RE: random mutation, selection and low probabilities

> -----Original Message-----
> From: Don Winterstein [mailto:dfwinterstein@msn.com]
> Sent: Monday, December 01, 2003 3:46 AM
> Glenn,
>
> I haven't personally calculated the kinds of inversions you're talking
> about, but I do know the systems are always far better constrained than
> you've indicated, and hence the probabilities of success are much higher
> than your numbers would indicate. If there's a well in or near the survey
> area, one can usually get a fairly detailed set of constraints. At sites
> where companies do 3D surveys, there often is at least one such well.

First, we need to clarify what type of inversion you are speaking of. If it
is the old 1980s style deterministic inversion, in which low frequency
control is added to the high frequency component from the seismic, then we
are speaking of separate types of processes. In the simulated annealing
process, the tie to the well consists of constraining the inversion at the
site of the well by the data actually measured at the well. But within about
100 m from any well, all bets are off in most reservoirs. There are faults,
there are sedimentological differences, saturation differences etc all of
which affect the velocity and density. So, lets see how much a restriction
of the velocity field will affect the probability.

I used 7000 velocity values. But lets see what the probability is for
getting the model right with 2000 ft/sec restraints. There are most
assuredly places where the velocity in a reservoir can vary by 2000'/s. And
lets further limit the calculation to only 200 samples (400 milliseconds).
We still get a probability of getting the AI inversion correct as one chance
in 10^23,000,000,000. Ok, it isn't 10^126,000,000,000 but even so, it makes
a mere one chance in 10^300 pale by comparison.

I would say that this won't affect the conclusion I drew at all.
Geophysical models are so much more complex than biological molecules that
if we can get usable answers from geophysical models, we can certainly
expect to get them from biological molecules.

>
> If there's no well, a lot of constraints are nevertheless obtainable from
> the seismic data themselves. First, moveout velocities often
> provide a good
> picture of the low-frequency velocity structure as a function of time.

You are speaking of the old style inversion, not the simulated annealing
which doesn't use the move out velocities at all. It produces a relative
impedance volume which is then used without adding in the low frequency
velocity control.

> Second, reflection signs and amplitudes allow for better-than-chance
> calculations of the high-frequency velocity variations.

Of course that is a constraint. That is why we take the AI, turn it into a
synthetic seismogram, and compare it with the recorded seismic. I think I
said that in my note.

 Third, density is
> often closely related to velocity, and invertors usually use some standard
> relationship.

More so in the Gulf of Mexico, where they don't do much inversion work. In
the North Sea, where they do, the relationship is less. We have volcanic
tuffs which really mess the relationships up. But once again, this
procedure applies to the older more deterministic inversions.

 Fourth, to a good approximation the inversion
> calculated for
> one trace is identical to the inversion of nearest-neighbor
> traces.

Only if you are dealing in sheet sands. Try saying that where we were
running this process in the North Sea when we had injectite sands which have
dips of up to 80 degrees and widths varying from inches to 300 feet. It was
difficult image some of these injectites. In this situation, one trace is
NOT identical to the nearest neighbor. That was what the problem was.

  Fifth,
> many inversions of this sort use only stacked section traces;
> this would cut
> down hugely on the total number of relevant traces.

We WERE using stacked traces. So there is no reduction from this direction.
When did you leave the business?

You do raise an important point, there are now pre-stack inversions in which
multiplies the number of models to be calculated by at least 5 fold above
what I calculated.

And it might be a while since you left the business. You should know that
the last seismic I acquired in the North Sea had a stacked trace every 3.125
m in the inline direction and every 12.5 m in the crossline direction. I
was kind and didn't calculate the odds off of that dense a spacing.

 More sophisticated
> inversions use amplitude-variation-with-offset (AVO). While these latter
> would use more traces, the calculations on such traces are mostly
> deterministic.

Not so any more. CGG is doing statistical inversions prestack. BP now
inverts subsets of the prestack data and uses that then to calculate the AVO
which is deterministic.

As I said, you are thinking of the old style inversions, not the new stuff.
All of the above applies to the older inversion methodology.

>
> Knowledge of the seismic wavelet is essential for unraveling the
> reflectivity accurately, but stochastic methods are often used to
> calculate
> the wavelet itself.

Agreed and we never actually obtain a fully designatured section. The
wavelet changes with time, with multiples, with absorption, etc etc ad
nauseum.

>
> In summary, seismic inversions are better constrained and hence more
> deterministic than you've indicated. This fact may not nullify
> your point,
> but it at least takes off some of your zeroes. On the other hand, I don't
> really know how you do your inversions, so maybe you really do need all
> those zeroes! <G>

Would you accept 10^23,000,000,000? If so, I will be able to sleep tonight.
:-)

Now, lets let the other shoe drop. Some inversions are being done for
exploration purposes and as you know, we don't often have lots of wells in
areas of exploration interest. Thus, the original numbers are probably
closer to being correct in those cases.
Received on Mon Dec 1 19:57:44 2003