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Understanding the Previous HitSeismicNext Hit Wavelet*

By

Steven G. Henry1

 

Search and Discovery Article #40028 (2001)

 

1Geolearn, Houston, TX ([email protected])

 

*Adapted for online presentation from two articles by same author, entitled “Catch the (Previous HitSeismicNext Hit) Wavelet” in Geophysical Corner, AAPG Explorer, March, 1997, and “Zero Previous HitPhaseNext Hit Can Aid Interpretation” in Geophysical Corner, AAPG Explorer, April, 1997. Appreciation is expressed to the author and to M. Ray Thomasson, former Chairman of the AAPG Geophysical Integration Committee, and Larry Nation, AAPG Communications Director, for their support of this online version.

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uSummary statement

uFigure captions

uGoals of deconvolution

uComparison of different methods of deconvolution

uConclusion

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary Statement

The Previous HitseismicNext Hit wavelet is the link between Previous HitseismicNext Hit data (traces) on which interpretations are based and the geology (reflection coefficients) that is being interpreted, and it must be known to interpret the geology correctly. However, it is typically unknown, and assumed to be both broad band and zero Previous HitphaseNext Hit. Providing this broad band, zero Previous HitphaseNext Hit wavelet is the processing goal of deconvolution. Unfortunately, this goal is rarely met and the typical wavelet that remains in fully processed Previous HitseismicNext Hit data is mixed-Previous HitphaseNext Hit. Differences in mixed-Previous HitphaseNext Hit wavelets result in mis-ties and often incorrect interpretations.

The purpose of this article is to show interpreters that significant improvements in Previous HitseismicNext Hit data quality and, correspondingly, their interpretations of those data are easily obtainable by converting from mixed-Previous HitphaseNext Hit to zero Previous HitphaseNext Hit wavelets.

Figure Captions

Figure 1: Lithologic boundaries define a Reflection Coefficient series, which when convolved (*) with the field wavelet results in a simulated raw field trace. Interpreting the highest amplitude event (2.5 seconds) as the reservoir sand would be wrong. This mixed-Previous HitphaseNext Hit wavelet provides a distorted image of the actual geology.

Figure 2: When the field wavelet is known, deterministic deconvolution is able to produce a processed trace that contains the desired broad band zero Previous HitphaseNext Hit wavelet. Note, the highest amplitude in the processed trace is now associated with the largest Reflection Coefficient at the top sand.

Figure 3: Extracted wavelet and the associated amplitude and Previous HitphaseNext Hit spectrum. 

 

Figure 4: Previous HitSeismicNext Hit data containing this mixed-Previous HitphaseNext Hit wavelet will display a changing peak trough relationship (-90 degrees to +60 degrees) and time shift (linear Previous HitphaseNext Hit) due to the earth’s attenuation of higher frequencies with depth. For simplicity, the waveforms shown here are only for the top sand reflector.

Figure 5. These wavelets have been extracted from the Previous HitseismicNext Hit in Figures 7 and 8 using the well reflection Coefficients Statistical Deconvolution (a) commonly produces mixed-Previous HitphaseNext Hit wavelets. The broad band - zero Previous HitphaseNext Hit processing goal of deconvolution has been met using Deterministic Deconvolution (b).

Figure 6. The mixed-Previous HitphaseNext Hit wavelet (Figure 5a) has the character of “Pinocchio with a beer-gut.”  Each reflector has a sharp nose followed by a low-frequency “beer-gut.”  The zero Previous HitphaseNext Hit wavelet (Figure 5b) has all the energy moved up to Pinocchio’s nose. Reflectors lacking the wavelet’s beer-gut more clearly image the subsurface geology.

Figure 7. Previous HitSeismicNext Hit data identical to Figure 8 other than the method of deconvolution, Statistical. This Previous HitseismicNext Hit data contains the mixed-Previous HitphaseNext Hit wavelet of Figure 5a. The “Pinocchio with a “beer-gut” character can be seen as the trailing low frequencies beneath the high amplitude reflectors. Mixed-Previous HitphaseNext Hit wavelets reduces the ability to accurately resolve the subsurface geology. 

Click here for sequence of Figures 7  and 8.

Figure 8. Previous HitSeismicNext Hit data identical to Figure 7 other than method of deconvolution, Deterministic. This Previous HitseismicNext Hit data contains the desired zero Previous HitphaseNext Hit wavelet (Figure 5b). Note that reflectors are sharper and lack the low-frequency “beer-gut” of the mixed- Previous HitphaseNext Hit wavelet. In general reflector continuity, fault breaks, and stratigraphic relationships are significantly improved.

Click here for sequence of Figures 7  and 8.

Figure 9. Enlargement of corresponding parts in upper left of Figures 7 and 8, showing significantly different Previous HitseismicNext Hit images from the same subsurface geology. The zero Previous HitphaseNext Hit (b) Previous HitseismicNext Hit data not only “looks” better, but also provides a more accurate image. Mixed-Previous HitphaseNext Hit wavelets distort the Previous HitseismicNext Hit image and can lead to incorrect interpretations.

Figure 10. Enlargement from corresponding parts in lower right of Figures 7 and 8 showing significant improvements in the definition of faults are seen on the zero Previous HitphaseNext Hit Previous HitseismicNext Hit data (b). “Pinocchio’s beer-gut” in the mixed-Previous HitphaseNext Hit Previous HitseismicNext Hit data (a) hangs over the faults, distorting the image. Reflector continuity and stratigraphic relationships are also improved in the Previous HitseismicNext Hit data containing the zero Previous HitphaseNext Hit wavelet.

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Goals of Deconvolution

Previous HitSeismicNext Hit data can provide a remarkably good image of the subsurface. However, without knowing the Previous HitseismicNext Hit wavelet, there are many equally valid surface geologic interpretations of the actual subsurface geology. The Previous HitseismicNext Hit wavelet is the filter through which geology is viewed when interpreting the image provided by Previous HitseismicNext Hit data.

The common assumption that Previous HitseismicNext Hit data contain a broad band - zero Previous HitphaseNext Hit wavelet is nearly always wrong. The majority of mis-tie problems between Previous HitseismicNext Hit and synthetics, Previous HitseismicNext Hit to Previous HitseismicNext Hit of different vintages, and many of the misinterpretations based on modeling (lithology prediction, trace attributes, AVO, etc.) are the result of mixed-Previous HitphaseNext Hit wavelets remaining in fully processed Previous HitseismicNext Hit data.

The convolutional model is useful for understanding how changes in rock properties (velocity and density) result in the waveform changes observed in Previous HitseismicNext Hit data. At lithologic boundaries the magnitude of change (reflection coefficient) in these rock properties determines how much of the wavelet’s energy is reflected to the surface. In acquiring Previous HitseismicNext Hit data (Figure 1), the subsurface is illuminated with sonic energy (field wavelet), which is reflected from these acoustic boundaries and recorded at the surface as a raw field trace.

Where lithologic boundaries are widely separated, the field wavelet can be seen “hanging” below the reflector at 2.2 seconds (Figure 1). When boundaries are more closely spaced (2.3-2.5 seconds), the wavelet is not as easily seen due to the wavelets being summed together. This summing is also known as convolution.

The convolutional model states that all Previous HitseismicNext Hit traces are the result of convolving (summing) the wavelet with the reflection coefficient series. In Figure 1, the raw field trace images the desired geology (lithologic boundaries = reflection coefficients), but it is through the complex filter (convolution) of the field wavelet.

Exploring for the sand in Figure 1 and assuming the wavelet is broad band - zero Previous HitphaseNext Hit, the sand should be the largest peak. The largest peak, however, is at 2.5 seconds, due to the field wavelet not being zero Previous HitphaseNext Hit. When the wavelet in the Previous HitseismicNext Hit trace is unknown, the geology is unknown. Interpretations are not made on raw field traces, but even on processed Previous HitseismicNext Hit traces, the wavelet must be known to more correctly interpret the geology.

The Previous HitseismicNext Hit processing procedure designed to convert the field wavelet to the desired broad band - zero Previous HitphaseNext Hit wavelet is deconvolution. The two common methods of deconvolution are deterministic deconvolution and statistical deconvolution.

Deterministic deconvolution can be applied when the field wavelet is known (measured and/or modeled). As shown in Figure 2, when the wavelet is known, an inverse can be determined and the field trace deconvolved to contain the desired zero Previous HitphaseNext Hit wavelet. When processed traces contain a zero Previous HitphaseNext Hit wavelet, increases in rock velocity (shale to sand) will result in peaks (positive reflection coefficients). 

More typically, the field wavelet is unknown and statistical deconvolutions must be used. Statistical deconvolutions must make assumptions about both the wavelet and the reflection coefficient series. The most common assumption is that the wavelet is minimum Previous HitphaseNext Hit and that the reflection coefficient series is random.

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Over 90 percent of all Previous HitseismicNext Hit data are processed assuming minimum Previous HitphaseNext Hit. Examples of a few of the more popular minimum Previous HitphaseNext Hit deconvolutions include Spiking, Gapped, Predictive, and Adaptive. Unfortunately, most field wavelets are not minimum Previous HitphaseNext Hit, and that basic assumption is not met. Using minimum Previous HitphaseNext Hit deconvolutions typically results in processed traces that contain mixed-Previous HitphaseNext Hit rather than the desired zero Previous HitphaseNext Hit wavelets.

A wavelet extracted deterministically from Previous HitseismicNext Hit data (using the known reflection coefficient series from the well) that had been deconvolved assuming minimum Previous HitphaseNext Hit is shown in Figure 3. Note that this wavelet is not zero Previous HitphaseNext Hit (Previous HitphaseNext Hit spectrum: constant zero value for all frequencies) but is mixed Previous HitphaseNext Hit (non-linear, variable for all frequencies).

In describing mixed-Previous HitphaseNext Hit wavelets, it is useful to group frequency into bands in which a linear fit can be extrapolated to the Previous HitphaseNext Hit axis (Previous HitphaseNext Hit spectrum). For the wavelet in Figure 3, the higher frequencies (20-65 Hertz) have a Previous HitphaseNext Hit of -90 degrees, while the lower frequencies (5-20 Hertz) have a Previous HitphaseNext Hit of +60 degrees.

The description of this mixed-Previous HitphaseNext Hit wavelet is interpretive, and could be described differently by using other frequency bands. Using the bands shown in Figure 3, with most of the power (amplitude spectrum squared) in the 20-65 Hertz band, this wavelet has the Previous HitphaseNext Hit characteristic of -90 degrees (trough-peak).

An important ramification of mixed-Previous HitphaseNext Hit wavelets is that their peak-trough relationships will change with depth due to the effects of earth filtering. In the case of the wavelet shown in Figure 3, shallow in the section where the earth has not filtered the higher frequences (maximum power 20-60 Hertz), positive reflectors (low to high velocity) will display -90 degrees (trough-peak). Deep in the section where the high frequencies have been attenuated (dashed line in the amplitude spectra, Figure 3), the wavelet will appear with the Previous HitphaseNext Hit characteristics of the lower frequencies and will have a Previous HitphaseNext Hit of +60 degrees (peak-trough).

Mixed-Previous HitphaseNext Hit wavelets are the most common wavelets found in Previous HitseismicNext Hit data and can have a strong affect on interpretations. This is shown in Figure 4 by filtering back (5-20 Hertz) the processed wavelet to illustrate strong earth filtering. The identical reservoir sandstone would appear as a trough-peak (-90 degrees) shallow (1.0 seconds) in the section and as a peak-trough (+60 degrees) deeper (3.0 seconds) in the section. This change in the peak-trough relationship due to earth filtering is commonly observed when comparing constant Previous HitphaseNext Hit synthetics (from well logs) to Previous HitseismicNext Hit data. Typically this problem is compensated by applying a bulk time shift (linear Previous HitphaseNext Hit shift) and changing the constant Previous HitphaseNext Hit wavelet used in making the synthetic.

Combining these corrections will approximate the curved shape of the mixed-Previous HitphaseNext Hit (Figure 3) with a single sloping line (time shift) that intersects the Previous HitphaseNext Hit axis at the desired constant Previous HitphaseNext Hit. A different time shift and constant Previous HitphaseNext Hit is required to match the curve deeper in the section due to the earth’s absorption of higher frequencies.

Due to the mixed-Previous HitphaseNext Hit wavelet, peak-trough relationship change as a function of earth absorption (Figure 4), and interpretations based on amplitudes, AVO, attributes, etc., are likely to be incorrect. The solutions to these problems are to convert the mixed-Previous HitphaseNext Hit wavelet to zero Previous HitphaseNext Hit in Previous HitseismicNext Hit processing or to extract the mixed-Previous HitphaseNext Hit wavelet, know its effects, and use it when modeling.

When interpreting Previous HitseismicNext Hit data, it is important to realize that the actual subsurface geology is always being viewed through the filter of the Previous HitseismicNext Hit wavelet. Although deconvolution is designed to provide a broad band - zero Previous HitphaseNext Hit wavelet, this goal is typically not met, and most Previous HitseismicNext Hit data contain mixed-Previous HitphaseNext Hit wavelets. Mixed-Previous HitphaseNext Hit wavelets affect interpretations and, as noted below, degrade the quality of Previous HitseismicNext Hit data.

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Comparison of Previous HitSeismicNext Hit Data After Different Methods of Deconvolution

The wavelets shown in Figure 5 were extracted from the Previous HitseismicNext Hit data in Figures 7 and 8. Both sets of Previous HitseismicNext Hit data were processed identically, other than the method of deconvolution (statistical-minimum Previous HitphaseNext Hit vs. deterministic). The wavelets were extracted deterministically, by cross-correlating (Wiener-Levinson filter) Previous HitseismicNext Hit traces with the known geology derived from the subsurface well reflection coefficient series. At first glance, most interpreters would be content having either of these “spike-like” wavelets convolved on the subsurface reflectors. The primary difference between these wavelets is that statistical deconvolution has resulted in a mixed-Previous HitphaseNext Hit wavelet (Figure 5 Previous HitphaseNext Hit spectrum), whereas the deterministic deconvolution provided the desired broad band, zero Previous HitphaseNext Hit wavelet. These seemingly minor differences in the Previous HitphaseNext Hit spectra (Figure 5) have a significant effect on the Previous HitseismicNext Hit data’s overall quality. Although the “quality” of Previous HitseismicNext Hit data has always been in the “eye of the beholder,” the conversion from mixed-Previous HitphaseNext Hit to zero Previous HitphaseNext Hit provides a more accurate image of the subsurface geology.

The reason for the improved accuracy is illustrated in Figure 6. The extracted wavelets (Figure 5) have been convolved on a single reflector (Top Sand). Note that the mixed-Previous HitphaseNext Hit wavelet has sharp “Pinocchio-like” nose at the top of the sand, but is followed by a low-frequency “beer-gut.” When Previous HitseismicNext Hit data contains a mixed-Previous HitphaseNext Hit wavelet, each reflector has this “Pinocchio with a beer-gut” character. Neighboring reflectors deeper in the section (base sand) are Previous HitphaseNext Hit rotated and lose amplitude as their “noses” are summed with the “beer-guts” from above.

The zero Previous HitphaseNext Hit wavelet’s sharp “nose” provides a clear image of the top sand, and its “flat belly” does not interfere with neighboring reflectors. The comparison of the Previous HitseismicNext Hit data in Figures 7 and 8 illustrate typical improvements that are easily obtainable by converting from mixed-Previous HitphaseNext Hit to zero Previous HitphaseNext Hit. Both Previous HitseismicNext Hit sections “look” good, and visual advantages can be found in each. In general, however, the Previous HitseismicNext Hit data containing the zero Previous HitphaseNext Hit wavelet (Figure 8) have a better overall reflector continuity, better fault definition and more easily identified stratigraphic relationships. Mixed-Previous HitphaseNext Hit wavelets may occasionally tune to enhance a particular reflector (Figure 7 – increased continuity), but the overall quality of mixed-Previous HitphaseNext Hit data is lower.

The Previous HitseismicNext Hit data comparison for the shallower section is shown in Figure 9.

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Due to minor earth absorption, the majority of the wavelet’s Previous HitphaseNext Hit characteristics, as noted above, are derived from the higher frequencies (20-65 Hertz). The lower frequencies, although contributing less, still influence the character of the reflectors. The non-zero Previous HitphaseNext Hit components (5-20 Hertz) of the mixed-Previous HitphaseNext Hit wavelet (Figure 9a) can be seen distorting the image of the geology.

These two images (Figure 9a and b) of the same geology would likely result in different interpretations. For example, laterally discontinuous reflectors within the high amplitude package (2.2-2.3 seconds) appear with different Previous HitseismicNext Hit character and even in different locations. Interpretation of them (channel sands? carbonate mounds?) and their position relative to the deeper high amplitude reflector (within/below--Figure 9a, or above--Figure 9b) are in question. Knowing that mixed-Previous HitphaseNext Hit wavelets distort the Previous HitseismicNext Hit image, the interpretation should be made from the zero Previous HitphaseNext Hit Previous HitseismicNext Hit data.

In general, the zero Previous HitphaseNext Hit wavelet provides a much sharper (broad band - zero Previous HitphaseNext Hit) image of the subsurface geology. Stratigraphic relationships above 2.0 seconds (Figure 9) are more clearly defined, and reflector continuity in general (especially 2.6 seconds) is improved. Deeper in the section (Figure 10), as the earth’s filtering of the higher frequencies increases, the lower frequencies contribute more strongly to the wavelet’s Previous HitphaseNext Hit characteristic (as described above). In the mixed-Previous HitphaseNext Hit Previous HitseismicNext Hit data, the non-zero (135 degrees) low-frequency (5-20 Hertz) components begin contributing more. This adds to the distortion seen shallow in the section (Figure 9), further reducing the ability to image the geology accurately.

Absorption also affects the zero Previous HitphaseNext Hit wavelet, reducing high frequencies (narrowing the bandwidth) and thereby stretching out the wavelet. However, since all frequencies (5-65 Hertz) are zero Previous HitphaseNext Hit, the Previous HitseismicNext Hit image provides an accurate representation of the geology. 

The most striking improvement seen in the zero Previous HitphaseNext Hit Previous HitseismicNext Hit data (Figure 10b) is the ability to define faults more accurately. The mixed-Previous HitphaseNext Hit wavelet’s “beer-gut,” which has grown with depth due to absorption (loss of high frequencies), is hanging in the fault zones. “Noses” on the other side of the faults are smeared out by the “beer-guts” from above. Other significant improvements seen in the zero Previous HitphaseNext Hit Previous HitseismicNext Hit data are the improved continuity of reflectors and the imaging of geologic details needed for stratigraphic interpretations. The zero Previous HitphaseNext Hit wavelet, as shown in these examples, provides a more accurate image of the subsurface geology than the mixed-Previous HitphaseNext Hit wavelet.

Conclusion

Significant improvements in the quality of Previous HitseismicNext Hit data are shown here to be easily obtainable when wavelets are converted from mixed-Previous HitphaseNext Hit to zero Previous HitphaseNext Hit by extracting the wavelet and filtering the data. This added effort to provide Previous HitseismicNext Hit data that meets the zero Previous HitphaseTop assumption will improve the accuracy of the interpreted subsurface geology and provide the correct input to many software packages (Attributes, Amplitudes, AVO) used to reduce exploration risks.

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