Abstract— In this paper an attempt is made to generate a synthetic

seismic signal by using wavelets. There are many wavelets to generate

synthetic seismic signals; some of them are klauder, ormsby, ricker wavelets,

etc. Each wavelet varies in their frequency of operation. Seismic reflection is

well-known geophysical technique which can give the information about earth and

its inner core, the earthquakes. The information given by seismic reflection is

used to monitor the earthquakes, petroleum exploration, determination of the

earth’s core structure, etc. Earth quake has become a serious problem in the

world due to its damage. There are many methods to analyze the signals due to

earthquakes. Among those, we are using a sophisticated method called wavelet

transformation. The advantage of this technique is that, it suppresses the

noise and enhances the signal strength there by seismic information due to the

earthquake. Seismic signal is synthesized by convoluting a klauder wavelet with

a seismic signal.

Keywords—

Seismic signal, Klauderwavelet,

Convolution, Synthetic signal.

I.

Introduction

Wavelet

transforms method having its basis in applied mathematics. This method having

high resolution when compared to other frequency based methods using Fourier

transforms. The specific advantage of this method is to drive low frequency

components with considerably good resolution when compared to other methods.

The drawback of using Fourier series is overcome by wavelet transform method, particularly

for short time analysis of seismic signals (or) earthquake signals.

The wavelet is nothing but a wave

like structure, which initially oscillates at zero amplitude and increases

thereby decreasing the initial oscillated amplitude to zero. To get information

from an unknown signal a wavelet can be convoluted with portion of a known

Signal.

Convolution is a mathematical way of combining two signals in order to form a

third signal. The technique is popularly used for processing the signals

digitally (DSP). The method involves in finding the zero phase of a given

signal. The wavelet transform is a

method, which decomposes the signal giving details as a function of time.

This involves

Scattering and shifting properties to generate a wavelet and it is limited to a specified length.

. The wavelets has two major characteristics namely 1) wavelets are compact support in time domain, and 2) The wavelet alternates from positive to negative. The process includes two steps 1) shifting the

function of

the wavelet and 2) making product

with an inner scale function.

For best resolution wavelet is a method giving

complete picture for the signals such as of seismic origination. Here the resolution of the signal is controlled by

the bandwidth of the signal. Moreover seismic

signals are transient in nature radiating

natural (or) manmade noise along with the seismic sources. This finally locates the, source mechanisms and the structure of the propagation medium through which they travel. The data taken from the seismograms, where

the amplitude of the seismic waves are

recorded as a function of distance from the epicenter, where earthquake occur the intensity

of this earthquake is measured in terms of

the magnitude taken

over a scale called

Richter scale.

The output of a monitoring

instrument namely

seismograph gives a signal corresponding

to the earthquake, by

analyzing these seismic signals one can design an earth warning system for predicting

the earth quakes in future avoid natural

disasters.

II.

Methodology

A Klauder

wavelet represents the autocorrelation of a linearly swept frequency-modulated

sinusoidal signal. It is defined by its terminal low frequency, “f1”;

its terminal high frequency, “f2”; and the duration of the input

signal “T”, often 6 or 7 seconds. The real part of the following

formula will generate a Klauder wavelet.

Klauder(t)

=real sin(tkt(T-t))/(tkt) exp (2ifot)

where k = (f2 – fl)/T (rate of change of frequency with

time)

fo=

(f2 + fl)/2 (midfrequency of bandwidth)

i = 1

(an imaginary number)

Figure-1

a Klauder wavelet (fig 1) is

symmetrical about a vertical line through its central peak at time zero.

Figure-2

The frequency

spectrum of a Klauder wavelet (fig 2) shows the substantial

similarities between a Klauder and an Ormsby wavelet.

1Kluader

wavelet is taken as an input signal and is represented as x(t) 2Impulse signal

h(t) is taken as an seismic signal(earthquake signal) 3Y(t) is the output of

the which is obtained by convoluting input signal and the impulse signal 4Noise is added to the y(t) in

order to obtain an noisy seismic signal 5 Due to unwanted waves such as surface waves ,

corrupt the seismic signal by adding

noise.6So on comparing the y(t) the output signal without noise and with

noise we can easily understand about the

disturbance caused to our original signal.

III. Result and

discussion

Abstract— In this paper an attempt is made to generate a synthetic

seismic signal by using wavelets. There are many wavelets to generate

synthetic seismic signals; some of them are klauder, ormsby, ricker wavelets,

etc. Each wavelet varies in their frequency of operation. Seismic reflection is

well-known geophysical technique which can give the information about earth and

its inner core, the earthquakes. The information given by seismic reflection is

used to monitor the earthquakes, petroleum exploration, determination of the

earth’s core structure, etc. Earth quake has become a serious problem in the

world due to its damage. There are many methods to analyze the signals due to

earthquakes. Among those, we are using a sophisticated method called wavelet

transformation. The advantage of this technique is that, it suppresses the

noise and enhances the signal strength there by seismic information due to the

earthquake. Seismic signal is synthesized by convoluting a klauder wavelet with

a seismic signal.

Keywords—

Seismic signal, Klauderwavelet,

Convolution, Synthetic signal.

I.

Introduction

Wavelet

transforms method having its basis in applied mathematics. This method having

high resolution when compared to other frequency based methods using Fourier

transforms. The specific advantage of this method is to drive low frequency

components with considerably good resolution when compared to other methods.

The drawback of using Fourier series is overcome by wavelet transform method, particularly

for short time analysis of seismic signals (or) earthquake signals.

The wavelet is nothing but a wave

like structure, which initially oscillates at zero amplitude and increases

thereby decreasing the initial oscillated amplitude to zero. To get information

from an unknown signal a wavelet can be convoluted with portion of a known

Signal.

Convolution is a mathematical way of combining two signals in order to form a

third signal. The technique is popularly used for processing the signals

digitally (DSP). The method involves in finding the zero phase of a given

signal. The wavelet transform is a

method, which decomposes the signal giving details as a function of time.

This involves

Scattering and shifting properties to generate a wavelet and it is limited to a specified length.

. The wavelets has two major characteristics namely 1) wavelets are compact support in time domain, and 2) The wavelet alternates from positive to negative. The process includes two steps 1) shifting the

function of

the wavelet and 2) making product

with an inner scale function.

For best resolution wavelet is a method giving

complete picture for the signals such as of seismic origination. Here the resolution of the signal is controlled by

the bandwidth of the signal. Moreover seismic

signals are transient in nature radiating

natural (or) manmade noise along with the seismic sources. This finally locates the, source mechanisms and the structure of the propagation medium through which they travel. The data taken from the seismograms, where

the amplitude of the seismic waves are

recorded as a function of distance from the epicenter, where earthquake occur the intensity

of this earthquake is measured in terms of

the magnitude taken

over a scale called

Richter scale.

The output of a monitoring

instrument namely

seismograph gives a signal corresponding

to the earthquake, by

analyzing these seismic signals one can design an earth warning system for predicting

the earth quakes in future avoid natural

disasters.

II.

Methodology

A Klauder

wavelet represents the autocorrelation of a linearly swept frequency-modulated

sinusoidal signal. It is defined by its terminal low frequency, “f1”;

its terminal high frequency, “f2”; and the duration of the input

signal “T”, often 6 or 7 seconds. The real part of the following

formula will generate a Klauder wavelet.

Klauder(t)

=real sin(tkt(T-t))/(tkt) exp (2ifot)

where k = (f2 – fl)/T (rate of change of frequency with

time)

fo=

(f2 + fl)/2 (midfrequency of bandwidth)

i = 1

(an imaginary number)

Figure-1

a Klauder wavelet (fig 1) is

symmetrical about a vertical line through its central peak at time zero.

Figure-2

The frequency

spectrum of a Klauder wavelet (fig 2) shows the substantial

similarities between a Klauder and an Ormsby wavelet.

1Kluader

wavelet is taken as an input signal and is represented as x(t) 2Impulse signal

h(t) is taken as an seismic signal(earthquake signal) 3Y(t) is the output of

the which is obtained by convoluting input signal and the impulse signal 4Noise is added to the y(t) in

order to obtain an noisy seismic signal 5 Due to unwanted waves such as surface waves ,

corrupt the seismic signal by adding

noise.6So on comparing the y(t) the output signal without noise and with

noise we can easily understand about the

disturbance caused to our original signal.

III. Result and

discussion

Representation of a klauder wavelet

Representation of a klauder wavelet