--> Interpretation Value of Anomalous (‘Impossible’) Frequencies, by Bob Hardage, #40286 (2008)
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GC Interpretation Value of Anomalous (‘Impossible’) Frequencies*

By

Bob Hardage1

 

Search and Discovery Article #40286 (2008)

Posted April 30, 2008

 

*Adapted from the Geophysical Corner column, prepared by the author, in AAPG Explorer, April, 2008, and entitled “Finding the Value of ‘Impossible’.” Editor of Geophysical Corner is Bob A. Hardage. Managing Editor of AAPG Explorer is Vern Stefanic; Larry Nation is Communications Director.

 

1 Bureau of Economic Geology, The University of Texas at Austin ([email protected])

 

General Statement

Two constraints can be imposed on the Previous HitfrequencyNext Hit behavior of a digital seismic wiggle trace:

1) Each Previous HitfrequencyNext Hit component of the trace is a positive quantity. Frequencies can have a negative algebraic sign in some mathematical operations, such as Fourier transforms, but when the oscillatory behavior of an actual wiggle trace is visually examined to estimate seismic Previous HitfrequencyNext Hit, the Previous HitfrequencyNext Hit estimate is always a positive number. The situation is much like trying to dial a radio to a negative Previous HitfrequencyNext Hit to listen to music. Negative frequencies are just not a part of the real world.

2) No Previous HitfrequencyNext Hit component can exceed the Previous HitNyquistNext Hit limit fN, which is defined as:

fN = 1/(2Δt),

where Δt is the time sample interval of the digital data in units of seconds.

Because of these constraints, when an instantaneous Previous HitfrequencyNext Hit attribute is calculated along the time extent of a seismic trace, the Previous HitfrequencyNext Hit value should never be negative at any time coordinate, nor should the value ever exceed the Previous HitNyquistNext Hit limit.

Instantaneous frequencies, however, always exhibit negative values and values greater than Previous HitNyquistNext Hit at numerous locations throughout a 3-D seismic data volume. The term “impossible frequencies” is used in this article to refer to these anomalous Previous HitfrequencyNext Hit values that violate the constraints just stated.

 

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Figure Captions

Figure 1. Map of instantaneous Previous HitfrequencyNext Hit behavior across a thin-bed turbidite system. Negative frequencies (red) and frequencies greater than Previous HitNyquistNext Hit (darkest black) are impossible Previous HitfrequencyNext Hit values but are commonly created by software that generates instantaneous seismic attributes. Arrows show where three arbitrary profiles intersect trends of impossible frequencies.

Figure 2. Vertical seismic section along profiles (a) A and (b) XL57 (Figure 1). The map in Figure 1 is 10 ms below and conformable to horizon K. Circled locations show where the profile crosses a trend of impossible frequencies.

Figure 3. Map of hypothetical reservoir compartment boundaries that follow trends of impossible frequencies. The map implies that area A has small reservoir compartments and area B is a large reservoir compartment.

 

Example

Figure 1 shows an example of impossible frequencies occurring in a 3-D seismic volume; the surface being analyzed in this instance is a horizon that passes through the Brushy Canyon Formation in an area of the Delaware Basin in New Mexico. At this prospect area, the Brushy Canyon is a sequence of fine-grained siliciclastic units deposited in a deepwater turbidite environment.

The color bar used to display the instantaneous Previous HitfrequencyNext Hit behavior was chosen to emphasize impossible frequencies, with all negative frequencies shown as bright red and all frequencies that equal or exceed the Previous HitNyquistNext Hit limit (125 Hz in this case) shown as darkest black. The arrows positioned along arbitrary lines A, XL91, and XL57 mark where each profile crosses a reasonably continuous trend of these impossible frequencies.

Vertical profiles along lines A and XL57 are displayed as Figure 2 to illustrate the wavelet character that is associated with these impossible frequencies. The position of the attribute surface in Figure 1 is 10 ms below the K horizon along these profiles. The location of each anomalous Previous HitfrequencyNext Hit arrow shown along the map horizon (Figure 1) is indicated by a circle.

At each of these circled coordinates there is a reflection termination or some type of abrupt change in the wave form of the reflection wavelet. Interpreters working with these particular attribute displays concluded that most of these anomalous frequencies were marking stratigraphic pinch-outs or reservoir compartment boundaries. If true, then “impossible frequencies” have great interpretational value.

Applying the assumption that, in this instance, impossible frequencies define boundaries of reservoir compartments, a tentative reservoir-compartment map such as that shown in Figure 3 can be constructed. The compartments on this map were created by drawing boundaries along trends suggested by the alignments of the impossible frequencies. Each boundary defined by this “connect-the-dots” method is arbitrary; other interpreters would connect the dots in different ways and cause some compartments to have sizes and shapes that differ from those shown on this map.

Is the assumption that impossible frequencies define compartment boundaries valid in this case? At this prospect, there is circumstantial evidence that the answer is “yes.”

1) Drilling has confirmed that wells in area A (Figure 3) penetrate small reservoir compartments at this stratigraphic level – the same principle implied by the Previous HitfrequencyTop-based map.

2) A horizontal well drilled across area B has been the most prolific Brushy Canyon producer across a broad area of the basin, confirming that the well penetrated a large compartment, as indicated by the compartment map.

 

Conclusion

Will impossible frequencies be valuable indicators of stratigraphic terminations and/or compartment boundaries in other areas and in other depositional environments? Always consider the possibility that they will.

Incidentally, some commercial interpretation software arbitrarily deletes the negative algebraic sign of any negative frequencies created by their algorithms, a practice that may not be a desirable thing to do. Those negative frequencies can be important information.

 

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