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Long period multiple removal.

Plot of 1000 trace stack (procs diskin prout wbt nmo smute stack gains plot end)
This example uses a 48 trace shot with 25m trace spacing from the Ross Sea. One trace is bad and was dropped. Plot of the raw shot, the shot with agc, and the shot with constant velocity (1475m/s) nmo. The agc plot was used to examine the direct wave for water velocity (1432m/s). Plot of 4 rp gathers (procs diskin prout wbt nmo3 mute gains plot end) where wbt defines the water bottom and mute xtp 0 0 800 0 1500 .4 and gains (type 5 alpha .4) are hung from the water bottom.

Inner mute

Plot of 4 rp gathers with innner mutes applied (addwb 2x fno 1500 xsets 0 -.05 9 500 -.05 9 501 9 9) Plot of the stack with the same inner mutes. This technique is not as successful as hoped probably because the streamer is so short.

A DISKIN tangent

The SEG-Y dataset consisted of RP gathers, without the killed (dead) trace. Since tx2tp needs as many different ranges as possible, the data were sorted back to shot gathers using process sort. Process tx2tp with np 100 caused diskin parameter noinc 100 to not work properly. Diskin parameters ftr 1 ltr 48 alleviated this problem.

TX to Tau-P transformation and Tau-P to TX transformation example

Plot of the tau-p domain using sioseis process tx2tp parameters: sep .04 .7 fc 100 setau 0 3 The righthand side plot is with each trace scaled independently and shows an aliasing problem due to the 25m group spacing. Plot of the tau-p domain using sioseis process tx2tp parameters: sep 0 .7 fc 100 setau 0 3 The righthand side plot is with each trace scaled independently. P = 0 implies infinite velocity or dip. The Plot of the inversion of the above Tau-P gather yielded some noisy traces. Increasing the number of p traces to 100 (parameter np 100) solved that. Plot of input and after tx2tp tp2tx (with additional scaling of 1.6), Plot was created using TP2TX parameters nx 48 sex 138 1313 for interpolation and recovery of the bad trace. (Plot of the input at the same scale). (Every trace scaled independently.) Tau-P domain plot of shots 326, 426, 526, 626 with tx2tp parameters: sep .04 .7 np 100 prestk 1 fc 100 setau 0 3 Plot of the stack after tx2tp tp2tx gather nmo smute stack gains, TX2TP and TP2TX parameter fc 125 was used since the frequencies seem to have been lowered (fc 150 produces an unusable plot).

Exploiting periodicity of multiples (Yilmaz section 7.5)

The plot of the autocorrelation of the taup-p domain traces. Autocorrelation of the Tau-P domain plot of shots 326, 426, 526, 626 with parameters: tx2tp: sep .04 .7 np 100 prestk 1 fc 125 setau 0 4 acorr: sets .7 2.7 olens 2 "Inverse Velocity Stacking for Multiple Elimination", Dan Hampson, Journal of the Canadian Society of Exploration Geophysicists. Vol 22, Dec 1986 p44-55 says: "Just as the tau-p transformation can be calculated by summing along linear trajectories, the calculations of U(p,tau) in equation (2) involves summing along hyperbolic trajectories". Furthermore, "replace the hyperbolic equation (2) by the parabolic form:"

Building a model and subtracting the multiple in Tau-P

Free USP program RMMULT "The user models the seismic data with a series of \fInp\fR curves, (linear, parabolic or hyperbolic) which are fit to the data in a least squares sense, thereby generating a modeled response. That subset of the curves defined as 'noise' is subtracted from the data. The remaining curves are considered to be modeled 'signal' and as an option, can be used to intelligently interpolate dead traces."

FK filter

The FK filter technique is also based on the principle of separating the primary events from the multiples. Unmoved-out or undermoved-out events with residual move-out slope or dip downward (increase in time with increasing distance). Events with perfect move-out form a line without any dip. Events that have move-out with too high a velocity (over-moved-out) slope upward (decrease in time). I created a synthetic (filtered spikes) with a water-bottom event at .49s with velocity 1500m/s, a water-bottom multiple at .98s with velocity 1500m/s, and reflector with a velocity of 1600m/s at 1.0s. The plot shows the unmoved-out record, the record with constant velocity nmo at 1500m/s, and the record as it would be stacked (1500m/s at .49 and 1600m/s at 1.0). When using nmo velocities 1500m/s at .49 and 1600m/s at 1.0, the only dipping event is the multiple, which has residual nmo. The plot does not have time lines on it because the interfere. Under correcting with 1450ms at .49 and 1550m/s at 1. will make the primary events dip up (negatively) slightly and the multiple will remain with positive dip. PLOT The plot of shot gather 326 shows: 1) The raw shot with AGC (winlen .25) only. 2) The shot with nmo with the stacking velocity of: fno 326 vtp 1471 0.720 1550 .9 1710 1.037 1941 1.375 2200 3 end 3) The shot with over corrected nmo (slow velocity of: vtp 1450 .7 1700 1.4) 4) Slow velocity and dip filter parameters: tx2fk nxpad 100 fkfilt deltax 25 dipcut 3 -.01 dippas 3.5 -.01 5) Slow velocity nmo, dip filter, and inverse nmo to undo the slow velocity. (vtp 1471 0.720 1550 .9 1710 1.037 1941 1.375 2200 3 end) 6) Slow velocity nmo, dip filter, inverse nmo, and nmo with stacking velocity: vtp 1471 0.720 1550 .9 1710 1.037 1941 1.375 2200 3 end (NOTE THAT THIS IS A HIGHER VELOCITY - NMO and INVERSE NMO AREN't QUITE PERFECT) 7) #6 with inner mutes applied SETBACKS: 1) FKFILT assumes a constant deltax. This data is missing a trace.