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1、I.1 Diffraction Stack Modeling,1. Forward modeling operator L,Forward Modeling,Forward Modeling: Sum of Weighted Hyperbolas,G(x|x) =,GREENs FUNCTION,G(x|x) =,ASYMPTOTIC GREENs FUNCTION,A(x,x),ASYMPTOTIC GREENs FUNCTION,G(x|x) =,A(x,x),e,Diffraction Stack Modeling = ZO Modeling,Diffraction Stack Mode
2、ling = ZO Modeling,Dipping Reflector,Diffraction Stack Modeling = ZO Modeling If c for DS is that for ZO Modeling,ASYMPTOTIC GREENs FUNCTION,d(x) =,A(x,x),e,QUICK REVIEW FOURIER TRANSFORM, (t),Forward Modeling Operator,d(x,t) =,R(x),A(x,x),Forward Modeling Operator,d(x,t) =,R(x),A(x,x),SUMMARY,d(x,t
3、) =,1. Exploding Reflector Modeling = Diffraction Stack Modeling,A(x,x),R(x),Data variables,Sum over reflectors,2. High Frequency Approximation (i.e c(x) variations 3* ),3. Approximates Kinematics of ZO Sections, but not Dynamics,MATLAB Exercise: Forward Modeling,1. To account for the source wavelet
4、 W(t), weconvolve data with W(t) (recall (t- )*W(t)= W() )so that modeling equation becomes (neglect A),A). Execute MATLAB program forw.m to generate synthetic data for a point scatterer and a 30 Hz wavelet. B). Execute MATLAB program forwl.m to generate synthetic data for a dipping layer model C).
5、Execute MATLAB program forw.m to generate synthetic data for a syncline model. Note diffractions and multiple arrivals. Adjust for new models. Why thesecond time derivative?,MATLAB Exercise: Forward Modeling,for ixtrace=1:ntrace; for ixs=istart:iend; for izs=1:nz; r = sqrt(ixtrace*dx-ixs*dx)2+(izs*dx)2); time = 1 + round( r/c/dt ); data(ixtrace,time) = migi(ixs,izs)/r + data(ixtrace,time); end; end; data1(ixtrace,:)=conv2(data(ixtrace,:),rick); end;,* Src Wave,
