Lab 5: 2D FFT (Fortran version)

Transcription

1 Due Date: 17:00, Tuesday, November 1, 2011 TA: Xukai Shen Lab 5: 2D FFT (Fortran version) Conrad Schlumberger 1 ABSTRACT In this lab you will modify programs to filter data based on the dip in the frequency domain, and use it to process a VSP and remove multiples from a cmp gather. This lab is, once again, available online. Download the tar file at labs:lab5.tar.gz Then untar it with tar -xvzf Lab5.tar.gz VSP wavefield separation Figure 1 shows a common shot gather from a VSP (vertical seismic profile) shot by Schlumberger somewhere in Italy. A VSP is a seismic survey where the shots are near the surface and the geophones are down a well. Processing VSP s is done differently than conventional surface seismic. This shot gather was recorded by three component receivers, hence the three panels in the Figure. Each represents a different direction of Earth motion. A simple way to process VSP s is to separate the wavefield into upgoing and downgoing waves, apply a linear moveout correction, and stack to give an estimate of the reflectivity profile. For this part of the exercise, you just need to separate the upgoing and downgoing wavefields. You need to do two things, first you need to open fourier.f90 and implement the function fth, input and output definitions are given, along with some intermediate variables, dont change the input or the output, add variables if necessary, make sure you implement the correct forward and adjoint, then you need to modify Dip filter.f90 to apply the 2D FFT correctly and to apply an appropriate mute, 1 conrad@schlum.com

2 BEI - Lab 5 2 2D FFT Figure 1: VSP shot gather preferably with a taper.. You will need to put the parameters you use to describe dip in the parameter files up.p and down.p. Then compile the code by typing gmake Dip filter.x. You can then run gmake upgoing.view and gmake downgoing.view to create and view your results. Once you like your results, find the plot commands in paper.tex and un-comment them to include your results in the paper. You can view the results in the F k domain with the command gmake up fk domain.view and gmake down fk domain.view. Include these in the paper by un-commenting the appropriate plot commands. F k multiple suppression You have just written a program to separate upgoing and downgoing wavefields. You can now use this program to suppress multiples in the CMP gather displayed in Figure 2. Create the file intervel.h containing an RMS velocity field somewhere between the primary and multiple moveout velocities by typing gmake intervel.h. This velocity function will be used to apply normal moveout. The command gmake nomultiples.h will moveout the data cmp.hh with the SEPlib program NMO so that the multiples will now be dipping downwards and the primaries upwards, and will then apply your wave-field separation (dip-filter) program to remove the multiple energy. Put your dip limitations in the parameter file multiple.p. Be conservative - it is better to keep a bit of multiple energy rather than throw out any signal. Finally, we apply inverse NMO (NMO inv=1) to transform the

3 BEI - Lab 5 3 2D FFT data back to a normal cmp gather. You can create and view your results with gmake nomultiples.view. To see the results of your filtering in the F k domain, you can type gmake cmp fk domain.view. Include this result by un-commenting the plot commands in paper.tex. Next, run gmake subsampled.view to subsample the data along the x-axis, and try to remove the multiples using the parameter file sub.p. Having fewer spatial offsets leads to data-aliasing and means the primaries and multiples are poorly separated in the Fourier domain. You can view the Fourier domain result with gmake sub fk domain.view. Include these results in paper.tex also. Figure 2: Multiple contaminated cmp. VSP QUESTIONS 1. Which VSP panel do you think is measuring the vertical component of Earth motion? Why? 2. VSP s are usually higher frequency than surface seismic. Why do you think this is the case?

4 BEI - Lab 5 4 2D FFT 3. When you look at the VSP result in the frequency domain, you see that there is a blank strip in the middle. What caused this? Multiple suppression 1. Seismic amplitudes can often be inverted to estimate rock properties (impedance, etc). Multiples can corrupt the amplitudes though, making this kind of analysis impossible. Do you think F k multiple suppression makes the amplitudes more or less reliable? 2. How did you choose the mute range for the multiples? How did it change for the subsampled case? Extra Credit: Who was Conrad Schlumberger, what was he/she famous for? Who was his/her brother? Extra Credit: With a green pen mark all spelling and gramar error s in this Lab. Also comment on confusing statements in the Lab or other broken and outdated features/questions.! Fourier transform and apply dip f i l t e r program D i p f i l t e r use f o u r i e r i m p l i c i t none complex, a l l o c a t a b l e, dimension ( :, : ) : : data i n t e g e r n1, n2 i n t e g e r hetch, putch c a l l i n i t p a r ( ) c a l l doc ( /homes/ sep / c l a u d i o /sepwww/lab5/lab5/ D i p f i l t e r. r s ) i f (0>= hetch ( n1, d, n1 ) ) then c a l l e r e x i t ( Trouble reading n1 from h i s t o r y ) i f (0>= hetch ( n2, d, n2 ) ) then c a l l e r e x i t ( Trouble reading n2 from h i s t o r y ) a l l o c a t e ( data ( n1, n2 ) )

5 BEI - Lab 5 5 2D FFT c a l l d i p f i l t ( n1, n2, data ) end program D i p f i l t e r s ubroutine d i p f i l t ( n1, n2, data ) i n t e g e r nw, nk, n1, n2, iw, ik, i3, n3 r e a l dw, dk, d1, d2, w, k, w0, k0, vel, wt complex data ( n1, n2 )! Un comment and put your dip parameters here! from param : SOME THAT YOU DECIDE ON i n t e g e r hetch, putch, auxputch i f (0>= hetch ( n1, d,nw ) ) then c a l l e r e x i t ( Trouble reading n1 from h i s t o r y ) i f (0>= hetch ( n2, d, nk ) ) then c a l l e r e x i t ( Trouble reading n2 from h i s t o r y ) i f (0>= hetch ( n3, d, n3 ) ) then c a l l e r e x i t ( Trouble reading n3 from h i s t o r y ) i f (0>= hetch ( d1, f, d1 ) ) then c a l l e r e x i t ( Trouble reading d1 from h i s t o r y ) i f (0>= hetch ( d2, f, d2 ) ) then c a l l e r e x i t ( Trouble reading d2 from h i s t o r y ) i f ( 0. ne. auxputch ( n1, d, n1, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g n1 to aux fk domain ) i f ( 0. ne. auxputch ( n2, d, n2, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g n2 to aux fk domain ) i f ( 0. ne. auxputch ( e s i z e, d,8, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g e s i z e to aux fk domain ) dw = 1/((nw 1) d1 ) dk = 1/(( nk 1) d2 ) w0 = 1/(2 d1 ) k0 = 1/(2 d2 ) i f ( 0. ne. auxputch ( d1, f,dw, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g d1 to aux fk domain ) i f ( 0. ne. auxputch ( d2, f, dk, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g d2 to aux fk domain ) i f ( 0. ne. auxputch ( o1, f,w0, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g o1 to aux fk domain ) i f ( 0. ne. auxputch ( o2, f, k0, fk domain ) ) then c a l l e r e x i t ( Trouble w r i t i n g o2 to aux fk domain ) do i 3 =1,n3 c a l l s r e e d ( in, data, n1 n2 8)

6 BEI - Lab 5 6 2D FFT! Un comment and f i x t h e s e 2 c a l l s to FFT! c a l l f t 1 a x i s (?,?,?,?,?)! c a l l f t 2 a x i s (?,?,?,?,?) do iw = 1, n1 w = ( iw 1) dw + w0 do i k = 1, n2 k = ( i k 1) dk + k0!#####! Fix t h i s so t h e r e i s a dip f i l t e r, p r e f e r a b l y with a taper!##### wt = 1. 0 data ( iw, i k ) = data ( iw, i k ) wt! Un comment and f i x t h e s e 2 c a l l s to i n v e r s e FFT c a l l s r i t e ( fk domain, data, n1 n2 8)! c a l l f t 1 a x i s (?,?,?,?,?)! c a l l f t 2 a x i s (?,?,?,?,?) c a l l s r i t e ( out, data, n1 n2 8) return module f o u r i e r i m p l i c i t c o n t a i n s none s ubroutine f t 1 a x i s ( adj, sign1, n1, n2, cx ) i n t e g e r i2, adj, n1, n2 complex cx ( n1, n2 ) r e a l s i g n 1 do i 2= 1, n2 c a l l f t h ( adj, sign1, 1, n1, cx ( 1, i 2 ) ) s ubroutine f t 2 a x i s ( adj, sign2, n1, n2, cx ) i n t e g e r i1, adj, n1, n2 complex cx ( n1, n2 ) r e a l s i g n 2 do i 1= 1, n1 c a l l f t h ( adj, sign2, n1, n2, cx ( i1, 1 ) ) s ubroutine f t h ( adj, sign, m1, n12, cx ) i n t e g e r i, adj, m1, n12 r e a l s i g n

7 BEI - Lab 5 7 2D FFT complex cx (m1, n12 ) complex temp ( n12 )! implement f t h using f t u s ubroutine f t u ( s i g n i, nx, cx )! complex f o u r i e r transform with unitary s c a l i n g!! 1 nx s i g n i 2 pi i ( j 1) (k 1)/nx! cx ( k ) = sum cx ( j ) e! s q r t ( nx ) j=1 for k = 1, 2,..., nx=2 i n t e g e r! i n t e g e r nx, i, j, k, m, i s t e p r e a l s i g n i, s c a l e, arg complex cx ( nx ), cmplx, cw, cdel, ct c a l l pad2 ( nx ) s c a l e = 1. / s q r t ( 1. nx ) do i= 1, nx cx ( i ) = cx ( i ) s c a l e j = 1 k = 1 do i= 1, nx i f ( i<=j ) then ct = cx ( j ) cx ( j ) = cx ( i ) cx ( i ) = ct m = nx/2 do while ( j>m. and. m>1) j = j m m = m/2! && means.and. j = j+m do i s t e p = 2 k cw = 1. arg = s i g n i / k c d e l = cmplx ( cos ( arg ), s i n ( arg ) ) do m= 1, k do i= m, nx, i s t e p ct=cw cx ( i+k ) cx ( i+k)=cx ( i ) ct cx ( i )=cx ( i )+ ct cw = cw c d e l k = i s t e p i f ( k>=nx ) then

8 BEI - Lab 5 8 2D FFT e x i t = s ubroutine pad2 ( nx ) i n t e g e r : : nx, ni ni=1 do while ( nx > ni ) ni=ni 2 nx=ni end module