Errors in traditional velocity analysis for statics computation

(View the PDF document here. Adobe Acrobat is required:)

Traditional velocity analysis, as done by most commercial software, follows these steps (SeismicStudio can be run in this mode if you'd like to try it):

  1. Branch assignment.
  2. Compute an initial velocity model. This is done by fitting a line through the picks for sources and detectors, and possibly the CMP locations. The resulting velocity field is then usually smoothed. The line fitting may be done either manually or automatically.
  3. Initial delay time analysis.
  4. Recompute the velocity field using the initial delay time solution.
  5. Final delay time analysis.

The problem lies in step 2. Briefly stated, at any point where delay times vary over the area of the survey, step 2 becomes inaccurate.

Back-of-the-envelope error analysis

Consider a source located at x=0 being shot into receivers extending in the positive x direction. The surface is perfectly flat. The refractor dips down to the right.

D(x) = delay time as a function on x

D(x) = D0 + M * x    (if M > 0 then the refractor dips down to the right)

Pick(x) = T(x) = Source delay + offset term + detector delay = T0 + x / V + (T0 + M * x) = 2 * T0 + x * (M + 1 / V)

The measured velocity will be a function of the refractor velocity and the dip term:

1 / V(measured) = M + 1 / V

V(measured) = V / (1 + M * V)

Example: Let V=3000m/sec, and let M=15 millisecond per kilometer. The measured velocity will be 2870 m/s.

Comments

bullet The problem will be worse near the survey edges
bullet The greater the delay time variation, the worse the problem
bullet Steps 3 through 5 DO NOT "HEAL" the velocity!

Why isn't this problem more widely known?

It seems as though very few people actually test their software on very simple, well-understood models. This is why we included in SeismicStudio the ability to create synthetic picks using imported geometry.

Can anything be done?

SeismicStudio contains a proprietary algorithm called Residual Velocity Correction (RVC). Based on extensive tests on synthetics and real data it can dramatically improve the velocity field.

Please test you current software!

(You don't need a SeismicStudio license)

  1. Download and install SeismicStudio
  2. Import your current survey geometry (either GLI files or SEGY).
  3. Create synthetic picks (Model menu ==> Synthetic picks (flat refractor)). Save them in a file.
  4. Import the picks into your current software. Do you obtain the correct velocity field?