PROCESS PSMIGR ------- ------ Document date: 28 July 2000 Phase Shift Migration Reference: Stoffa et al., Split-step Fourier Migration, Geophysics,55,p.410-421,1990. This process performs a "split-step" Fourier migration on stacked seismic data. The method is designed to provide a fast f-k approach to migration in laterally varying velocity media. The approach is straightforward. The data are migrated in small depth increments of dz. For each dz a loop over a frequency range fmin to fmax is performed in which the data are: 1) transformed from f-x to f-k; 2) phase shifted by exp(i*dz*Kz) [Kz=csqrt(w^2*u0^2-Kx^2)] using a reference slowness u0; 3) transformed from f-k to f-x; 4) phase shifted by exp(i*w*(u(x,z)-u0)) Imaging is then done at depth Zj by a sum over frequencies from fmin to fmax. Notes: The complex square root calculation of Kz results in an exponentially damped response to inhomogeneous interface waves, a difficulty in other implementations of this type of phase-shift-plus-correction method. Extreme lateral velocity variations, such as seen at some continental margins, may be handled by breaking the migration into several overlapping panels which are later spliced together. Big step, ZSKIP: You may migrate in one big step through an upper constant slowness region such as the water column. No imaging is done for this region. If there is a deep water delay in your data, you may want to remove delay to negate temporal wrap-around. This is most easily done through start-end-time pair in process DISKIN (i.e. set 0.0 8.0) Migration bandwidth, FMIN, FMAX: Runtime increases in direct proportion to migration bandwidth and the number of frequencies migrated. The number of frequencies is initially computed from the FFT. The larger the FFT, the larger the number of frequencies (a 2048 point fft has 2049 frequencies). It is worthwhile doing a couple of small tests to see what frequencies are actually useful and adjusting the parameters FMIN and FMAX accordingly. Depth step, DELTAZ: The migration depth step dz need not be tiny, but in general small enough to provide unaliased sampling of the smallest vertical wavenumber of interest. Data tapers, BPAD, EPAD: The user is given the option of padding either side of the data panel being migrated. The padded region is filled with copies of the end traces which are tapered down within the pad region. This is highly recommended as it reduces Gibbs phenomena and Nyquist noise. It should be kept in mind, however, that a power of 2 FFT is used and that the length of the FFT is determined as the next power of 2 above (data panel length)+BPAD+EPAD. So if you are migrating 1900 traces and you pad with 100 on each side, you will be using a 4096 FFT for each depth step. If you had padded with 50 on each you would be using a 2048 FFT, much faster. Migration taper, MTAP: In addition to the tapered padding of the first and last trace, an exponential taper can be applied to the ends of the spatial window at each migration step. This inhibits "wraparound" of migration smiles from the data panel ends sides. An exponental taper on the order of MTAP=25 traces is recommended. The example below should clarify the issue. It is important to note that the FFT length is not based on the length of the exponential taper, only on the (data panel length)+BPAD+EPAD, so that if care is not taken data may be affected by the exponental taper. MTAP=5 |<5>| |<5>| eeeee1111111111111111111111111111eeeee <-*1 tttttttdddddddddddddddddttttttt0000000 |< 7 >|| ||< 7 >| | |BPAD=7| |EPAD=7 | | | | | | || | | | |<--- 2^n based on 17+(2*7) = 32 --->| <-*2 *1) this vector is applied to each frequency at each depth step. In f-k jargon this type of taper is called a sponge. *2) if EPAD were given as 9 in this case, then the code would use an n=6 (2^n=64) would be used for the FFT. Present limitations include 8192 traces, 5000 depth steps & 800 frequencies. If the number of depths (nz) times the number of traces (nx) exceeds 500,000 use sioseis.BIG, which allows nz*nx = 3,500,000. Padding should be incluiding when estimating nx. EXAMPLE MIGRATION: Shallow Sediments near ODP HOLE 504B diskin ipath 504B.dmo.stack.224.624 set 0.0 8.0 end end psmigr deltax 12.5 deltaz 10 vskip 1500 zskip 3000 ez 10000 bpad 50 epad 50 mtap 25 twinlen 0.30 ref 0 nvsmth 3 vpath v.scratch fmin 5 fmax 20 path ps.scratch sgypath vmodel.segy fno 224 lno 224 vdp 1500.0 3480.0 1850.0 3490.0 1850.0 3721.3 end fno 424 lno 424 vdp 1500.0 3442.5 1850.0 3452.5 1850.0 3785.5 end fno 524 lno 524 vdp 1500.0 3397.5 1850.0 3407.5 1850.0 3694.3 end fno 624 lno 624 vdp 1500.0 3390.0 1850.0 3400.0 1850.0 3686.8 end end PARAMETER DICTIONARY --------- ---------- EZ - End Depth, in meters. The number of samples output will be EDEPTH / DELTAZ + 1. The first output sample is ALWAYS 0. - Required. e.g. ez 6000 DELTAX - The distance between traces, in meters. Required. DELTAZ - The output sample interval in meters per sample. DELTAZ may not exceed 32 since it is carried in the SEGY header in millimeters and as a 16 bit integer (thus 32767 millimeters is the maximum). This is analogous to the sample interval in time which the SEG-Y format carries as nanoseconds (milliseconds / 1000). Required. TWINLEN - Time WINdow LENgth of temporal taper at end of trace. This taper is exponential in nature and is given in seconds. The time taper should reduce energy migrating from truncation of time trace. Preset = 0.25 MTAP - Migration TAPer. The exponential spatial taper discussed above. preset = 25 FMIN - Minimum frequency of interest. Preset = 0 e.g. fmin 5 FMAX - Maximum frequency of interest. Run time may be reduced significantly by using FMIN/FMAX. The Nyquist frequency is 2/(sample interval) or (sample rate)/2, thus 4 mil data has has FMAX preset to 125/2 or 62.5. - preset = nyquist / 2 or (4/si) e.g. fmax 50 VDP - The interval velocity to use in migration, given as a list of Velocity Depth Pairs. The velocity should be in units of meters per second and the depth should be in units of meters. Required. velocity range 350 to 32000 NVSMTH - This parameter specifies the number of Velocity SMooTHing operations desired before constructing velocity file. The NVSMTH parameter is useful for smoothing across velocity contrasts which otherwise can cause distortion in depth migration. The running average of NVSMTH velocities is calculated after the VDP velocity function is expanded into an uniformly sampled function. NVSMTH applies in depth, not spatially. Preset = 3 FNO - The first shot/rp number the parameter list applies to. Preset = the first shot/rp received. e.g. fno 101 LNO - The last shot/rp number the parameter list applies to. Preset = the last shot/rp received. e.g. lno 101 BPAD - The number of zero amplitude traces to insert prior to the first trace. Preset = 1 range 1 to 500 e.g. bpad 10 EPAD - The number of zero amplitude traces to append after the last trace. Preset = 1 range 1 to 500 e.g. epad 10 ZSKIP - The first depth to compute. The first output sample is ALWAYS 0. This saves computer time! The first velocity of VDP of the first FNO/LNO list is used as the velocity for time to depth conversion unless parameter VSKIP is given. Preset = 0. VSKIP - Velocity used in extrapolation for parameter ZSKIP, usually the water velocity in marine work. If using ZSKIP, then VSKIP is required. REF - Reference slowness, u0, from a given depth. The minimum slowness may provide a better reference than the average slowness for imaging features such as a rough basement surface beneath low velocity sediments. =0, minimum slowness. =1, average slowness. =2, maximum slowness. Preset = 1 PATH - The pathname (filename) of a scratch file PSMIGR should use for the intermediate transposed data. The purpose of this parameter is to allow the user to specify the exact disk partition to use in case the "current" partition does not have enough space. preset = a scratch file in the current directory e.g. path /user/scratch/moreroom VPATH - The pathname (filename) of a file PSMIGR should use for the transposed velocity slices. If the file exists, PSMIGR will not calculate a new velocity model; VDP will be ignored. If the file does not exist, PSMIGR will write the velocity slices to VPATH so that it may be used in other runs of PSMIGR without having to recalculate the velocities. The velocity slices may be quite large and VPATH allows the user to specify the exact disk partition to use in case the "current" partition does not have enough space. preset = a scratch file in the current directory e.g. path /user/scratch/vmoreroom SGYPATH - The pathname (filename) of an additional SEGY compatible velocity file to be output for external purposes. Includes the smoothing operators. preset = none e.g. sgypath /user/scratch/vmoreroom.segy Copyright (C) 1995 by: Woods Hole Oceanographic Institution and The Regents of The University of California, 1995 Written by Dan Lizarralde, WHOI, adapted by Paul Henkart, SIO Modifications by Graham Kent & Dan Lizarralde, WHOI ALL RIGHTS RESERVED.Go to the list of seismic processes. Go to SIOSEIS introduction.