In the specific implementation process, three aspects of issues are mainly discussed: forced randomization of time windows, logarithmic spectrum smoothing, and wavelet picking and shaping.

5.9.2.1 Forced randomization of time windows

Slightly improve the method of randomly selecting time windows on the profile mentioned before, and select the signal-to-noise ratio on the profile A superposition segment near the target layer with higher resolution, consistent event axis and better continuity, and then forcibly randomize the time window, that is, the starting time of each time window in the same selected superposition segment point, artificially forcibly adding a random number to make the starting point of each time window obey random distribution. The reflection coefficient sequence contained in the corresponding time window is also redistributed, thus satisfying the condition that the formation reflection coefficient sequence changes but the seismic wavelet remains unchanged. As shown in Figure 5-14, take three channels as an example. Among them, t0 is the initial value of the starting time of the time window, L is the length of the time window, d is the adjustment range of the time window, Tn is a random number between (0, 1) generated by the computer, and Tn is the randomized The time window starting time value n=1, 2,...,N, N is the number of multi-channel superpositions, that is,

Figure 5-14 Simple schematic diagram of forced randomization

(a ) Three records within the selected time window before randomization; (b) New time window after randomization

dn= (tn-0.5)·d (5-33)

Tn=tdn (5-34)

According to the above formula, Tn is the new starting time of the time window, then the superimposed time window will achieve randomness the purpose of chemical processing.

5.9.2.2 Logarithmic spectral smoothing

In actual seismic records, the passband of seismic wavelets is mixed with various interference noises, such as excitation conditions, receiving conditions, instruments and the influence of multiple waves. These noise interferences are difficult to filter out in the time domain using filtering methods. According to the theoretical analysis of wavelet spectrum, the wavelet spectrum should change slowly and have smooth properties (as shown in Figure 5-15, this wavelet logarithmic spectrum is a model when mixed phase seismic wavelet t0=16). If the above various interference noises exist, the wavelet smooth spectrum will be destroyed, thus affecting the characteristics of the wavelet logarithmic spectrum, resulting in a large error between the extracted wavelet and the actual wavelet. In order to eliminate this effect, we thought of using a method similar to time domain smoothing to smooth the transformed logarithmic spectrum in the frequency domain to eliminate the interference mentioned above.

5.9.2.3 Wavelet picking and shaping

Wavelet picking and shaping are all involved in wavelet extraction, which directly affects the effect of wavelet extraction. , which is also one of the key issues in the process of wavelet extraction.

The so-called wavelet picking is the average result of the logarithmic spectrum, which is returned to the time domain through inverse transformation. However, since the seismic record is a convolution signal, its length must be greater than the wavelet length, and the real wavelet is unknown. We cannot determine its starting point and exact length, so we need to pick up the wavelet.

Figure 5-15 Mixed phase theory seismic wavelet logarithmic spectrum spectrogram

(1) Automatic parameter picking method

In Figure 5-16, for The result directly output by the inverse transformation after averaging the number spectrum cannot be called a wavelet. It needs further processing. Automatic parameter selection method, the steps are as follows:

Figure 5-16 Inverse transformation after logarithmic spectrum averaging, the wavelet is a mixed phase t0=16

1) By scanning Find the position of the maximum peak point in Figure 5-16;

2) Use the energy of the waveforms on both sides of the maximum peak point to determine the number of retained phases and determine the starting point;

3 ) Pick up the wavelet according to the wavelet length parameter;

4) Truncate the wavelet;

5) Finally perform polarity processing to obtain the picked up wavelet.

(2) Window shaping of wavelet

After automatically extracting the wavelet by parameter method, there is still high-frequency interference in the wavelet, and the amplitude of the wavelet is often the same as that of the wavelet. The real wavelet does not match well, so for high-frequency interference, a low-pass filter is used for filtering. Seismic wavelets are divided into minimum phase, mixed phase, and maximum phase according to different phases. The maximum peak of the minimum phase wavelet appears at the front of the wavelet, the maximum peak of the mixed phase wavelet appears in the middle of the wavelet, and the maximum The maximum peak value of the phase wavelet appears at the tail of the wavelet. Therefore, according to the different positions where the wavelet peak appears, the window function of the filter to be selected is also different. For the minimum phase wavelet, the shaping window to be added is a bandpass ideal filter plus a half cosine window function. The window function is It is estimated that the frequency response of the wavelet causes aliasing. The curve of this window function is semi-bell-shaped. According to the position where the maximum peak value of the minimum phase wavelet appears, it is appropriate to select this window function.

For the mixed phase and the maximum phase, if the window function selected for the minimum phase is the same, the maximum peak value of the wavelet will be attenuated greatly, which will destroy the phase characteristics. This is Because the cosine window has an attenuating weighting effect.

Therefore, for the wavelets of these two phases, we need to choose another window function whose mathematical formula is:

Basics of Geophysical Information Processing

where: α is the weight Coefficient; T0 is the time of the maximum peak value of the wavelet; T is the sampling time. The curve of this window function is the graph of a bilateral exponential pulse. Here, the mixed phase wavelet t0=16 is taken as an example. After interacting with the wavelet, the weighting only changes relative to the maximum peak point without destroying the phase characteristics of the wavelet.

Figure 5-17 The results of minimum phase wavelet separation using the homomorphic method

(a) Given wavelet s (n); (b) Given reflection coefficient sequence ρ ( n); (c) Synthetic seismic trace x (n); (d) Amplitude spectrum of single-channel logarithmic spectrum; (e) Phase spectrum of single-channel logarithmic spectrum; (f) Average amplitude of multi-channel stacked logarithmic spectrum Spectrum; (g) The average phase spectrum of multi-channel stacked logarithmic spectra; (h) The wavelet obtained by inversely transforming the spectra of (f) and (g)

Figure 5-18 Randomly distributed Reflection coefficient sequence, use homomorphic method to separate and extract wavelets

(a) Given wavelet s (n); (b) Given reflection coefficient sequence ρ (n); (c) Synthetic seismic trace; (d) Wavelet＾s(n) after homomorphic separation

Figure 5-19 Average complex cepstral and wavelet

(a) Amplitude spectrum of the average complex cepstrum ; (b) The phase spectrum of the average complex cepstral; (c) The wavelet obtained by the inverse transformation of (a) and (b); (d) Using the inverse of the above wavelet as the deconvolution operator

Synthetic recording test results: Synthetic recording only has a single channel. How to obtain the multiple channels (f) and (g) in Figure 5-17? The time zero point in (b) is shifted up and down by a random number, shifted 4 times, and superimposed with the original 5 traces for average.

Random movement up and down is equivalent to random changes in the reflection coefficient sequence ρ(n), while the wavelet remains unchanged, so after superposition, is eliminated and retained. In (d) in Figure 5-17, the low-frequency background is, the high-frequency changes are, after superposition (f), the high frequency disappears, the low-frequency background becomes smooth, and the wavelet (h) after inverse transformation is consistent with the original wavelet (a) . The effect is the same when the reflection coefficient is dense, as shown in Figure 5-18.

Figure 5-20 Ordinary superposition profile

Actual profile test results: Figure 5-20 is an ordinary superposition profile. The average complex cepstrum obtained through random time window analysis is as shown in Figure 5 -19 (a), (b), after inverse transformation, the wavelet is obtained as shown in Figure 5-19 (c), and the deconvolution operator is obtained by using this wavelet to invert as shown in Figure 5-19 (d). The result of using this operator to deconvolve the section in Figure 5-20 is shown in Figure 5-21. Compared with the ordinary superposition section, it can be seen that the third phase of the wave at 1500 ms and the third and fourth phases of the wave at 2000 ms have increased continuity. , the resolution is improved. Use the operator in Figure 5-19(d) to convolve with the section in Figure 5-20.

Figure 5-21 Homomorphic wavelet deconvolution profile