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Can Q Explain Observations Made from a VSP?
(1) RPS Energy, London, United Kingdom.
Summary
We present some downgoing direct arrivals from a VSP which show a higher frequency content on some deeper depth levels than observed on some shallower depth levels. An increase in frequency with increased depth must be caused by a mechanism other than Q. If we could develop an understanding of what causes this increase in frequency with depth, we will have extracted new information from our seismic data.
Introduction
Q has been offered as an explanation for many observations. We have all observed that the frequency content of our seismic data is lower at the bottom of the section than it is at the top of the section and this has been explained as the result of Q. This has led to the desire to design and apply inverse Q filters to compensate for this effect. These efforts have only had marginal success for many reasons including the lack of a good way to select an appropriate Q.
It has been hypothesized that Q is an intrinsic rock property like velocity or density. This has led to idea that if we could measure Q, we would have a new and perhaps useful tool to characterize rocks. Perhaps Q measurements could be the attribute that could distinguish hydrocarbon bearing rocks from water bearing rocks.
Background
There have been many attempts to measure Q from geophysical data. The industry has tried to measure Q from surface seismic data, from VSP data, from log data, from full waveform sonic logs and from laboratory core measurements. One compilation of such attempts may be found in chapter 7 of the Practical Handbook of Physical Properties of Rocks and Minerals edited by Robert S Carmichael. Another review of attempts to measure Q from VSP data was published by Tonn in Geophysical Prospecting. While each of these attempts has had some success, a good understanding of Q and how to measure it and how to use those measurements in our exploration efforts has not yet been achieved.
All of the papers that have attempted to measure Q have discussed the problems associated with making these measurements. Xu and Parra for example posit that if the seismic wavelet is altered by 
reflection
or transmission effects between the source and the receiver of a full waveform sonic tool, these alterations make the extraction of a Q difficult if not impossible. Even if we could make measurements where there were no reflections such as on the downgoing waves of a VSP or on full waveform sonic data from a thick homogeneous bed, we still have difficulty is making reliable measurements because of variations from shot to shot in the source or problems in how to calculate the spectrum of the wavelet . Some researchers have observed that Q varies depending on the frequency content of the source wavelet. Most researchers have measured Q values that are unreasonable but have simply discarded these measurements as contaminated and then tried to make their conclusions on the basis of the remaining supposedly uncontaminated measurements.
We would like to hypothesize that the problem is not that the complexities of the geophysical world make it difficult to make an accurate measure of Q, but that we are asking the wrong question. The phenomenon we are observing in our seismic data may be partly due to Q but can not be fully explained with Q. Therefore trying to measure Q using observations that are only partly caused by Q is a futile effort.
Methodology
We started out to write yet another paper where we measured Q. We obtained a set of downgoing waves from a VSP (Figure 1). As expected, if we examined the direct arrival wavelet, we observed that the direct arrival from the shallow depth level appeared to have a higher frequency content then the direct arrival wavelet from the deeper depth levels (Figure 2). We decided to quantify this observation by making a few measurements. One measure of the frequency content of the direct arrival wavelet is to measure the time separation between the first break and the first zero crossing following the direct arrival trough. As can be seen if Figure 3, while there is an expected overall broadening of the direct arrival wavelet from top to bottom, there are several intervals where the width of the direct arrival wavelet gets narrower with increasing depth. Q can not cause a narrowing of the direct arrival wavelet with increasing depth. Thus any attempt to measure Q from these observations will be fruitless.
We then repeated these measurements by calculating an fft on the direct arrival wavelets. These results are shown in Figure 4. Again we see that over certain depth intervals, the dominant frequency of the direct arrival wavelet increases with increasing depth. Again, this can not be caused by Q
As a sidelight, notice that the high end of the frequency spectrum is anomalous near depth level 120. It appears as though there are some missing high frequencies in the direct arrival spectrum. The hydrocarbons in this well occur near depth level 120.
Conclusions
We are going to end this paper here. We have made measurements showing the frequency spectrum from the direct arrivals of a downgoing VSP at some intervals INCREASE with increasing depth. This observation can not be explained by Q since Q would cause a decrease in frequency content with increasing depth. If Q can not explain our observations, what does? This is the subject of continuing research. Some people have proposed frequency dependant reflection coefficients
which might cause a transfer of energy from one frequency band to another. If frequency dependant reflections are possible, than frequency dependant transmissions are also possible. What effect does mode conversion have on the frequency content of the reflected and transmitted waves? If the frequency content of the seismic wavelet changes due to factors in addition to Q, we will have to move beyond the convolutional model of seismic data in order to understand these effects.
Can the missing high frequencies near depth level 120 be used as the basis for a hydrocarbon detection methodology? We at Apex Spectral Technology think so.
Disclaimer
The VSP data presented here is from a borehole of undisclosed location. The operator of the well has given us permission to show this data on condition that we state “that the analyses and the interpretations herein may not be the opinion of the Operator and or any JV partner.”