为了解决这个问题定义均方电平:
新的目标函数是:
最小化5-24反射系数序列r同时努力使地震道与初始预测约束匹配。由于约束很好的定义了低频成分,这往往解决低频漂移问题。
约束反演
约束反演用初始预测约束作为反演的出发点,设置绝对的或硬的边界对任何的参数偏
w1(L?Hr)T(L?Hr)(1?w1)(T?Wr)T(T?Wr)J??(5-24) LMSTMS离初始预测多远。让初始预测波阻抗为:
I0(i) i=1,NSAMP
i??2??r(j)?r3L(i)?L(0)(j)?r5(j)???j?1?35?? iL ( i ) ? L (0 ) ? ?
2 r ( j ) j?1
r = (W?TLW)(0-1)W?T
W
?L??L(1)???????L(m)????r(0)?r??r(1)???????r(m)?????11000??D?1/2?0?1100??(5-26) ??00?110?????????LL(0)???L0(0)???LU(0)?L??LL(1)?L(1)?L??L0??0L??LU(1)?U???????L?????L(M)??L?0(M)?????L?U(M)?LL(i)?L(i)?LU(i)?11/2??2???1?1?NSAMP00?0?r2?0i0(i)??0????1?220??1000???00.1???????0?.10?.?0.1??0????110???1???2???0.2??0?2??0.1?0??00??1??12?0?0?.21??0??????00.??1?????????0.1???0???0?0?.2???0.2??0?0020??00?10??12?1??0?12???0?.20.?4?????0?0???.2???0.4???0.2??或W r =T ??1??r????10?????12?1000??20?????000?12?1?????10???????02???????0?1??????0.1???0.2?????12?1000??000?12?1???0.1????0.2????0.4???0.2?????60??1??0.6?1?60???06????1.2????0.6???0.1?36??06????1.2?????0.2??H???20??22??L???0???0.2???1r??????22??02????20???22??0??22??????02?????0.2???1???84??44????22??02??0?????0.2???1?4?4??2216???48?????02????0???0.2?????0???0.1?? A(t) = (s(t)2+ h(t)2)1/2 W(t)?d?(t)dt(6-2)