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![]() | Local seismic attributes | ![]() |
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The definition of the local frequency attribute starts by recognizing
equation 5 as a regularized form of linear
inversion. Changing regularization from simple identity to a more
general regularization operator provides the definition
for local frequency as follows:
Figure 2 shows the results of measuring local frequency
in the test signals from Figure . I used the shaping
regularization formulation 7 with the shaping
operator
defined as a triangle smoother. The chirp signal
frequency (Figure 2a) is correctly recovered. The
dominant frequency of the synthetic signal (Figure 2b) is
correctly estimated to be stationary at 40 Hz. The local frequency of
the real trace (Figure 2c) appears to vary with time
according to the general frequency attenuation trend.
This example highlights some advantages of the local attribute method in comparison with the sliding window approach:
Figure shows seismic images from compressional (PP)
and shear (SS) reflections obtained by processing a land
nine-component survey. Figure
shows local frequencies
measured in PP and SS images after warping the SS image into PP time.
The term ``image warping'' comes from medical imaging (Wolberg, 1990)
and refers, in this case, to squeezing the SS image to PP reflection
time to make the two images display in the same coordinate system. We
can observe a general decay of frequency with time caused by seismic
attenuation. After mapping (squeezing) to PP time, the SS image
frequency appears higher in the shallow part of the image because of a
relatively low S-wave velocity but lower in the deeper part of the
image because of the apparently stronger attenuation of shear waves. A
low-frequency anomaly in the PP image might be indicative of gas
presence. Identifying and balancing non-stationary frequency
variations of multicomponent images is an essential part of the
multistep image registration technique
(Fomel and Backus, 2003; Fomel et al., 2005).
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![]() | Local seismic attributes | ![]() |
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