Output Least Squares: nonlayered model, 30Hz data, Kirchhoff Common Offset simulation etc.

First series: Effect of source aliasing, 03.03.95

enlarged Mark's model to permit 61 shot simulation with same coverage as gascloud synthetics. Grid is 8m x 8m. Generated 61 shot COG data set with 30Hz Ricker source, 2ms time sampling:

Prestack Migration at constant velocity:

Observed very large amount of spatially aliased noise in prestack migration section - obvious in coherency panels. To investigate whether this is discretization error, set up 4 single offset simulation - migration jobs with 15, 20, 25, 30 Hz Ricker sources, all using same model on 8m x 8m grid and 2ms time sample rate, offset = 96m.

Examination of 15 and 30 Hz jobs made clear that the origin of the noise is simply aliasing in the shot direction.

Production of fwd and mig jobs with 45 deg. (rather than 65 deg.) aperture limits verifies this diagnosis. Smaller aperture migrations have less aliased energy, though it is not entirely eliminated (see fwd 30 Hz 45 deg., mig 30 Hz 45 deg., fwd 15 Hz 45 deg., and mig 15 Hz 45 deg.).

Aliasing analysed on pp. 105 ff. of Large Notebook 2. Max shot spacing permissible for 15 Hz and 45deg aperture is about 35m. Redesigned experiments with 24m shot spacing. Gives very clean migrations with 15Hz source. Not aliased at peak for 30Hz, but is aliased for high end of spectrum - which is obvious in migration - see mig 30 Hz 45 deg 24 m dshot, mig 15 Hz 45 deg 24 m dshot.

Some experimentation with offsets and prestack migrated image volume make clear that there is simply not much residual moveout for this velocity model, even at const. velocity - see the coherency panels mentioned before.

ALL OF THIS STUFF UP TO THIS POINT STORED IN masc39:datb/nlay60.

Second Series: scans

Built new velo model = v8a.sep by doubling difference with const velo.

First try: set up line of 121 shots, 33 offsets, far offset = 1680m, offset spacing = shot spacing = 24m, 30Hz Ricker source, aperture = 65 degrees. Results of simulation and prestack migration stored in masc39:datb/nlay60a. Upshot: no significant amount of data or image until about trace 20, at offset roughly 1200. SO...

Second try: everything the same, but far offset = 1224. This time plenty of data at near and far offsets, also image at near and far offsets. Results stored in masc39:datb/nlay60b. image begins for all offsets slightly below 400m, whereas for the nearer offsets there is considerable aliased energy in the migrations above 400m. Coherency panels at constant velocity show lots of moveout; detail at trace 650 gives idea of noise in simulation + migration. Remember that the range of offsets here is only 456m (near) to 1224m (far), as opposed to the 160 - 1760 m. range of the earlier example.

OLS scans: go with second data set. Set reflectivity cutoff at 400m. Distribute scans amongst nodes on texas cluster, running on local disks. Scan records stored in scanx_sum.hdr, reflectivity estimates in r8esx.sep, x=0,...,20, where the scan offset in each case is h=0.05*x.

Plot of OLS scan

Image at const. velocity

Image at 0.5(const. vel.)+0.5(target vel.)

Image at target velocity

Summary:

  data norm:         .12087510E+02

h=0.0:

     ms error       diffl semblance     damping term      total DSO cost
   .69762421E+02      .00000000E+00      .13808806E-05      .69762421E+02

     rms error     norm of inner state 
   .11812063E+02      .16618547E+02

h=0.05:

     ms error       diffl semblance     damping term      total DSO cost
   .69232315E+02      .00000000E+00      .16725306E-05      .69232315E+02

     rms error     norm of inner state 
   .11767099E+02      .18289509E+02

h=0.1:

     ms error       diffl semblance     damping term      total DSO cost
   .68611153E+02      .00000000E+00      .20308523E-05      .68611153E+02 

     rms error     norm of inner state 
   .11714192E+02      .20153671E+02 

h=0.15:

     ms error       diffl semblance     damping term      total DSO cost
   .68018181E+02      .00000000E+00      .25567965E-05      .68018181E+02

     rms error     norm of inner state 
   .11663463E+02      .22613255E+02

h=0.2:

     ms error       diffl semblance     damping term      total DSO cost
   .67509651E+02      .00000000E+00      .32013909E-05      .67509651E+02

     rms error     norm of inner state 
   .11619781E+02      .25303719E+02

h=0.25:

     ms error       diffl semblance     damping term      total DSO cost
   .67026131E+02      .00000000E+00      .41048329E-05      .67026138E+02

     rms error     norm of inner state 
   .11578094E+02      .28652514E+02

h=0.35:

     ms error       diffl semblance     damping term      total DSO cost
   .65687202E+02      .00000000E+00      .66334514E-05      .65687210E+02

     rms error     norm of inner state 
   .11461867E+02      .36423759E+02

h=0.4:

     ms error       diffl semblance     damping term      total DSO cost
   .64642380E+02      .00000000E+00      .84921476E-05      .64642387E+02

     rms error     norm of inner state 
   .11370346E+02      .41212009E+02

h=0.5:

     ms error       diffl semblance     damping term      total DSO cost
   .61503914E+02      .00000000E+00      .13260361E-04      .61503925E+02

     rms error     norm of inner state 
   .11090889E+02      .51498276E+02

h=0.55:

     ms error       diffl semblance     damping term      total DSO cost
   .59135445E+02      .00000000E+00      .16121054E-04      .59135460E+02

     rms error     norm of inner state 
   .10875242E+02      .56782135E+02

h=0.7:

     ms error       diffl semblance     damping term      total DSO cost
   .46103771E+02      .00000000E+00      .27037566E-04      .46103798E+02

     rms error     norm of inner state 
   .96024761E+01      .73535797E+02

h=0.85:

     ms error       diffl semblance     damping term      total DSO cost
   .23080196E+02      .00000000E+00      .41168321E-04      .23080238E+02

     rms error     norm of inner state 
   .67941442E+01      .90739540E+02

h=1.0:

     ms error       diffl semblance     damping term      total DSO cost
   .46885290E+01      .00000000E+00      .56574390E-04      .46885858E+01

     rms error     norm of inner state 
   .30621982E+01      .10637141E+03
William W. Symes (symes@rice.edu)