There
are four different Ricker wavelets, called Ricker Type 1, Type
2, Type 3, and Type 4 respectively. The higher types have more
peaks and valleys, representing more "ringing", and
are less symmetrical.
2: FOR I = 1 TO WVLTLENGTH / SAMPRATE 3: X = (I * SAMPRATE - 1) * G - 3.75 4: Wvlt [I] = (X * X - 1) / EXP (X * X / 2) 5: NEXT I
2: FOR I = 1 TO WVLTLENGTH / SAMPRATE 3: X = (I * SAMPRATE - 1) * G - 3.85 4: Wvlt [I] = (X * X - X - 1) / EXP (X * X / 2) 5: NEXT I
2: FOR I = 1 TO WVLTLENGTH / SAMPRATE 3: X = (I * SAMPRATE - 1) * G - 3.85 4: Wvlt [I] = (-X^3 + 3 * X) / EXP (X * X / 2) 5: NEXT I
2: FOR I = 1 TO WVLTLENGTH / SAMPRATE 3: X = (I * SAMPRATE - 1) * G - 3.2 4: Wvlt [I] = 0.1*(-X^6+X^5+15*X^4-10*X^3-45*X*X+15*X+15)/EXP(X*X/2) 5: NEXT I When comparing synthetic seismograms with different wavelets, it is important that each wavelet have the same initial energy. The energy can be found by squaring and summing each of the Wvlt[I] terms. The sum is then compared to a standard energy of 1.0 and a scale factor derived, which is multiplied against each Wvlt[I] term to obtain normalized wavelet values. The Klauder wavelet is generated in the frequency domain, which gives the amplitude and phase spectra of the wavelet. The autocorrelation of the spectra produces the wavelet shape in the time domain. This wavelet is used when the synthetic is to match Vibroseis data.
STEP
1: Generate chirp signal amplitude and phase Calculate
phase Calculate
amplitude Put
phase in all 4 quadrants STEP
2: Calculate autocorrelation to get wavelet in time domain. This
double nested loop takes the first 100 data points and cross correlates
them with the last 100 data points of the sweep. Since the number
of data points is small, there is little advantage to using the
FFT for the correlation. To
see the wavelet shape, the correlation string is reversed and
paired with itself: |
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