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Introduction

Seismic signals are nonlinear, aperiodic and
non-stationary in nature. Hilbert Huang Transform (HHT) is used for the signal
processing and is effective in case of non-stationary and non-linear signals 2.
This transform consists of two different techniques i.e. Empirical Mode
Decomposition (EMD) followed by Hilbert Spectral Analysis (HSA) due to Huang et
al. and Huang and Wu 2,3. The seismic signal consists of numerous traces and
this transform is applied on each trace present in the seismic signals. EMD
technique will decompose a seismic signal into Intrinsic Mode Functions (IMFs)
which are the monocomponents of frequency. Since HHT is the data adaptive
method, it proves to be one of the most effective techniques for determining
the spatio-temporal characteristics of the signal 1.

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HHT algorithm is applied to the seismic
data of the Upper Cenozoic fluvio-deltaic system of F3 block situated in the
Dutch sector of Southern North Sea provided by OpendTect (dGB Earth Science).
The seismic data contains inline range from 100 to 750, crossline range from
300 to 1250 and time (ms) from 0ms to 1848ms with a sampling interval of 4ms.
Our target area is located in the inline section 425 at around 1600ms (two way
travel time). The inline section 425 is decomposed into 5 different frequencies
from highest frequency (1st IMF) to lowest frequency (5th
IMF).

 

Methodology

The EMD technique is applied on
each trace of inline section 425 and time slice of 1600ms. EMD technique is an
adaptive technique and suitable for non-stationary and nonlinear data 2.

1.     
All the maxima and minima of a
seismic signal s(t) are joined by interpolation to form upper envelope (u1)
and lower envelope (l1) respectively and their mean is calculated (m1).

2.     
Mean of both envelopes is subtracted
from the original signal. The new signal is termed as proto IMF (h1=s(t)-m1).
This is the first sifting process.

3.     
This sifting process is
repeated k times, i.e. h1k = h1(k-1)-m1k.

4.     
For
second shifting process, h1 is considered as data, and m11
is the mean of the upper envelope and lower envelope of h1.

h11=h1-m11

5.     
Stopping
criterion decides the number of times the sifting process is repeated.
Normalized square difference between two sifting operations is the stopping
criterion and at the end it gives IMF1. IMF must have 2 properties:
(a) the difference between number of extrema and number of zero crossing must
be zero or one (b) mean should be zero. 3

6.     
Subtract
IMF1 from the original signal s(t) say x1(t). All the
above steps are repeated for signal x1(t). This will give IMF2.

7.     
Similarly,
each trace in a seismic data goes through the mentioned procedure and left with
certain amount of IMFs along with a trend i.e. a monotonic signal.

8.     
IMF1
of all the traces are put together to give IMF1 for the section of a
seismic data. Similarly, all the IMFs of the seismic data is determined.

 

Hilbert
Spectral analysis is done on all the IMFs generated using EMD technique.
Hilbert transform of each IMF is calculate which will ultimately help in
determining Instantaneous Amplitude, Instantaneous Frequency and Instantaneous
Phase. In this study Instantaneous Amplitude is calculated which is plotted on
a 2D plane in which amplitude is showing the color variation. Hilbert transform
give the analytic representation of the signal.

After applying Hilbert, analytic signal can be
represented as:

And
Instantaneous Amplitude= absolute value of Hilbert transform i.e. a(s)2+b(s)21/2,
Instantaneous Phase (?(s)) =tan-1b(s)/a(s) and
Instantaneous Frequency ?(s) = d(?(s))/ds 2,3.

Highest
frequency component i.e. IMF1 mostly comprises of noise. On moving
to the later IMFs, a geological structure at around 1600ms remains prominent.
This behaves as an anomaly which is further studied in a time slice of 1600ms.

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