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.

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.