A list of inversion error causes that all attribute junkies should really understand:

1. Definition of inversion – A seismic trace is the product of the down wave convolved against the series of the coefficients of reflection between lithologic boundaries. Primary seismic events are the wave trains coming from individual bed interfaces. These events seem to travel their own paths, the overlapped complex being resolved at the receivers. The function of inversion is to solve backwards for the reflection coefficients.

2. Wavelet purity – It should be obvious that interface solutions are dependent on there being only one wavelet shape involved. Even when no noise events are present, the down wave goes through its own shape evolution with depth, introducing error when it is necessary to average over a time span to achieve statistical balance. Almost all data volumes have been subjected to deconvolution. Today’s programs effectively modify the spectra of the input to a desired output form. I call this pre-whitening. All of the problems we have in estimating inversion waveforms were there at the start, so the result of pre-whitening is a heavily averaged input matrix that drastically affects the capability of any inversion. While non-linear logic allows us to get the best answer possible, it is an uphill battle.

3. Refracted noise – The stack effectively minimizes the effect of random noise. The major coherent noise problem I have seen comes from some primary reflections cloning into “horizontally traveling refraction events”. Moving to the outside, the energy appears to separate into vertical and horizontal components. Early on, this combination shows up as a thickening. After the critical angle there seems to be a strong reverberation creating new noise events, as well as an explosion of apparent event amplitudes. This phenomenon often completely obliterates the outside traces, and even inside traces can be effected by expanding noise wave fronts.

4. Trace span determination – Much improvement in the ADAPS results comes from careful pre-stack optimization (including the dynamic trace selection made necessary by the coherent noise discussed in point 3). Unless one has seen the gathers, there is no way of knowing what problems existed during stacking. Of the dozens of gather volumes I have worked on, none were free of trace selection needs. Heavy error possibilities exist here.

5. Velocity variations - Stack resolution is directly dependent on accurate NMO. While strong amplitudes may force their way through, the resulting event wave-train is distorted by any non-random miss-alignment. Obviously any velocity error is a serious problem for inversions. Interestingly, we have noted inter-layer NMO variations that further complicate the issue.

6. Tuning considerations – Overlapping of primary events creates the effect known as “seismic tuning”. The major goal of inversion is to correct for this by solving for interfaces. Inverting after stack assumes the wave shape remains constant along the spread. However, as we will see later, this consistency is too much to ask for. Increased travel time to the outside traces dampens the high frequencies, affecting tuning. In other words this is a major source of inversion error.

7. Time-series spiking limitations – Inversion solutions are dependent of the distribution of vital information in the working domain. Transforming time data into descriptive frequencies is a modeling process. Repeat patterns readily visible in time, can require incredibly complex combinations of frequency values, making such answers more susceptible to the effect of noise. Forcing these routines to go for single spike answers makes them unstable, so they back off. Use of non-linear optimization allows guesses to be statistically averaged, giving the best answer under the noise circumstances.

8. The need for integration – If all bed boundaries were clean, linear inversions would only be faced with the computational problems stated above. Unfortunately many are layered. On the next slide you will see that ADAPS does a great job in detailing interfaces, but hopefully you will also see that mapping them is not easy. For this reason I have opted for simulating lithology by integration (the individual interfaces are the first differences of a sonic curve).

Click elsewhere to go on, or on green arrow for router that will take you to important supporting details.

The unadulterated stack The ADAPS inverted spike guesses. The simulated sonic log section.

Putting inversion into some perspective -Few interpreters today would choose the second screen over the first even though it comes close to truth and beauty. Single point spikes don’t display well, and analysts are not used to working with them. What is more, we are looking at interfaces rather than beds, and it is hard to immediately see if we are dealing with “red or blue” lithologic events. Of course the simulated sonic log sections tries to help us differentiate. I have preached on the need for “eye” training ad infinitum, and this is the reason.

Step 1 –

I repeat the unadulterated stack on the far left, then the ADAPS pre-stack optimization. On the next slide I will take you inside the stack to show what was done to get this fairly major improvement. Remember this is before inversion. The lesson is to pay attention to what is going on in the gathers.

Before you go on, take some time to really look at the individual events, and how they change Following the inside details I will again compare the raw input to the final sonic simulation, pointing out some important differences.

The unadulterated stack Optimized stack

And here we are, inside the stack, looking at a set of gathers (at one depth point) -

The red line defines the deep mute used in the pre-processing. Everything below was thrown out. The two bottom traces are stacks, before and after optimization (but using the same mute). The optimization system was looking for multiple repeats, but found none. This is a working display I use to control the preliminary action. The display starts at the top of the zone of interest and the lines are drawn every 100 samples.

There are two major phenomena of interest showing here. You will note several sharp bends (marked with red arrows). The bend junctures point to where the true reflections are cloning into horizontally traveling refractions (see noise study pointed to later). Blue arrows mark interesting examples of tuning caused by the changing frequency content of the down wave. Of course this is caused by the increased travel time. Setting the mute is interpretive of course. A lot of time is spent comparing before and after preprocessing, as on slide 2.

Obviously, the better the vertical lineup the better the resolution. If you take the time you will see intermediate events that bend within the selected zone, even though others are straight, both above and below. While I have no answer for this problem, it is important that we take this type of thing into account when we are bragging about attribute accuracy. Again we are looking for the best results possible, given the quality of the input data.

Back to the justification for integration –I start with what I consider a fact. The normal seismic section does not represent lithology, since Individual reflections come from interfaces (both from the top and the bottom of simple beds). As we have seen on slide two, even thought ADAPS can solve for the interfaces accurately, interpreting them is another matter. Given perfect input there is little doubt that the generated spikes could be integrated into a true picture of the lithology. The question has always been how close could the system come when there were problems. This is why I have put so much emphasis on honest well image matching. First I had to convince myself. That done, my confidence has built to a comfortable level

Here, at the top left, I repeat the unadulterated stack of the client input. Below I show the ADAPS integrated inversion results. Most inversion neophytes would pick the upper picture, and that is my major communication problem. The first challenge is for the reader to accept what I have stated: That is that integration completely rearranges the reflected energy, and that this the way it should be technically.

If we can get by this vital point, we can look at important differences. For simplicity let us assume we are looking at a sand shale sequence. First consider complex A. Here the normal interpretation from the straight stack would be a shale over a bight spot sand. On the integrated result we see a variable thickness shale below a sand. Just the opposite of course. Towards the center of the section we see some pretty fair fault evidence on our result. While a hint of this shows above, the integration has broken the continuity in a very believable way, supporting the existence of a fault.

If you believe I’m right in my assumptions, the ramification is that inversion / integration is an interpretation necessity rather than a luxury. So take some time to examine other events and be sure to visit the examples among the branch options below. After a long and frustrating battle to gain acceptance I now place a high value on technical closure.

In the order of important things, my coherent noise study comes high on the list. Please click on the illustration to go there.

In non-linear work, proof lies both in logic and results. Please spend some (more) time in my “examples” show, paying particular attention to the before and after case where I point to the lobe simplification proven by the well image overlay. To get there click on the self-satisfied icon at the left and give it time to load.

Or click on the oval for the main ADAPS router (where you might find other answers or even generate more questions).