CN107436450A - A kind of seismic signal bandwidth broadning method based on continuous wavelet transform - Google Patents

Abstract

The invention discloses a method for expanding the bandwidth of seismic signals based on continuous wavelet transform, which includes the following steps: Step 01: read the single-channel data of the original seismic recording signal; Step 02: select a reference frequency in the amplitude spectrum of the original signal, and Calculate the frequency range that needs to be expanded through the reference frequency; step 03: perform continuous wavelet transformation on the single-channel data read in step 01, and convert from the time domain to the time-scale domain; step 04: expand the signal bandwidth in the time-scale domain, And carry out the inverse transformation of continuous wavelet transform, reconstruct the high-resolution time signal of spread spectrum, and obtain the single-channel time-domain signal after bandwidth expansion; repeat steps 01-04 until all channel data processing is completed. The seismic signal bandwidth expansion method based on the present invention can effectively predict the energy information of the high-frequency end and the low-frequency end, expand the seismic signal bandwidth, significantly improve the resolution of the signal, and maintain a high signal-to-noise ratio.

Description

A Method of Seismic Signal Bandwidth Expansion Based on Continuous Wavelet Transform

technical field

The invention belongs to the field of seismic exploration data processing, in particular to a method for expanding the bandwidth of seismic signals based on continuous wavelet transform.

Background technique

Seismic exploration is one of the important methods in geophysics. It is a method to detect the physical properties of the formation medium by analyzing and measuring artificially excited seismic waves and studying the propagation laws of seismic waves in the formation according to the characteristics of the rock. During the downward propagation of the seismic wavelet excited by the surface, the resolution of the obtained seismic data is relatively low due to the absorption of the stratum. As the exploration objects in oil and gas field exploration become more and more complex, people put forward higher requirements for the processing and interpretation of seismic data. For example, it is required to describe the formation structure, lithology changes and fluid properties more accurately and finely. Therefore, in order to solve these problems, improving the resolution of seismic data has become one of the main tasks of seismic data processing. On the basis of breakthroughs in seismic data acquisition technology, to obtain high-resolution seismic sections, it is often necessary to use resolution-enhancing processing technology. In view of the deficiencies of traditional methods for improving resolution, it is necessary to explore new methods for improving resolution.

Prior art 1:

Deconvolution method. As an important and effective means to improve the resolution of post-stack seismic data, deconvolution can improve the resolution by compressing seismic wavelets in seismic records. There are already many practical methods, such as pulse deconvolution Convolution, Predictive Deconvolution, Minimum Entropy Deconvolution, Surface Consistent Deconvolution, and more. Each deconvolution method has its own field of application.

Disadvantages of prior art 1:

1. The deconvolution method must make certain assumptions about the statistical law of the reflection coefficient sequence of the formation and the phase of the wavelet. Whether these assumptions are similar to the actual situation determines the deconvolution effect. The actual seismic data usually cannot fully satisfy these assumptions, which will affect the application effect of the deconvolution method.

2. Another defect of the deconvolution method is that it is sensitive to high-frequency noise. Usually, after deconvolution, the signal-to-noise ratio of seismic data will decrease significantly;

Prior art 2:

Spectral whitening method. The resolution of seismic data can be improved by equalizing the energy in different frequency bands, which can be done in the time domain or in the frequency domain.

Disadvantages of prior art 2:

1. The spectral whitening method does not consider the time-varying characteristics of the wavelet during propagation. Therefore, the seismic record results obtained by the spectral whitening method usually show a rigid waveform;

2. The effect on events with weak energy is poor.

Contents of the invention

The purpose of the present invention is to provide a method for expanding the bandwidth of seismic signals based on continuous wavelet transform to solve the above technical problems. The present invention decomposes the seismic trace into the time-scale domain by performing continuous wavelet transform on the single-trace seismic data, selects a reference frequency in the amplitude spectrum of the original signal, and calculates the frequency range to be expanded through the reference frequency, and The bandwidth is expanded in the time-scale domain, and finally the high-resolution time signal of the spread spectrum is reconstructed through the inverse transformation of the continuous wavelet transform. The effectiveness of the method is verified by the model and actual examples.

In order to achieve the above object, the present invention adopts the following technical solutions:

A method for expanding the bandwidth of seismic signals based on continuous wavelet transform, comprising the following steps:

Step 01: Read the single-channel data of the original seismic recording signal;

Step 02: Select a reference frequency in the amplitude spectrum of the single-channel data read in step 01, and calculate the frequency range that needs to be expanded through the reference frequency;

Step 03: Perform continuous wavelet transformation on the single-channel data read in step 01, from the time domain to the time-scale domain;

Step 04: Expand the signal bandwidth in the time-scale domain, and perform the inverse transformation of the continuous wavelet transform, reconstruct the high-resolution time signal of the spread spectrum, and obtain the single-channel time domain signal after the bandwidth expansion;

Repeat steps 01-04 until the data processing of all traces of the original seismic recording signal is completed, and the time-domain signal after the bandwidth expansion is obtained.

Further, step 02 to determine the reference frequency and the frequency extension range specifically includes:

The reference frequency is the standard used to calculate harmonics and sub-harmonics, and is also the standard for predicting the fundamental frequency range of the amplitude spectrum of harmonics and sub-harmonics. Therefore, the selection of the reference frequency has a direct impact on the effect of signal bandwidth expansion. The reference frequency is generally selected from the amplitude spectrum of the original signal, and its selection is related to the attenuation degree and attenuation speed of the amplitude spectrum, and depends on the amplitude spectrum of the specific signal. The present invention adopts dB as the unit for displaying the amplitude spectrum and calculating and expressing the reference frequency.

Define a ratio parameter r for the reference frequency, set the amplitude spectrum of a known signal, when the amplitude spectrum drops from the peak value to xdB, then r=x/20. r corresponds to the two frequency points on the amplitude spectrum to become the reference frequency for expanding the low-end frequency and high-end frequency respectively.

After the reference frequency is selected and determined, calculate the extended frequency range of the high-frequency end and the low-frequency end. The calculation of the extended range adopts the concept of octave, and the frequency information of the extended high-frequency component is called harmonics (first harmonic, second harmonic wave, etc.), the frequency information of the extended low-frequency component is called sub-harmonic (first sub-harmonic, second sub-harmonic, etc.). The harmonic is an integer multiple of the base frequency, and the sub-harmonic is the reciprocal of the integer multiple of the base frequency. Point A represents the selected reference frequency, B=A/2; the frequency between BA is the base frequency range; the frequency range of the first harmonic is twice the base frequency range, and the frequency range of the second harmonic is the base frequency range Four times of ; point A is the starting point of the first harmonic frequency range, and the end point of the first harmonic frequency range is the starting point of the second harmonic frequency range.

Further, in step 03, continuous wavelet transform is performed on the read single-channel data, from the time domain to the time-scale domain:

For any energy finite signal f(u), its continuous wavelet transform is defined as:

In the formula, W(t, s) is the continuous wavelet transform coefficient of the signal to be analyzed, s is the scale factor, f(u) is the signal to be analyzed, ψ(u) is the Morlet mother wavelet, u is the time, t is the translation amount , - means conjugation.

In the wavelet transform, the larger the scale factor s, the wider the time window of the wavelet function, the narrower the frequency window and the more the center of the frequency window moves to the low frequency direction; on the contrary, the smaller the s, the narrower the time window and the wider the frequency window And its center moves toward the high frequency direction. That is, in order to obtain the information of the low-frequency part of the signal, it should be observed for a longer period of time, which has a better frequency resolution. In order to obtain the high-frequency part information of the signal, a short-term observation is made, which has a better time resolution at this time.

Further, in step 04, the signal bandwidth is expanded in the time-scale domain, and the inverse transformation of the continuous wavelet transform is performed to reconstruct the high-resolution time signal of the spread spectrum, and the single-channel time domain signal after the bandwidth expansion is obtained, including:

Multiply the wavelet coefficient W(t,s) in the time domain scale corresponding to the harmonic and sub-harmonic frequency bands by a corresponding weight factor to obtain the weighted wavelet coefficient The weight factor is given according to the characteristics of the data, and the value is between 0.5 and 1.

Wavelet coefficients for extended frequency bandwidth Carry out the inverse transformation of the continuous wavelet transform to reconstruct the high-resolution time signal f(u) of the spread spectrum, see the following formula:

In the formula, C _ψ is the allowable condition.

Compared with the prior art, the present invention has the following beneficial effects:

1) The method of the present invention can preferably not damage the signal-to-noise ratio of the data;

2) The inventive method uses continuous wavelet transform, and the efficiency is higher;

3) The effect of the method of the present invention is obviously better than that of the spectral whitening method.

The invention can effectively realize the expansion of the seismic bandwidth, can improve the data resolution, does not damage the signal-to-noise ratio of the data, and the effect is obviously better than that of the spectrum whitening method.

Description of drawings

Figure 1 is a schematic diagram of expanding the frequency range selection;

Figure 2A is a schematic diagram of the reference frequency selection of a raised peak in addition to the main peak in the amplitude spectrum; Figure 2B is a schematic diagram of the reference frequency selection of the amplitude spectrum with only one main peak;

Fig. 3 is the time-domain representation schematic diagram of wavelet function after stretching;

Figure 4 is a wavelet function time-scale diagram;

Fig. 5A is the Morlet complex wavelet time domain diagram; Fig. 5B is the Morlet complex wavelet frequency domain diagram;

Figure 6 is the amplitude spectrum before and after expanding the bandwidth;

Fig. 7A is the original band-pass wavelet signal with high-band bandwidth expansion; Fig. 7B is the amplitude spectrum before expansion; Fig. 7C is the time signal after expansion; Fig. 7D is the amplitude spectrum after expansion;

Fig. 8 is a comparison diagram of the amplitude spectrum before and after the high frequency band expansion of the bandpass wavelet shown in Fig. 7A;

Fig. 9A is the original bandpass wavelet signal with high and low frequency end bandwidth expansion; Fig. 9B is the amplitude spectrum before expansion; Fig. 9C is the time signal after expansion; Fig. 9D is the amplitude spectrum after expansion;

Fig. 10 is a comparison diagram of the amplitude spectrum before and after the bandpass wavelet shown in Fig. 9A is broadened at the high and low frequency ends;

Figure 11 is the record map of the 400th track of the original seismic data;

Fig. 12 is the recording diagram of the 400th track of the seismic data after the resolution is improved;

Figure 13A is the original profile; Figure 13B is the seismic profile with improved resolution;

Figure 14A is a partial enlarged view of Figure 13A; Figure 14B is a partial enlarged view of Figure 13B;

Fig. 15A is a partial cross-sectional view of continuous wavelet transform method to improve resolution; Fig. 15B is a partial cross-sectional view of spectral whitening method to improve resolution;

Figure 16A is a partial enlarged view of Figure 15A; Figure 16B is a partial enlarged view of Figure 15B;

Figure 17 is a comparison diagram of continuous wavelet transform method and spectral whitening method for expanding seismic data bandwidth;

Fig. 18 is a flowchart of a method for expanding the bandwidth of seismic signals based on continuous wavelet transform in the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

The present invention is a seismic signal bandwidth expansion method based on continuous wavelet transform, which decomposes the seismic trace into the time-frequency domain by performing continuous wavelet transform on the single-trace seismic data, selects a reference frequency in the amplitude spectrum of the original signal, and The frequency range that needs to be expanded is calculated through the reference frequency, and the bandwidth is expanded in the time-scale domain, and finally the inverse transformation of the continuous wavelet transform is performed to reconstruct the high-resolution time signal of the spread spectrum.

Please refer to FIG. 18 , a method for expanding the bandwidth of seismic signals based on continuous wavelet transform in the present invention implements steps 01-04 for seismic recording signals, specifically including:

Step 01: Read the single-channel data of the original seismic recording signal;

Step 02: Select a reference frequency in the amplitude spectrum of the single-channel data read in step 01, and calculate the frequency range that needs to be expanded through the reference frequency;

Step 03: Perform continuous wavelet transformation on the single-channel data read in step 01, from the time domain to the time-scale domain;

Step 04: Expand the signal bandwidth in the time-scale domain, and perform the inverse transformation of the continuous wavelet transform, reconstruct the high-resolution time signal of the spread spectrum, and obtain the single-channel time domain signal after the bandwidth expansion;

Repeat steps 01-04 until the data processing of all traces of the original seismic recording signal is completed, and the time-domain signal after the bandwidth expansion is obtained.

In step 02, select a reference frequency from the amplitude spectrum of the single-channel data, and calculate the frequency range that needs to be expanded through the reference frequency:

As shown in Figure 1, it is a schematic diagram for expanding the frequency range selection. Among them, point A represents the selected reference frequency, B=A/2. The frequency between BA is the basic frequency segment. The frequency range of the first harmonic is twice that of the fundamental frequency range, and the frequency range of the second harmonic is four times that of the fundamental frequency range. Point A is the starting point of the first harmonic frequency range, and the end point of the first harmonic frequency range is the starting point of the second harmonic frequency range.

The low-frequency end of the extended spectrum is similar to the above, and the reference frequency needs to be reselected. As shown in Figure 1, the dotted line is the reference frequency of the extended low end.

As shown in FIG. 2A and FIG. 2B , they are schematic diagrams of reference frequency selection for different amplitude spectrum attenuation trends. The amplitude spectrum in Figure 2A has a raised peak besides the main peak. This form can be considered as the result of the earth filter composed of all the formations above this layer and the frequency response of the formation. The peaks other than the main peak are also Reflect the effective information in the signal, so the basic frequency segment should contain the frequency information of this part, so the selection of the reference frequency should be biased towards higher frequencies. The amplitude spectrum in Figure 2B has only one main peak. The reference frequency of this signal is better selected. The frequency at the higher frequency of the main peak is selected as the reference frequency, so that the basic frequency section contains the main information of the main peak, so the harmonic and sub-harmonic forecast is more accurate.

In step 03, continuous wavelet transform is performed on the single channel data of seismic data:

Choose Morlet complex wavelet function as the basis function of continuous wavelet transform. Figure 3 shows the representation of the same mother wavelet at different scales s. It can be seen that the scale factor affects the shape of the mother wavelet. The mother wavelet shown in the figure is a Ricker wavelet whose main frequency is 30Hz.

Figure 4 is a time-frequency diagram of the wavelet function. It can be seen that for a fixed mother wavelet, the area of its time-frequency window is constant. The translation factor t only affects the window position of the wavelet function in the time domain. The scale factor s determines the size of the observation window of the wavelet function in the time domain and frequency domain, that is, the range or scale that can be observed. In the wavelet transform, the larger the scale factor s, the wider the time window of the wavelet function, the narrower the frequency window and the more the center of the frequency window moves to the low frequency direction; on the contrary, the smaller the s, the narrower the time window and the wider the frequency window And its center moves toward the high frequency direction. That is to say, in order to obtain the information of the low frequency part of the signal, it should be observed for a long time, which has a better frequency resolution; correspondingly, in order to obtain the information of the high frequency part of the signal, it should be observed for a short time, which has a better frequency resolution. time resolution.

Wavelet ψ(u) is a wave with a very short duration, which must satisfy the following conditions:

In the formula, is the Fourier transform of the wavelet time function ψ(u), the wavelet that satisfies the above formula is called admissible, and the above formula is also called the admissibility condition. The time function ψ(u) satisfying the above formula is called mother wavelet or basic wavelet, usually called wavelet. The wavelet function ψ(u) must fluctuate positively and negatively, and satisfy the condition of square integrability, its Fourier transform It has the frequency characteristics of a bandpass filter. Wavelet is local in time domain and frequency domain, which is the most important feature of wavelet. The local characteristic of wavelet in the time-frequency domain is actually the concentration of its energy in the time-frequency domain. Wavelet is local in time domain and frequency domain, which is actually the concentration of its energy in time-frequency domain;

The time-frequency atomic family of wavelet analysis is obtained after expansion and translation of the mother wavelet ψ(u):

The commonly used wavelet transform is when When , the time-frequency atomic family is:

In the formula, u represents time, Ψ _{s, t} (u) is a time-frequency atomic group, t is a translation factor, which can take any real number, s is a scaling factor or scaling factor, and generally takes a positive real number; when s > 1, the wavelet The function is stretched along the time axis, and when s<1, the wavelet function is compressed along the time axis; where the factor In order to keep the energy constant after scaling, that is, ||ψ _s,t (u)||=||ψ(u)||;

Decompose the single-channel data read in step 01 into the time scale domain, W(t,s) is the wavelet transform coefficient of the single-channel data:

Mother wavelet adopts the Morlet complex wavelet of parameter σ＞5.33 among the present invention, and the wavelet at this moment satisfies the admissibility condition, and its expression is:

Fig. 5A and Fig. 5B show the Morlet complex wavelet function (σ=2π) time domain and frequency domain distribution diagrams. Morlet complex wavelets have localized properties in the time-scale domain, and this method is a pure amplitude operation, which will not affect the phase of the signal.

In step 04, the bandwidth information of the signal is expanded in the time-scale domain, and the inverse transformation of the continuous wavelet transform is performed to reconstruct the high-resolution time signal of the spread spectrum, and the single-channel time domain signal after the bandwidth expansion is obtained, including:

Adjust the energy density of the harmonic and sub-harmonic amplitude spectrum, that is, multiply the wavelet coefficient W(t,s) by the weight factor in the time-scale domain, and the weight factor is between 0.5 and 1 to obtain the weighted After the wavelet coefficient

Through wavelet inverse transformation, a high-resolution signal f(u) with extended bandwidth is obtained, so that it produces a good amplitude spectrum:

where C _ψ satisfies the admissibility condition.

As shown in Fig. 6, the effective bandwidth of the amplitude spectrum after expanding the bandwidth is wider, and the peak of the spectrum is flat, that is, a good amplitude spectrum is produced.

The present invention has following beneficial effect:

1) The method of the present invention can preferably not damage the signal-to-noise ratio of the data;

2) The inventive method uses continuous wavelet transform, and the efficiency is higher;

3) The effect of the method of the present invention is obviously better than that of the spectral whitening method.

Next, the continuous wavelet transform-based seismic signal bandwidth expansion method of the present invention is applied to model calculation examples and post-stack actual data. The application results show that the present invention has better fidelity to signals than other methods.

Fig. 7A is a single band-pass wavelet with a main frequency of 30 Hz (bandwidth of 15 Hz to 45 Hz). Taking this wavelet as a time series, performing continuous wavelet transform on it to expand the bandwidth, the obtained time domain signal is shown in Fig. 7C. Fig. 7B is the amplitude spectrum of the original bandpass wavelet, and Fig. 7D is the amplitude spectrum of the bandpass wavelet after bandwidth expansion. The reference frequency parameter r=0.25, the amplitude spectrum of the bandpass wavelet is smooth and the energy is concentrated, and the value of r is smaller so as to basically include the part of the energy concentration in the amplitude spectrum. Here, only the high frequency of the signal is expanded. It can be seen that the bandwidth becomes wider after expansion, the bandpass wavelet is effectively compressed, and the time resolution is significantly improved. The comparison (dB) of the normalized amplitude spectrum before and after expansion is shown in Figure 8. It can be seen that the amplitude of the original wavelet has been effectively broadened, from the original 15Hz-45Hz to about 15Hz-120Hz.

Similarly, taking the band-pass wavelet as the input signal, and expanding the low-end and high-end frequencies at the same time, the results are shown in Figures 9A to 9D, where Figure 9A is the original band-pass wavelet; Figure 9B is the original band-pass wavelet The amplitude spectrum of ; Fig. 9C is the time-domain signal of the wavelet after bandwidth expansion; Fig. 9D is the amplitude spectrum of the wavelet after bandwidth expansion. The comparison (dB) of the normalized amplitude spectrum before and after expansion is shown in Fig. 10 . It can be seen that this method is very effective for both high frequency and low frequency extension of the signal. For seismic signals, expanding the high-frequency end of seismic data can effectively improve the time resolution of seismic data, and the expansion of low-frequency end also plays a very important role in the inversion of seismic data.

Next, it is verified using a real data study. There is an original seismic record with a total of 481 traces, each trace has 701 sampling points, and the sampling interval is 1ms. Figure 11 shows the 400th trace randomly extracted from the original seismic record. It can be seen that the signal energy distribution of each trace of the seismic record is relatively uniform. Directly process the seismic data trace by trace. The ratio parameter r=0.5 of the reference frequency is selected based on the average amplitude spectrum of 481 traces of the seismic data. Figure 11 shows the signal after the bandwidth expansion of the data shown in Figure 12. It can be seen that the time resolution of the seismic data has been effectively improved.

The 201st to 481st sections of the seismic record are taken for display. Figure 13A is the section of the original seismic record, and Figure 13B is the corresponding section of the seismic record after the continuous wavelet transform improves the resolution, the abscissa indicates the number of traces (201-481), and the ordinate indicates the time (0.0-0.7s).

It can be seen from Fig. 13A and Fig. 13B that after the bandwidth expansion, the separation effect of thin layers of seismic data is very good, and the time resolution on the section is significantly improved. In order to observe some details more clearly, the time from the above section is taken from 100ms to 400ms, the track number is observed from the section of track 301 to track 401. The original profile is shown in Figure 14A, and the enhanced resolution profile is shown in Figure 14B. From Fig. 14A and Fig. 14B, it can be seen that the continuous change of the event axis can be clearly seen on the profile after the resolution is improved. Compared with the original profile, the resolution is significantly improved, and the stratum level and contact relationship are clear, as shown in the figure Faults at circles and arrows.

Compare this method with spectral whitening. For example, Figure 15A is the continuous wavelet transform to improve the resolution profile, and Figure 15B is the traditional spectral whitening method to improve the resolution profile. Partial sections of the two figures were taken respectively, the time was from 100ms to 400ms, and the track number was from 301 to 401, as shown in Figure 16A and Figure 16B. Figure 17 shows the comparison of the amplitude spectrum after the two methods improve the resolution and the amplitude spectrum of the original data. It can be seen that although the spectral whitening method can also effectively expand the bandwidth of seismic data, it can be obtained through comparison that in the case of approximately the same expanded frequency band, compared with the spectral whitening method, the continuous wavelet transform method improves the resolution. The signal level of the signal is clearer, especially for weak events. This advantage of the method based on continuous wavelet transform is just the embodiment of the time-frequency localization characteristic of wavelet transform.

In the above actual data calculation examples, the seismic signal bandwidth expansion method of the present invention can effectively expand the bandwidth of seismic data, making the seismic profile event clearer and the underlying information clearer. authenticity.

Finally, it should be noted that the above models and actual data calculation examples provide further verification for the purpose of the present invention, technical solutions and beneficial effects, which only belong to the specific implementation calculation examples of the present invention, and are not used to limit the protection scope of the present invention. Within the spirit and principles of the present invention, any modifications, improvements or equivalent replacements should fall within the protection scope of the present invention.

Claims (4)

1. A kind of 1. seismic signal bandwidth broadning method based on continuous wavelet transform, it is characterised in that comprise the following steps：

   Step 01：Read the single track data of original seismic data signal；

   Step 02：A reference frequency is selected in the amplitude spectrum for the single track data that step 01 is read, and passes through the reference frequency Calculate the frequency range for needing to expand；

   Step 03：The single track data read to step 01 do continuous wavelet transform, m- scale domain when being transformed into from time domain；

   Step 04：When m- scale domain expand signal bandwidth, and carry out the inverse transformation of continuous wavelet transform, rebuild the height of spread spectrum Resolution temporal signal, obtain the single track time-domain signal after bandwidth broadning；

   Repeat step 01-04 until original seismic data signal all track datas handle complete, obtain bandwidth broadning after when Domain signal.
2. A kind of 2. seismic signal bandwidth broadning method based on continuous wavelet transform as claimed in claim 1, it is characterised in that Step 02, which calculates, determines that reference frequency domain needs the frequency range expanded, and specifically includes：

   A ratio parameter r is defined for reference frequency, if the amplitude spectrum of a known signal, when its amplitude spectrum is from peak-fall During to xdB, then r=x/20；Two Frequency points that r corresponds on amplitude spectrum, which are referred to as, expands low end frequency and high end frequency Reference frequency；

   After reference frequency selection determines, the frequency range that front end and low frequency end are expanded is calculated；A points represent selected base Quasi- frequency, B=A/2；Frequency band based on frequency between BA；The frequency range of first harmonic is the two of base frequency scope Times, the frequency range of second harmonic is four times of base frequency scope；A points are the starting points of first harmonic frequency range, once humorous The terminal of wave frequency range is the starting point of second harmonic frequency scope.
3. A kind of 3. seismic signal bandwidth broadning method based on continuous wavelet transform as claimed in claim 1, it is characterised in that Continuous wavelet transform is done to the single track data in step 01 in step 03, m- scale domain, is specifically included when being transformed into from time domain：

   For any finite energy signal f (u), its continuous wavelet transform is defined as：

   <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>s</mi> </msqrt> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mover> <mi>&amp;psi;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>u</mi> <mo>-</mo> <mi>t</mi> </mrow> <mi>s</mi> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>u</mi> <mo>,</mo> </mrow>

   In formula, W (t, s) is the Continuous Wavelet Transform Coefficients of signal to be analyzed, and s represents scale factor, and f (u) represents letter to be analyzed Number, ψ (u) represents Morlet morther wavelets, and u is the time, and t is translational movement ,-represent conjugation.
4. A kind of 4. seismic signal bandwidth broadning method based on continuous wavelet transform as claimed in claim 1, it is characterised in that In step 04 when m- scale domain expand signal bandwidth, and carry out the inverse transformation of continuous wavelet transform, rebuild the high-resolution of spread spectrum Rate time signal, the single track time-domain signal after bandwidth broadning is obtained, is specifically included：

   When m- scale domain in, the energy density of harmonic wave, subharmonic amplitude spectrum is adjusted：When m- scale domain to small echo Coefficient is multiplied by weight, and weight value is between 0.5~1；By continuous wavelet inverse transformation, the height of expansion frequency range is obtained Resolution signal.