^h�z<91;SkJC1®�g��!�S�S�>FPg�MJh6;3�Sh=@;>LShce?BkJCJ]Jced�QD�yQld�`¨?S��d�M^h3Rfh�x+}1Y QZce=�?BkJR�QZR��|�3x�)#x3(Á�S��° �+}B)§�¤x3( }~v6° x3(Á�+}~�f���>x+}

�x3( }~vH� )��w 4 No?S��ce?B]^=@R�h��jF

X"hh_KQDkJL�QDk1Y QDkJC¥d�MJ;>d�d�M^h!ce?BkJCJ]Jced�QD�yQld�`�?S��d�M^h!z:9 QDR�¯3(Á¯S� )$�w,4!G-�+Y ;SkKC¥?S��d�M^h�®�g��!�S�S��R�]^IKR�df=@;>dfhv=(Á� )#�w 4 G��+Y)NJ�rh�LShd<d�MJ;>d�d�M^h�_Uh=jceh3kad�;>LShSN ��NJ?S�od�M^h&x+}�Y QDce=@?BkJRTd�MJ;>d�QDR�ce?u�Sh=@h3C�Iy`�d�M^h6z:9�QDRTLBQD�Sh3kI~` x3( }~v

�¯3(Á¯S� )�� °�v=(Á� ) �|��(# �8�jNP?S= �

�w (Á�S�Bv~FC�^=�?BY d�MJQDR!�rh�LShd d�MJ;>d�d�MJh�Alh3k^LSd�Mª?S��z<9 QDR

w (Á�S�Bv8)�x+}��3�3(Á�S�yFP��h&R�]JY Y�;>=@Ql�h�d�M^h3Rfh6=@h3R�]JAld�RTQDk�d�MJh"�«?BADAD?u��QDkJL&d�;>IVAlh �

nr?BY�_K]^dfh3C q�=jQlLBQDkJ;SA&o° �S��(ÁxH� )#�w,4 �3�3(Ìw )#�w,4& �3( }ax8)#�w 4 �3( }>)#�w 4z:9 �3�yFÁ�S��Y QDce=�?BkKR �>wHFÌw�Y QDce=@?BkJR

E<AI5q�7 �S�yFÌw�Y�QDce=�?BkJR ¯>w Y QDce=�?BkKR

�uv

Page 18: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

��������� ��� � 3��^/���� � �� ���/�� �� �� -�! / ! (&� ��� ! .�,+ !� .��.�� +.� ( ! +�%�$4������� ��� !�� +.-0/%1�3 g�M^hp��¨E��S�Sx�ce?B;>d�QDk^L�QDR�Y�?S=@h�ce?BY�_KADQZc;>dfh3C�Y�hd�;SADAZ]^=�LBQDc;SADAD`�d�MJ;Sk�d�M^h&®�g�¯S¯B°!NKI*h3c;S]JRfhSNU;SR�d�M^h�;SAZ]JY QDky]JYCJQ£¢�]JRfh3Ro?B]^d¡df?�=�h�«?S=jY d�M^h�_J=@?Sdfh3ced�Ql�Sh�?3t^QDC^h<ce?B;>d�QDk^L^N~;SkKC ;SADRf?6CJQl¢*]JR�h3R¡QDkadf?�d�M^h�R�]^IKR�df=@;>dfhSNad�M^h=@hT?ycc]^=jR;#df=@;SkKRf�«?S=jY ;>d�Ql?Bk ?S�"IUhd�; _KMJ;SRfh1{<QZE<A�QZkadf?$; LB;SY Y�; Y ;>df=@Qlt©?S�6Rf?BADQDC©kKQDc��Sh3A�Rf?BAD]^d�QD?Bk�N8��MJQDcjM©C^?yh3Rk^?Sd6;>_J_*h3;>=6QDk¨d�M^h�®�g<¯S¯B° ce?B;>d�QDk^L^F�g�MKQDR�LB;SY Y ;�Y ;>df=jQ£t1Y ;SkKQl�«h3R�d�R"Qld�Rfh3Al�r;SR6;�I*hd�;+�µ_KMJ;SRfh C^h_VAlhdfh3C�?Bk^h©��c;SADAlh3C . 9U?BkJhB��0 �jN<=�h3R@]JAld�QDk^L$QDk ; .ÁRfd�;SkJCJ;>=@C Y�?HC^h3A108R�M^?���k QDk ��QDLB]^=�hª�e}^F��J]^=@d�M^h=3N��<MJQDAlh¥d�M^hce?BkJCJ]Jced�QD�yQld�`§?S��d�M^h��+;>=jQl?B]JR��?Bk^h3R)=�h3Y�;SQDkJR� ^tHh3C ?u�Sh=�d�QZY�hSN�d�M^h#AZ;3`Sh=f�µd�MJQZc��Hk^h3R�Rfh3R)?S�&d�M^h3Rfh¨�?Bk^h3Rc@MJ;SkJLSh3RF6g�MJQDR<_J=�h3R�h3kad�R�;�_J=�?SIKADh3Y\d�MJ;>d"QDR�CJ]J;SA�df?�d�M^h�®�g�¯S¯B°&N�QDk¥��MJQZc@M¥d�M^h&ce?BkKCJ]Jced�Ql�HQld�`¥c@MJ;Sk^LSh3R3N��MJQDADh�d�MJh6d�MJQDc@�yk^h3R@R�?S�od�M^hF&�° ;SkJC�& �?Bk^h3R�=@h3Y ;SQDkJRT Jtyh3C�Frg�M^h6p��1E��S�Sx _K=�?SIKAlh3Y QDR�;�Y�?S=�h�QDka�Sh=jRfh_J=�?SIKADh3Y)F

Conductivity (x 10 5 )

7.8

Zone2 Beta Zone1 IZ GTD1110

Depth

3.32

7.0

8.4

�oQlLB]^=�h��e} �TGyd�;SkJCJ;>=jC�Y�?HC^h3A�?S�od�M^h�p��1E��S�Sx�d�MJh=@Y ;SA�IV;>=�=@Qlh=�ce?B;>d�QDkJL^F8g�M^h6ce?BkJCJ]Jced�QD�yQld�QDh3R�;>=�h�C^hdfh=��Y QDk^h3C���=�?BY\Y h3;SR�]^=�h3Y�h3k~d�RT?Bk)�Hk^?���k�R�;SY�_VAlh3RF

��R�QDk^L�d�MJhPR�;SY�hPRfhd�]^_!;SR���?S=�d�M^h8®�g�¯S¯B°&N>�rh�df?y?S��AD;>I*?S=@;>df?S=�`"CJ;>d�;�?Bk�;�ky]JY�I*h=i?S�^ce?B]^_*?BkH��R�;SY�_VAlh3R?S��p��¨E��S�Sx&ce?B;>d�QDkJLBRPd�MK;>drMJ;SC�]JkJCJh=�LS?Bk^h��>;>=@Ql?B]KR�Alh�Sh3ADRP?S�iC^hdfh=jQl?S=@;>d�Ql?Bk�F¡g�MJh<Y�h3;SR�]J=�h3C�QDY _Uh3CK;SkJceh3R;>=�h¥R@M^?u��k QDk �oQlLB]J=�h �3�yF�z�d�R@M^?B]JADCªI*h¥kJ?Sdfh3C�NT?BkJceh¥;>LB;SQZk�N�d�MJ;>d�d�M^h3Rfh¥CK;>d�; ;>=�h1cAlh3;Sk^h=�d�MJ;Sk d�M^hce?S=�=�h3Rf_*?BkJCKQDk^L)CJ;>d�;���?S=&d�M^h�®�g�¯S¯B°!N��<MJQDc@M R�M^?B]JADC�kJ?Sd�I*h df?y?¥R�]^=@_J=@QDR�QZk^L^N�R�QDkJceh d�MJh�Y�h3;SR�]J=�h3Y�h3k~d�R�Ph=@h<d�;>�Sh3k);>d8Alh3;SRfdrd��r?>�µ`Sh3;>=@R�;>_V;>=�dF¡��h�d�M^h3k�;>_K_KADQlh3C�d�M^h�����AZ;3`Sh=�;SAlLS?S=@QDd�MJY)N~QZk��Sh=�`�Y�]JcjM�d�M^h<R�;SY hY ;SkJk^h=�;SR<C^h3R�ce=@QDIUh3C�;>I*?u�ShSNVdf?�QDk~�Sh=�d�d�M^h3R�h�CJ;>d�;HFg�M^h�=�h3R�]JADd�R6?S�Td�M^h�QDka�Sh=jR�Ql?Bk#_K=�?yceh3R@R�;>=�h� Jdfdfh3C df?¥d�M^h .ÁRfd�;SkJCJ;>=jC Y�?HC^h3A10i?S�Td�M^h�p��1E��S�Sx1g�s�n�N

�3�

Page 19: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedances (Top)

b1b2b3b4b5w3w5

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedances (Top)

b1b2b3b4b5w3w5

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30 35 40 45 50

Res

ista

nce

Frequency (MHz)

Real Part of Normalized Impedances (Bottom)

b1b2b3b4b5w3w5

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0 5 10 15 20 25 30 35 40 45 50

Rea

ctan

ce

Frequency (MHz)

Imaginary Part of Normalized Impedances (Bottom)

b1b2b3b4b5w3w5

�oQlLB]^=�h��3� �<W�h3;SAT��Alh��dj�<;SkJC1QDY ;>LBQDkJ;>=@` ��=@QlLBM~dj�T_K;>=@d�R<?S��d�M^h&kJ?S=@Y ;SADQl�h3C¥c@MJ;SkJLSh QDk�QDY _Uh3CK;SkJceh���?S=�d�M^h.Ìdf?S_ 0Kp��1E��S�Sx R�;SY _KAlh3R���]^_K_Uh=8d��P?� JLB]^=�h3Rj�r;SkKC2.ÌI*?Sdfdf?BY�0Kp��¨E��S�Sx R�;SY�_VAlh3R6��Al?u�rh=�d��P?� JLB]^=�h3RÆ�jF

�3�

Page 20: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

d�MJ;>d!QDR�R�MJ?u��k QDk'�oQlLB]^=@h¥�e}^F¥g�M^h��>;SAD]^h3R�?S�Td�M^h�ce?BkKCJ]Jced�Ql�HQld�`¨?S��d�MJh��>;>=@Ql?B]JR�AD;3`Sh=@R!;>=�h�C^hdfh=@Y QZk^h3C�«=@?BY\QDk~�Sh=@R�Ql?BkJRr?Bk)�Hk^?���k�R�;SY�_VAlh3RF¡z|k�d�MJQDRTY ;SkJkJh=3N^�Ph6;>=@h�;>IKAlh�df?�C^hdfh=jY QDk^h�d�M^h6d�MKQDc��Hk^h3R�R8?S�oh3;Sc@M�?Bk^hSF�g�MJh"=�h3R�]JAld�RT;>=@h6d�;>IK]JAD;>dfh3C�QDk)g�;>IVAlh3R���;SkJC¥¯yF

GH;SY _KAlh nr?B;>d�QDk^L n8?B;>d�QDk^L E��Sh=@;>LSh nr?BY�_K]Jdfh3Cz|C^h3k~d�Ql Kc;>d�Ql?Bk mi?yc;>d�Ql?Bk z|C^h3k~d�Ql Kc;>d�Ql?Bk g�MJQDc@�ykJh3R�R g�MKQDc��Hk^h3R�R

��Y QDce=�?BkKRj� ��Y QZce=�?BkJRj�z|kJk^h=���Q£¢�]JR�Ql?Bk �wHFÁx �wHFÌw

gi?S_¨GHQDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C� �sPhd�;�p�MJ;SR�h 9U?Bk^h �3¯S�yFÌw �3¯S�yFÌw

�3�S�>w,�����f;SR�ce?B;>dfh3C�� q�]^dfh=�srhd�;���h_KADhdfh3C� ���s8AD]^he�@�u� z|kJk^h=���Q£¢�]JR�Ql?Bk �wHFD� �wHFÌw

sr?Sdfdf?BY G^QDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C� �sPhd�;�p�MJ;SR�h 9U?Bk^h �e}BwHFÁ� �e}a�yFÌw

q�]^dfh=�srhd�;���h_KADhdfh3C� �

z|kJk^h=���Q£¢�]JR�Ql?Bk �S�yF } �>wHFÌwgi?S_¨GHQDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C �yFÁ� �yF }

sPhd�;�p�MJ;SR�h 9U?Bk^h �3�S�yF } �3�>wHFÌw�3�S�>w,�����S�>w�ce`ycAlh3R q�]^dfh=�srhd�;���h_KADhdfh3C �e}^FÁ� �uv~F v

��s8AD]^he���B� z|kJk^h=���Q£¢�]JR�Ql?Bk �S�yFÁ� �S�yFÁxsr?Sdfdf?BY G^QDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C �yFD� �yFD�

sPhd�;�p�MJ;SR�h 9U?Bk^h �S�e}^FÁ� �S�3�yFÁ�q�]^dfh=�srhd�;���h_KADhdfh3C �S�>FÁx �>wHFÌwz|kJk^h=���Q£¢�]JR�Ql?Bk �+}^F } �SxyFÁ¯

gi?S_¨GHQDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C �e}^FÁ� �e}^F }sPhd�;�p�MJ;SR�h 9U?Bk^h �+}^FÁx �S¯yFÌw

�3�S�>w,�����>wSw�ce`ycAlh3R q�]^dfh=�srhd�;���h_KADhdfh3C �uv~FÁ� �3�yFÁ���s8AD]^he��¯B� z|kJk^h=���Q£¢�]JR�Ql?Bk �+}^FÁ� �S�yFÁ�

sr?Sdfdf?BY G^QDC^h z|kJk^h=�srhd�;���h_KAlhdfh3C �3xyFÁ� �3�yFÁ¯sPhd�;�p�MJ;SR�h 9U?Bk^h �S�yFÌw �+}^FÁ�

q�]^dfh=�srhd�;���h_KADhdfh3C �3�yF v �3�yF v

g�;>IKAlh�� �8nr?BY�_K;>=@QZRf?Bk�?S��Y h3;SR�]^=�h3C�;SkKC�ce?BY�_K]^dfh3C�ce?B;>d�QDk^L d�MJQZc��Hk^h3R�Rfh3R��«?S=�d�MJh6p��¨E��S�Sx dfh3RfdFz|k6Rfh�Sh=@;SA~c;SRfh3RN+d�M^h� KkJ;SASce?BY _K]^dfh3C6ce?BkJCK]Jced�Ql�HQld�`�_J=�?S KADh3R*�Ph=�h¡?SIKd�;SQDk^h3C"Iy`";8_J=�?Hceh3R�R�?S�#0 �«?Hc]JR�R@QDk^L 0

d�M^h&����AZ;3`Sh="QDk~�Sh=@R�Ql?Bk¥;SAlLS?S=@Qld�MJY�F8g�MJQDR�QDR<;Scce?BY�_KADQZR�M^h3C)Iy`�Rfd�;>=�d�QDkJL���Qld�M�; =@;>d�M^h=�ce?B;>=@Rfh&LS=@QDC�NJ��MJQDcjM;SADAl?���R�d�M^h�srhd�;!E<AD]KY QDkJQDCJh 9U?BkJh<;SkJC�z�k~dfh=@CJQl¢*]JR@Ql?Bk ;SkJC�z�kJkJh=Psrhd�;!�<h_VAlhdfh3C*9*?Bk^h&��df?�I*h<LSh3k^h=@;SADAl`Al?Hc;>dfh3C�=�h3AD;>d�Ql�Sh�df?�d�M^h�®�g��!�S�S��GH]^IKRfdf=j;>dfhSF g�M^h3k¨�rh =�h Kk^h!d�M^h�LS=jQDC¨I*hd��rhh3k#d�M^h�srhd�;�E�AD]JY�QDkJQDC^h9U?Bk^h!;SkJC#®�g��!�S�S��GH]^IVRfdf=@;>dfh&df?)LShd�;�Y�?S=@h&_K=�h3cQDRfh&�+;SAZ]^h���?S=�d�M^h&�+;>=@QD?B]JR��?Bk^h!IU?B]KkJCJ;>=@Qlh3R3NV;SR��rh3ADA;SRT;�Y ?S=�h�_J=�h3cQDRfh��>;SAD]^h���?S=Td�M^h�ce?BkJCJ]Jced�QD�yQld�` ?S� 9U?BkJh!��;SkJC�d�M^h�z|kadfh=@CKQ£¢*]KR�Ql?Bk 9*?Bk^hSF¡z�k�d�MJQDRrY ;SkJkJh=3N�Ph��rh=�h ;>IKADh&df?�AD?yc;>dfh d�MJh&z|k~dfh=@CJQ£¢�]JR�Ql?Bk 9U?Bk^hSN�;SkJC�C^hdfh=@Y QZk^h&QDd�R"ce?BkJCJ]Jced�Ql�HQld�`���?S=6d�M^h*0Ì;SR|��ce?B;>dfh3C 0R�;SY�_KADh3RNas��s©;SkJC s��g"Fyg�MJQDR¡QZR�;"��;SQl=@Al`&CJQl¦�c]JADdoce?BY _K]^d�;>d�Ql?Bk�df?&c;>=�=�`!?B]^d��<Qld�M^?B]^d�R�]Kc@M ;80ÌY&]JAld�QDLS=@QDC=�h�?BkJQDkJL 0^dfh3c@MJkJQZ�~]^hSFg�M^h�d�;>IK]JAD;>dfh3C�=�h3R�]JAld�R<ce?Bk^ J=@Y\d�MJ;>d<d�MJh�QDk~�Sh=@R�Ql?Bk�;SADLS?S=@Qld�MJY2_J=�?HCJ]Jceh3RThet^ceh3ADAlh3k~d�=�h3ce?BkKRfdf=@]Jced�Ql?BkKRN

��Qld�M��Sh=�`�LS?y?yC)=@h3Rf?BAD]^d�Ql?BkKRFoz�k)_V;>=�d�QDc]JAD;>=uN~�rh�k^?Sdfh6d�MJh"LS?~?HC�;>LS=�hh3Y�h3k~d�I*hd��Phh3k)d�MJh�ce?BY�_K]^dfh3C);SkKCY�h3;SR�]^=@h3C�d�MJQZc��Hk^h3R�R<?S�¡d�M^h�I*hd�;+�µ�?Bk^h!?S�¡h3;ScjM�R�;SY�_KAlhSF<g�MJQDR�QZR�d�M^h!ce=@Qld�QZc;SAiCJ;>d�]JY�NV��MJh3k�Qld�ce?BY�h3R�df?C^hdfh=@Y QZkJQDk^L&d�M^h6=�h3Y�;SQDkJQDk^L!ADQl��h�?S�od�M^h"d�M^h=@Y ;SA�IK;>=�=@Qlh=�ce?B;>d�QZk^L^F

�>w

Page 21: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

G^;SY�_KAlh nr?B;>d�QDkJL nr?B;>d�QDkJL E<�Sh=@;>LSh nr?BY _K]^dfh3Cz�C^h3k~d�Ql Kc;>d�QD?Bk m�?Hc;>d�Ql?Bk z�CJh3kad�Ql Vc;>d�Ql?Bk g�MKQDc��Hk^h3R�R g�MJQDc@�yk^h3R@R

��Y�QDce=�?BkJRj� ��Y QDce=�?BkJRÆ�z�kJkJh=���Q£¢*]KR�Ql?Bk �S�yFÁ� �SxyF }

g�?S_1GHQDCJh z|kJk^h=�srhd�;��<h_VAlhdfh3C ¯+}^FÌw ¯S¯yFÌwsrhd�;�pPMJ;SRfh 9U?Bk^h xS�yFÁx xS¯yFÁ�

�3�S�>w,���@�wSwSw�ce`HcAlh3R q�]Jdfh=�srhd�; ��h_KAlhdfh3C ¯Bv~FÁ� }J�>FÁ���s8AD]Jhe�µ}~� z�kJkJh=���Q£¢*]KR�Ql?Bk �S¯yF v �S�yFÌw

sr?Sdfdf?BY GHQDC^h z|kJk^h=�srhd�;��<h_VAlhdfh3C ¯S�yFD� }BwHFD�srhd�;�pPMJ;SRfh 9U?Bk^h �S�yFÁx �S¯yFÌw

q�]Jdfh=�srhd�; ��h_KAlhdfh3C ¯S¯yFÁ� ¯+}^FÁ�z�kJkJh=���Q£¢*]KR�Ql?Bk �S¯yFÁx �+}^FÌw

g�?S_1GHQDCJh z|kJk^h=�srhd�;��<h_VAlhdfh3C �S�3�yF v �S�3�yFÌwsrhd�;�pPMJ;SRfh 9U?Bk^h

� ��3�S�>w,���@�3�S¯S��ce`HcAlh3R q�]Jdfh=�srhd�; ��h_KAlhdfh3C�

¯+}^FÁ¯��s8AD]Jhe���B� z�kJkJh=���Q£¢*]KR�Ql?Bk �S�yF } �S�yFÌw

sr?Sdfdf?BY GHQDC^h z|kJk^h=�srhd�;��<h_VAlhdfh3C xH�>FÁ� x+}^FÌwsrhd�;�pPMJ;SRfh 9U?Bk^h �3�yFÁ� �3xyFÌw

q�]Jdfh=�srhd�; ��h_KAlhdfh3C }a�yFÁ� }axyFÁ¯z�kJkJh=���Q£¢*]KR�Ql?Bk �3¯yFÁ� �3¯yF v

g�?S_1GHQDCJh z|kJk^h=�srhd�;��<h_VAlhdfh3C }axyFÌw }a�yFÁ�srhd�;�pPMJ;SRfh 9U?Bk^h ¯S�yFÁ� ¯+}^FÁ�

�3�S�>w,����¯S�>wSw�ce`HcAlh3R q�]Jdfh=�srhd�; ��h_KAlhdfh3C �>wHFÁ� }S}^FÁx��� MJQldfhe���B� z�kJkJh=���Q£¢*]KR�Ql?Bk �e}^FÁ� �3�yFD�

sr?Sdfdf?BY GHQDC^h z|kJk^h=�srhd�;��<h_VAlhdfh3C }a�yFÁ� }a�yFÁ�srhd�;�pPMJ;SRfh 9U?Bk^h �Bv~FÁx �S�yFÁx

q�]Jdfh=�srhd�; ��h_KAlhdfh3C }axyFÁ� �S¯yFD�

g�;>IKAlh�¯ �8nr?BY�_K;>=@QZRf?Bk�?S��Y h3;SR�]^=�h3C�;SkKC�ce?BY�_K]^dfh3C�ce?B;>d�QDk^L d�MJQZc��Hk^h3R�Rfh3R��«?S=�d�MJh6p��¨E��S�Sx dfh3RfdF

�H�

Page 22: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

�����#���r01�*�+� ��� ����� 0�� �����2��;�-� " .)0)46�r�%$�� �&�"�����

q�]^=� J=jRfd"ce?BkJcAD]JR�QD?Bk¥QDR�d�MK;>d�d�MJh�®�g��!�S�S� R�]^IVRfdf=@;>dfh�MJ;SR";)ce?BkJCJ]Kced�Ql�yQDd�`�?S��v=(Á� ) �w 4 G��+Y�N�;SR"QDkd�M^h<p��1E��S�Sx&Y�?HC^h3A¤F¡g�MJQDR��r;SRr�Sh=@Ql Kh3C�;>drd�M^h�?B]^d�R�hdNHQZk ?S=@C^h=rdf?&=�h3Y�?u�Sh�;��+;>=@QZ;>IKAlh���=�?BY7d�M^h�GH;SY _KAlhE�N�GH;SY _KAlh�s�No;SkJC©GH;SY�_KADh�O�_J=�?SIVAlh3Y RF¨sr` ]JR�QDkJL¥QDY�_*h3CJ;SkKceh�Y�h3;SR�]J=�h3Y�h3k~d�R���=@h3;SAT;SkJC QZY ;>LBQDkJ;>=�`ce?BY�_*?Bk^h3k~d�Rj�¡?��Sh=8d�M^h���=�h3�y]^h3kJce`�=@;Sk^LSh<?S���Æ���>w�[�:<�SNH�Ph<LB;SQDk�QZkJR�QlLBM~d�QDk~df?�d�M^h�Rfd�;>d�]JRP?S��h3;Sc@M�ce?B;>d�QDkJL^F:<QDLBMH�µ�«=@h3�~]^h3kKce` Y�h3;SR�]^=�h3Y h3kad�Rr?S��d�M^h�k^?S=@Y ;SAZQl�h3C =�h3;Sced�;SkKceh"LBQl�Sh�]KRP;�LS?~?HC�h3Rfd�QDY ;>dfh�?S��d�M^h<d�MJQDc@�yk^h3R@R?S� 9��yN<��MJQDcjM�N�QDk d�]^=jk�N�LBQl�Sh3R)]JR�Rf?BY h#QDkJR�QlLBM~d�QZkadf?ªd�M^h�Rfd�;>d�]JR�?S��d�M^h�ce?B;>d�QDk^L^N�I*h3c;S]JRfh¨d�MJQDR�AD;3`Sh=ce?BkJR�QDR�d�R�?S�iE�A653q%7+Ny��MJQDcjM�LS=�?���RrI~`�d�M^hF.ÁR�;Sce=jQl Kceh,0H?S��d�M^h &�°�?u�Sh=@AD;u`�ce?B;>d�QDkJL!;SkKC!��?S=Pd�MJh &¨I*?BkJC�ce?B;>dF�J]^=�d�MJh=@Y�?S=�h�d�M^h3R�h�MJQlLBMH�µ��=�h3�y]^h3kJce`1Y�h3;SR�]^=�h3Y h3kad�RN�h3Rf_*h3cQD;SADAl`¥?S�Pd�MJh�k^?S=@Y ;SAZQl�h3C¨=�h3R�QDR�d�;SkJcehSN�M^h3AD_#]JRdf?�h3Rfd�QDY�;>dfh d�M^h ce?BkJCJ]Kced�Ql�yQDd�`�?S� &�°!N���MJQDcjM�QDR";)_J=jQDkJcQl_K;SA�C^hdfh=@Y QZkJ;Skad"?S�rd�M^h�=�h3Y�;SQDkJQDk^L)ADQD�«h&?S�8d�M^hce?B;>d�QDk^L^F�mi?u�rh=<��=�h3�y]^h3kJcQlh3RT;>=@h�]JRfh��]JA*QDk�C^hdfh=jY QDkJQDkJL�d�M^h6ce?BkKCJ]Jced�Ql�HQld�`�?S�od�M^h�& AZ;3`Sh=3F{<hetydN¡�rh�ce?BkKcAD]JC^h�d�MJ;>d�d�MJh�9��¥AD;u`Sh=&?S�<G^;SY�_KAlh�E MJ;SR!;�d�MJQZc��Hk^h3R�R�?S��;>IU?B]Jd!�S�¥Y QDce=�?BkKRN��<Qld�M

d�M^hF&�° AD;3`Sh=�MJ;3�HQDk^L ; ce?BkKCJ]Jced�Ql�HQld�`�?S�oI*hd��rhh3k1v )#�w 4 ;SkJC�� ) �w 4 G-�+Y)NK;SkJC)d�MJhF& AD;u`Sh=<MJ;u�yQDkJL�;ce?BkJCJ]Jced�QD�yQld�`�?S�¡x8)#�w 4 G-�+Y)F�g�MJQZRrce?S=@=�h3Rf_*?BkJCJR8df?�; & �C^h_KADhdfh3C�AD;3`Sh=uFGH;SY�_VAlh�O�QDR�d�M^h�I*h3Rfd�?S�rd�M^h�d�M^=�hhSN�MJ;3�HQDk^L); 9����µd�MJQDc��Hk^h3R�R�?S��¯>w)Y QZce=�?BkJRN�;�&o° ce?BkJCJ]Jced�Ql�HQld�`¥?S�

cAl?BRfh)df?©��(Á� )§�w,+�G��+Y)Nr;SkJCª;2& �ce?BkJCJ]Kced�Ql�yQDd�` ?S���3( }/)§�w 4 G��+Y)F z|kJC^hh3C�N�Ql���rh�;SR�R�]JY h�d�MK;>d ;Sk.Á;SR|��ce?B;>dfh3C 0KR@;SY�_KAlh�MJ;SR8;;&�°5ce?BkJCJ]Jced�QD�yQld�` ?S����(Á� )¥�w + G��+Y�Ny;SkJC�;;&#ce?BkJCJ]Kced�Ql�yQDd�` ?S�o�3( };)¥�w,4"G-�+Y)N;SR�QDk�d�MJh6p��¨E��S�Sx�ce?B;>d�QDk^L^NKd�MJh3k¥GH;SY�_KADh�O QDR�;SADY ?BRfd�QDk);Sk�;SR|��ce?B;>dfh3C¨ce?BkJCKQld�Ql?Bk�FGH;SY�_VAlhTs$QZR�d�MJh�Y�?BRfd�ce?Bk^��]JR�QDkJL�df?6QZkadfh=�_K=�hdF�g�M^hT=�h3R�]JADd�R�QZkJCJQDc;>dfhT;E9���C^h_Kd�M!?S�K?BkJAl`��3�"Y QDce=@?BkJRN

��M^h=�h3;SRid�M^h &�°©;SkJCF&�AD;3`Sh=jR�MJ;u�ShP;�ce?BkKCJ]Jced�Ql�HQld�`�?S�H?BkJAl`";>I*?B]^di� )<�w,4PG-�+Y)F�g�M^h3Rfh�Al?�� ce?BkJCJ]Kced�Ql�yQDd�Qlh3RR�]^LSLSh3RfdPd�MJ;>d�d�M^h<AD;3`Sh=rQDR¡�rh3ADA£�µ�r?S=@k�NB��MKQDc@M R@M^?B]JADC!ce?S=�=�h3R�_U?BkKC�df?�;6Y&]JcjM�AD;>=�LSh=��+;SAD]JhT?S�Ud�MJh�d�MJQDc@�yk^h3R@R?S� 9��yF#p�h=@MJ;>_VR&Y&]JcjM ?S��9��¥MJ;SR&IUhh3kª;>IKAZ;>dfh3C$CK]^=@QDk^L¥]JRfhSN�;SkJC$�rh�Rfhh�?BkJAD` ;¥R@Y ;SADAP=�h3R�QDCJ]K;SA¤NoIK]^dd�M^h�Y�?S=@h6ADQl�Sh3Al`�hety_KAZ;SkJ;>d�Ql?Bk�QDR�d�MJ;>d��rh�;>=�h�Rfh3kKR�QDk^L!d�M^h6_K=�h3Rfh3kJceh"?S��.Áce=@;>�h3C1ce=@;Sc��HQDk^L 0VQDk�d�M^h�ce?B;>d�QDkJL^N��MJQDcjM��P?B]KADC)QDk~�+;SADQZCJ;>dfh�d�M^h�R�QDY _KAlh�?Bk^he��CJQDY�h3kKR�Ql?BkJ;SAU��?B]^=f��AD;u`Sh=<Y�?HC^h3A*d�MJ;>d��rh�;>=�h�]JR�QDk^L^Fg�M^h3R�h =�h3R�]KAld�R�;>LS=�hh$��Qld�M d�M^h$Y hd�;SADAD]^=�LBQZc;SA"hetH;SY�QDkJ;>d�Ql?BkJR¥;SR¥ce?Bk~�Sh`Sh3C�df? ]JR�QDk�;Sk�h3Y�;SQDA6?S�

�e}~q6n8g�wB�yF

����������������

�£���&OPAlh3cedf=@QDc�p�?u�rh=�W�h3Rfh3;>=@cjM©z|kJRfd�Qld�]^dfhSN .Áp�h=��«?S=jY ;SkJceh���h3Y�?BkJR�df=@;>d�Ql?Bk©p�=�?Sdf?yce?BA �^?S=�W�?B]JkJC W�?SIVQDkg�h3Rfd�QDk^L�?S��nr?BY�IK]JR�d�Ql?Bk)g�]J=�IKQDk^h�s8AD;SC^h�nr?B;>d�QZk^LBRN 0J_J=jQl�+;>dfh3AD`�CJQDR�df=@QlIK]^dfh3C�N^GH]KY Y�h=��>wSwSwHF

� � ��q�LB;u�r;HNTX�FlNrg"FPGHM^?���Q¤N¡zÆF�E�I*hSNr;SkJC :�F�:�;SR�MJQZY�?Sdf?^N .����C��������{<��g ?S����hLS=@;SCJ;>d�Ql?Bk ?S��g�M^h=jY ;SAs8;>=�=@QDh=<nr?B;>d�QDk^LBR���R�QDkJL&z|Y�_*h3CJ;SkJceh�Gy_*h3cedf=�?BR@ce?S_~`SN 0V[¥;>dfh=@QD;SAZRTO��>;SAD]J;>d�Ql?Bk!�>[¥;>=@cjM��>wSwSwHNK_J_iFy}~v>x��}a�H�>F

� ¯ ��Gydf=j;Sk^LBY ;Sk�NJg"FJO�FlN#.Ág�M^h=@Y�;SA�sr;>=@=@Qlh=<nr?B;>d�QDkJLBRT�«?S=<g�]^=@IKQDk^h�E<QD=��«?BQZADRN 0���� �D������� ����� �����;�jNJb¡?BAD]KY�h�3�Bv~N��3�S�S�yNK_J_�FK�S¯��@�wB�yF

� }��&:�;>=�=@QDR�?Bk�N��&FÁ�JFlN�m�F��&F<�S?Bk^h3R3N�;SkJC5GUFTX�F�s8]^=��ShSN;.Ásrh3kJc@MJY�;>=�� p�=�?SIKADh3Y R��«?S=���h��h3ced¨GHQD�h¨;SkKCGHMK;>_Uh<�<hdfh=jY QDkJ;>d�Ql?Bk�QDk�O�CJCJ`a��n8]J=�=�h3k~d�{�?BkKC^h3Rfdf=@]Jced�QD�Sh<O��>;SAD]J;>d�QD?Bk�N 0H�B?B]^=@kJ;SAK?S�i{<?BkJC^h3Rfdf=@]Kced�Ql�ShO��+;SAD]K;>d�Ql?Bk�NHb¡?BA¤Fi�3�yNU{�?^Fi�>N��3�S�SxyNK_J_�FK�H�Æ��¯+}^F

� � �&E�Fr:�F�®&FrW<QDkJk^?y?u` X6;Sk�N�®&F8g"FPg�QZY Y�h=3N �@Gydf?Hc@MJ;SR�d�QDc#®�Al?SIK;SA"q�_Jd�QDY�Ql�3;>d�Ql?Bk§[�hd�M^?HCJR�p�;>=@d�z �n8AZ]JRfdfh=@QDkJL![�hd�M^?HCJRN ��[¥;>d�M^h3Y ;>d�QDc;SA�p�=�?SLS=j;SY Y QDk^L�¯S���|�3�S�BvS�jNV_J_iFK�Bvu���SxyF

� x �&E�F�:�FP®!F�W�QDkKk^?~?�` X6;Sk�N8®&F�g"F�g�QDY Y�h=3N �@Gydf?ycjMJ;SRfd�QDc1®�Al?SIK;SA�q�_Kd�QDY Ql�3;>d�Ql?Bk [�hd�M^?HCJR po;>=�d z�z �[¥]JAld�Q�mih�Sh3Ai[�hd�MJ?yCJR3N ��[�;>d�MJh3Y ;>d�QDc;SA�p�=�?SLS=@;SY�Y QDk^L ¯S���|�3�S�BvS�jNU_J_�FK�Bvu��v>�yF

�S�

Page 23: Depth - sabbagh.com · Al 0 Depth & ° & @ ¯

�Ìv�&W�Fr:�FTsP`y=@C�N�n�Frm�Fr��h=�dN�E�FT:�FT®!F8W<QDkJk^?y?u`©X�;Sk�N�W6FTs�F�GHc@MJkK;>IUh3AµN �@nr?BkJc]^=�=@h3kad�Gydf?Hc@MJ;SRfd�QZc[�hd�M^?HCJRT��?S=�®�Al?SIK;SA�q�_Jd�QDY QD�3;>d�Ql?Bk�N ��[�;>d�MJh3Y ;>d�QDc;SAip�=�?SLS=@;SY Y�QDk^L�}ax��|�3�S�>wa�jNU_J_�F��Æ���S�yF

� � �!�JFo[ F���?S�h3kKce=@;>�«d ;SkKC zÆFo[ F¡�B;Sce?SIKRN����������H�������� �� ��� ���;� ����������� ����� �����D�������������SN��B?BMJk � QDAlh`;SkJC1Gy?BkJRN^{<h� ¬�?S=��UNi�3�SxS�yF

�S¯