So where does the ADAPS optimization method fit into this framework?

1. So where does the ADAPS optimization method fit into this framework? The seismic trace equation does not fit the linear definition, since the values on both sides of the equal sign are unknown. A time series analysis group out of MIT achieved a linearity of sorts by moving into the frequency domain. Here, the seismic traces are modeled by frequency component, forming an observed composite spectrum.This vector is equated to an ideal spectrum convolved with an unknown filter to be established This target filter is then applied to all member traces, the results supposedly representing a cube of reflection coefficients. In order to achieve its goals, this total mathematical process has to effectively simulate the shape of the original down wave. This is a very sensitive operation, since very similar spectra can create drastically different shapes. In other parts of my series I expound on why I believe these results are error prone. However they form the base of current approaches. New, “stochastic” methods try to harness well information to improve on accuracy. My iterative solution also starts by loading an intelligent wavelet guess into the equation However, this initial guess is computed using pattern recognition tools and does not use any well information. This wavelet is correlated with the trace and spike guesses are created in a somewhat intelligent way. Once each guess is established, the system removes the correlative energy from the working trace and goes back for another guess. When it has done all it can do productively, it uses the set of spike guesses it has created to synthesize an improved wavelet guess. While the total set of overlapped iterations is complex, this is the gist of what it is doing. The total driving logic is the glory of the system. At the left you see a before and after example proving it knows what it is doing.Other examples are available. I believe there is a higher level of mathematical logic which ties such statistical approaches to linearity. Certainly once a set of guesses is plugged in the relationship fits the scheme. Breaking the internals into discrete steps that can be optimized is a major thing. The biggest advantage however lies in the ability to solve for individual spikes. Trying to go that far in our linear approaches creates instability. Essentially other processes have to settle for the elimination of side lobes. Obviously there will be positional and amplitude errors in our answers, but they are averaged statistically. Being able to solve for spikes opens up the possibility of integrating the spiked results to accomplish maximum detuning. All of this is described within my main series of course. Before After So back to the survey with a related question - Can I do seismic inversion without well control? Asked by Mahmoud Abu El Qader, it resulted in a very active give and take (27 comments). The bulk of the discussion was carried on between Scott Singleton and a few others. I took particular interest here, since my ADAPS system does not use well input. Singleton’s first entry essentially said it could, stating that the wavelet could be determined from the frequency spectrum of the seismic in the zone of interest, that phase could be determined from the sea floor and that interval velocities calculated from RMS stacking velocities can be used for the 0 –2 hz component. And I say would that it would be that easy. The raw data in the zone of interest represents highly overlapped wave shapes where the phase is confused by seismic tuning. Trying to get an accurate wave shape using time series methods is doomed to failure. Determining the phase from the sea floor ignores how the down wave evolves with time. Using low frequency components derived from velocities to further shape the wavelet is a rather gross process subject to error. Of course trying to do these things on land data is even more problematical. Singleton goes on to say “after this exercise you are still missing two things – (1) the 2–8 hz component of the low frequency model, which is normally supplied from well control, and (2) calibration of impedance result. Because of this, most people will opt for a relative inversion product and be happy with that.” I am assuming “relative inversion product” refers to an old fashioned, time series, frequency domain solution. In any case there seems to be a contradiction here, essentially saying any results without well control are substandard. Of course I agree with this, but for completely different reasons. Unfortunately my going through these comments is slow, because I keep getting hung up on statements that blow my mind. For example, the latest one maintained “the operator could be estimated from the frequency spectrum” which is wild in my mind. I hesitate to respond for fear I will be even more sarcastic than usual. Time ran out. More tomorrow. Click on oval to go to my router.