--> Reflection Events and Their Polarities Defined by the Hilbert Transform, Bob Hardage, #40564 (2010)
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GCPrevious HitReflectionNext Hit Events and Their Polarities Defined by the Hilbert Transform*

 

Bob Hardage1

 

Search and Discovery Article #40564 (2010)

Posted July 30, 2010

 

*Adapted from the Geophysical Corner column, prepared by the author, in AAPG Explorer, July, 2010, and entitled “Previous HitComplexNext Hit Traces: There’s an ‘App’ for That”. Editor of Geophysical Corner is Bob A. Hardage ([email protected]). Managing Editor of AAPG Explorer is Vern Stefanic; Larry Nation is Communications Director.  Please see closely related article “Instantaneous Seismic Attributes Calculated by the Hilbert Transform”, Search and Discovery article #40563.

 

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

 

General Statement

 

Previously we introduced the concept of a Previous HitcomplexNext Hit seismic trace (“Instantaneous Seismic Attributes Calculated by the Hilbert Transform”, Search and Discovery article #40563); here we’ll show how a Previous HitcomplexNext Hit trace provides a rigorous way to set the boundaries of data windows associated with distinct seismic reflections – and we’ll define the polarities of each of those Previous HitreflectionNext Hit events. This Previous HitcomplexNext Hit trace application is important because it is necessary to determine the polarity of every Previous HitreflectionNext Hit event that spans a layered system in order to determine whether impedance increases or decreases from layer to layer – which in turn provides insight into the lithology, porosity and type of pore fluid in each rock layer.

 

The principal problem involved in determining the polarity of a seismic Previous HitreflectionNext Hit event is the challenge of deciding what part of the seismic response represents the Previous HitreflectionNext Hit event. Questions that have to be answered include:

 

· Where does the Previous HitreflectionNext Hit event start and stop?

 

· How many peaks and troughs are embedded in the Previous HitreflectionNext Hit event?

 

· Which peak or trough of a Previous HitreflectionNext Hit event should be used to define Previous HitreflectionNext Hit polarity?

 

The amplitude-envelope function determined from a Previous HitcomplexNext Hit seismic trace provides a way to define the start time, stop time, wavelet character and polarity of overlapping – but distinct – Previous HitreflectionNext Hit events.

 

Figure Captions

 

General statement
Figures
Previous HitReflectionNext Hit events

Previous HitReflectionNext Hit polarity




















 

General statement
Figures
Previous HitReflectionNext Hit events

Previous HitReflectionNext Hit polarity




















 

General statement
Figures
Previous HitReflectionNext Hit events
Previous HitReflectionNext Hit polarity

















General statement
Figures
Previous HitReflectionNext Hit events
Previous HitReflectionNext Hit polarity




















 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fig01

Figure 1. The concept of an energy packet (or wavelet packet) being used to define the time extents and polarities of Previous HitreflectionNext Hit events. The wavelet that illuminates the geology is shown in the center. The resulting Previous HitreflectionNext Hit trace is displayed on the left. The display on the right is a Previous HitcomplexNext Hit seismic trace consisting of a real part (which is the real trace on the left repeated as a solid-line wiggle) and an imaginary part (the Hilbert transform of the real trace shown by the dash-line wiggle). The amplitude envelope is the function that bounds this Previous HitcomplexNext Hit trace on the left and right so as to touch every positive and negative extremum of the real and imaginary parts of the Previous HitcomplexNext Hit trace.

fig02

Figure 2. Example 2 of energy packets being used to define distinct Previous HitreflectionNext Hit events in the seismic trace on the left and also the polarities of those reflections.

 

Defining Previous HitReflectionNext Hit Events

 

An example seismic trace, its Previous HitcomplexNext Hit-trace equivalent and the associated amplitude envelope are shown as Figure 1:  the amplitude envelope of a Previous HitcomplexNext Hit seismic trace is an oscillating function that has alternating maxima and minima. The data window between two successive minima of an amplitude-envelope function defines a distinct packet of seismic energy. Terms that have been used to describe this interval between successive amplitude-envelope minima are energy packet, wavelet packet and Previous HitreflectionNext Hit event. Once you equate the term “Previous HitreflectionNext Hit event” with energy packet (or with wavelet packet), you can then ask the question: “How many Previous HitreflectionNext Hit events occur between time coordinates A and B on Figure 1?”

 

You will get the definitive answer “13.” A wavelet packet such as any of those defined on Figure 1 may be a Previous HitreflectionNext Hit from a single interface, or it may be a composite of several reflections from closely spaced interfaces. In either case, a wavelet packet represents the shortest-time concentration of Previous HitreflectionNext Hit of energy that can be recognized in a seismic response. Because amplitude-envelope minima can be determined numerically after an amplitude envelope is calculated, the start time, stop time and time extent of a Previous HitreflectionNext Hit event can be defined with mathematical rigor, as shown by each of the labeled “events” on Figure 1, and do not have to be left to interpreter judgment. The basic seismic wavelet that is embedded in the seismic trace on the left of Figure 1 is shown in the center part of the figure. A reader can compare this wavelet with its associated Previous HitreflectionNext Hit trace on the left of the display to attempt to decide how many Previous HitreflectionNext Hit events exist across the time interval A to B. In classroom and workshop exercises, people have tended to conclude that the number of Previous HitreflectionNext Hit events ranges from a low of five or six to a high of 17 or 18. Using the mathematical concept of amplitude-envelope minima to define the boundaries of a Previous HitreflectionNext Hit event, the correct answer is 13 Previous HitreflectionNext Hit events (right-hand panel) as already stated.

 

Defining Previous HitReflectionNext Hit Polarity

 

When a Previous HitreflectionNext Hit event is defined by this energy packet concept, the polarity of the Previous HitreflectionNext Hit event can be defined as the algebraic sign of the real-trace extremum (either peak or trough) that is closest to the maximum of the amplitude-envelope that encompasses the energy packet. Using this concept, the polarity of Previous HitreflectionNext Hit events 5 and 10 on Figure 1 are positive, and the polarities of Previous HitreflectionNext Hit events 7 and 12 are negative. Thus a Previous HitcomplexNext Hit-trace allows seismic Previous HitreflectionNext Hit polarity to be defined with the same mathematical rigor that defines the time extent of each Previous HitreflectionNext Hit event.

 

A second illustration of energy packets being used to define distinct Previous HitreflectionNext Hit events and their polarities is provided as Figure 2. In this case, there are excellent examples of energy packets distinguishing overlapping Previous HitreflectionTop events (events 7 and 8, and events 11 and 12) and defining the data windows spanned by faint, low-amplitude reflections (events 2 and 3).

 

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