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GCInstantaneous Seismic
Attributes
Calculated by the Hilbert Transform*
Bob Hardage1
Search and Discovery Article #40563 (2010)
Posted July 17, 2010
*Adapted from the Geophysical Corner column, prepared by the author, in AAPG Explorer, June, 2010, and entitled “Thin Is In: Here’s a Helpful Attribute”. 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 “Reflection Events and Their Polarities Defined by the Hilbert Transform”, Search and Discovery article #40564.
1Bureau of Economic Geology, The University of Texas at Austin ([email protected])
Geological interpretation of seismic
data is commonly done by analyzing patterns of
seismic
amplitude, phase and frequency in map and section views across a prospect area. Although many
seismic
attributes
have been utilized to emphasize geologic targets and to define critical rock and fluid properties, these three simple
attributes
– amplitude, phase and frequency – remain the mainstay of geological interpretation of
seismic
data.
Any procedure that extracts and displays any of these seismic
parameters in a convenient and understandable manner is an invaluable interpretation tool. A little more than 30 years ago, M.T. Taner and Robert E. Sheriff introduced the concept of using the Hilbert transform to calculate
seismic
amplitude, phase and frequency instantaneously – meaning a value for each parameter is calculated at each time sample of a
seismic
trace. That Hilbert transform approach now forms the basis by which almost all amplitude, phase and frequency
attributes
are calculated by today’s
seismic
interpretation software
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The action of the Hilbert transform is to convert a
These two traces combine to form a complex trace z(t), which appears as a helix that spirals around the time axis. The projection of complex trace z(t) onto the real plane is the actual
The orientation angle Ф(t) that defines where vector a(t) is pointing (Figure 2) is defined as the
The calculation of these three interpretation
Taner, M.T. and Robert E. Sheriff, 1977, Application of Amplitude, Frequency, and Other
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