7 0 –7 () - emf.ipgg.nsc.ruemf.ipgg.nsc.ru/work/conf99/r2_3.pdfjheh]bq_kdh]h h[_ki_q_gby...
Transcript of 7 0 –7 () - emf.ipgg.nsc.ruemf.ipgg.nsc.ru/work/conf99/r2_3.pdfjheh]bq_kdh]h h[_ki_q_gby...
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< gZklhys_c jZ[hl_ ijb\h^blky j_r_gb_ aZ^Zqb h g_klZpbhgZjghf
we_dljhfZ]gblghf ihe_ lhdh\h]h dhglmjZ� jZkiheh`_ggh]h \ ijh\h^y-s_c fZ]gblghc pbebg^jbq_kdb�kehbklhc kj_^_�
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fZ]gblghc ijhgbpZ_fhklvx �µ hl ���⋅µ0 ^h �� 000⋅µ0, µ0 = 4π⋅10–7=g�f ±
fZ]gblgZy ihklhyggZy�� Ihwlhfm \ h[eZklb l_hjbb ZdlmZevgZ aZ^ZqZ hih\_^_gbb g_klZpbhgZjgh]h we_dljhfZ]gblgh]h ihey \ pbebg^jbq_kdb�
kehbkluo ijh\h^ysbo fZ]gblguo kj_^Zo� WlZ aZ^ZqZ \Z`gZ dZd ^ey bam-q_gby nbabq_kdbo k\hckl\ kZfh]h \_s_kl\Z f_lZeebq_kdbo h[kZ^guo
dhehgg� lZd b ^ey ihke_^mxs_c ihklZgh\db b j_r_gby [he__ keh`guo
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we_dljhfZ]gblgh_ ihe_� fhgblhjbg]Z bo khklhygby�DZd ba\_klgh >�@� ^bgZfbq_kdb_ oZjZdl_jbklbdb n_jjhfZ]g_lbdh\�
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k\hckl\Zfb kZfh]h \_s_kl\Z b k we_dljh^bgZfbq_kdbfb k\hckl\Zfb
gZfZ]gbqb\Z_fh]h l_eZ� I_j\h_ hij_^_ey_lky ijbjh^hc ghkbl_e_c fZ]-gblgh]h fhf_glZ� kha^Zxsbo gZfZ]gbq_gghklv� Z lZd`_ bo \aZbfh^_c-kl\b_f� kljmdlmjhc n_jjhfZ]g_lbdZ b baf_g_gb_f wlhc kljmdlmju ijbgZfZ]gbqb\Zgbb� <lhjh_ hij_^_ey_lky hkh[_gghklyfb jZkij_^_e_gby
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IhklZgh\dZ aZ^Zqb
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( )( )
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(1)
A^_kv b \ ^Zevg_cr_f lhqdZ gZ^ nmgdpb_c hagZqZ_l ijhba\h^gmx
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∞
∫�
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5 U W ] GU
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+0
= U W ] G]
]=∞
∫�
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�πλ λ λ� � � �FRV� � . (4)
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U UU) =
∂∂
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�
U UU5 =
∂∂
λ� � = . (8)
Hlf_lbf� qlh σ0 = σ2 = 0, µ2 = µ0 �\gmlj_ggbc pbebg^j b \g_rgyykj_^Z g_fZ]gblgu b y\eyxlky baheylhjZfb� .
IhklZ\bf aZ^Zqm ^ey R� ihkdhevdm wlh h[jZa ghjfZevghc ih hlgh-r_gbx d ih\_joghklyf jZa^_eZ kj_^ dhfihg_glu �fZ]gblgZy fh^Z��
Ba khhlghr_gbc ���±��� ihemqZ_f mjZ\g_gb_
′′ + ′ − + =5U5
U
U5 5
UU U
� � � �
�
λ µσ � (9)
b ]jZgbqgu_ mkeh\by gZ ih\_joghklyo jZa^_eZ�
[µR] = 0, [R + r⋅ ′5U] = 0, ijb r = r 1 = r 2. (10)
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J_^mdpby d aZ^Zq_ RlmjfZ �Ebm\beey�
J_rZ_f aZ^Zqm ���±���� f_lh^hf� ij_^eh`_gguf :� G� Lbohgh\uf
^ey ]hjbahglZevgh�kehbkluo kj_^ >�@�
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; U ; U, U
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; U ; U. U
. U
� � � �� � � �� �
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= λλ
r ⊇ r2. (12)
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nmgdpbb X. < j_amevlZl_ ihemqbf�
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�
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.
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U ;U; U N ;UU U
� � ��� �′ + ′ − − =� � , r1 ⊆ r ⊆ r2,
; U ; D ;U+ ′ =� � , r = r1, (13)
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; U; $- NU %1 NU NU ; NUU+ ′ = + =� � � � �� �� � �
Ba ���� bf__f kbkl_fm ^ey hij_^_e_gby g_ba\_klguo dhwnnbpb_g-lh\ : b B:
NU $- %1 D $- D %1
NU $- %1 D $- D %1
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, (14)
]^_ - - NU - - NU 1 1 NU 1 1 NUL L L L L L L L� � � � � � � �= = = =� � � �� � �� � �� .
Hij_^_ebl_ev h^ghjh^ghc kbkl_fu ���� ^he`_g [ulv jZ\_g gmex�
qlh b ^Z_l mjZ\g_gb_ ^ey kh[kl\_gguo qbk_e k:
> � � � �@ > � � � �@
> � � � �@ > � � � �@ �
- N UD
N U- NU 1 NU
D
NU1 NU
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− ⋅ + −
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&h]eZkgh l_hjbb ^ey aZ^Zqb RlmjfZ�Ebm\beey� bf__lky ^bkdj_l-gh_ fgh`_kl\h kh[kl\_gguo agZq_gbc b kh[kl\_gguo nmgdpbc� LZdbf
h[jZahf� h[s__ j_r_gb_ ^ey nmgdpbb R _klv
5 U W & ; U HMM
M
WM� � � � �= ⋅=
∞ − ⋅∑�
α, (15)
]^_ Xj ± FR[kl\_ggu_ nmgdpbb aZ^Zqb RlmjfZ�Ebm\beey� αλ
µ σM
MN=+� �
� �
�
Dhwnnbpb_glu Kj ^he`gu [ulv hij_^_e_gu lZd� qlh[u m^h\e_l\h-jyehkv gZqZevgh_ mkeh\b_�
5 U W & ; U HMM
M
WM� � � � �==
∞−∑
�
α, (16)
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U 5U5 U 5UU UU
� � ��� �′′ + ′′ − + ′′ =� � �λ 0 ⊆ r ⊆ ∞,
> @ � > @µ5 5 U5U= + ′ =� � , r = r1 = r2, (17)
5 . U→ − ⋅��� �λ λ ijb r → 0,
5→ � ijb r → ∞.
>ey hij_^_e_gby Kj \hkihevam_fky hjlh]hgZevghklvx nmgd-
pbc U ; M � Mfgh`Zy \ujZ`_gb_ ���� gZ U ; N UQ⋅ � � b bgl_]jbjmy� ihem-
qbf
&
U5 U ; N U GU
U; N U GU
M
U
U
M
MU
U=∫
∫
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λ. (18)
Bgl_]jZe \ agZf_gZl_e_ \ujZ`_gby ���� \uqbkey_lky ZgZeblbq_kdb
U; GUU
N U; N U N U D D
U
N U; N U N U D D
U
U
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MM M
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Bgl_]jZe \ qbkebl_e_ \uqbkebf� bkihevamy lZ[ebqgh_ jZ\_gkl\h
���� >�@ b khhlghr_gby f_`^m nmgdpbyfb ;_kk_ey J(x�� G_cfZgZ N(x� bfh^bnbpbjh\Zggufb I(x), K(x� >�@� < j_amevlZl_ ihemqbf�
U5 U ; N U GU
$$
U- N U , U N U- N U , U
N
U
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M
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U
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=−
++
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λ
λ λ λ
λ
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U1 N U , U N U1 N U , U
N
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� � � � � � � �λ λ λ
λ� � � �
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(20)
−++
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λ λ Dhwnnbpb_glu :
b < k lhqghklvx ^h khfgh`bl_ey hij_^_ebf ba i_j\h]h mjZ\g_gby �����
hldm^Z
$ 1 N U D 1 N U % - N U D - N UM M M M= − = − +� � � � � � �� � � �� � � � ��
Ba mkeh\bc gZ ih\_joghklyo jZa^_eZ \ ���� gZc^_f dhwnnbpb_glu
:* b <
*
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%I , U . U , U . U
. U . U I , U . U , U . U
> � � � � � � � �
> � � � �� � > � � � � � � � �@�= +
− − +λ λ λ µ λ λ
λ λ µ λ λ µ λ λ
�
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λ λ µ λ λµ λ λ
IU , U , U
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µ λ λ λA^_kv µ ± hlghkbl_evgZy fZ]gblgZy ijhgbpZ_fhklv jZ\gZy µ1/µ0.
BlZd� \gmljb f_lZeebq_kdh]h pbebg^jZ j_r_gb_ gZc^_gh� hij_^_-e_gu \k_ nmgdpbb� \oh^ysb_ \ ����� < khhl\_lkl\bb k mkeh\b_f ���� gZ
ih\_joghklyo jZa^_eZ ijb r = r1 bf__f µ0 R0 = µ1 R1 � qlh iha\hey_l gZclb
j_r_gb_ aZ^Zqb \h \gmlj_gg_c ihehklb pbebg^jZ �r ⊆ r1):
5 &; N U
, U, U HM
M
M WM�
�
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� ��=
=
∞ −∑µλ
λ α� �
� �� � .
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jZ^bmkhf r� ihf_s_gghf \h \gmlj_ggxx h[eZklv ijh\h^ys_]h fZ]gbl-gh]h pbebg^jZ
εσ
λ λλ
µσ= +∞
=
∞− +
∫ ∑U
U*, U ]
, UP J & ; N U H GJM
MM M
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]^_ *0 J
U
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_keb bklhqgbd ± dhglmj k lhdhf� & & J U= =λ λ�� �� , J ± Zfieblm^Z ih-
klhyggh]h we_dljbq_kdh]h lhdZ�
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\ ijbkmlkl\bb ijh\h^ys_]h fZ]gblgh]h pbebg^jZ� <ujZ`_gb_ m^h[gh
^ey qbke_ggh]h ZgZebaZ� gh� dZd ke_^m_l ba ����� ijb fZeuo \j_f_gZo b[hevrbo fZ]gblguo ijhgbpZ_fhklyo koh^bfhklv jy^Z mom^rZ_lky�
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\h \gbfZgb_� jZkkfhljbf kh]eZkh\Zgghklv j_amevlZlh\ wdki_jbf_glZ b
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S� JZg__ >�@ ihemq_gh j_r_gb_ ^ey n pbebg^jbq_kdbo ijh\h^ysbo ie_-ghd� \eh`_gguo h^gZ \ ^jm]mx� >ey h^ghc pbebg^jbq_kdhc ijh\h^ys_cie_gdb w�^�k� \ dhglmj_� ihf_s_gghf \h \gmlj_ggxx h[eZklv� hibku\Z-_lky ke_^mxsbf bgl_]jZevguf \ujZ`_gb_f�
ε λ λ λλ µ λ λ
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a^_kv S ± bgl_]jZevgZy ijh\h^bfhklv ie_gdb� µ = µ0 = 4π⋅10–7 =g�f ±
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k m\_ebq_gb_f \j_f_gb klZ-gh\e_gby� qlh b ke_^h\Zeh
h`b^Zlv� GZ jZggbo \j_f_gZo
i_j_oh^gu_ ijhp_kku jZaeb-qZxlky� ihkdhevdm lhesbgZ
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1. Sato M., Fuziwara J., Miyairi M. et al. // Directional Induction Loggingmethods // Proc. of 35th SPWLA Symp., 1994.
2. Cheryauka A. B., Sato M. Directional induction logging for evaluation oflayered magnetic formations // Geophysics, 1999, 23 p. (submitted).
3. Sato M., Cheryauka A. B. Magnetic formation evaluation by directionalinduction logging – A modeling study // Proc. of 5th SPWLAJ Meeting, Chiba,1999, 11 p. (in publ.).