WO1998036293A1

WO1998036293A1 - Method for the automatic analysis of frequency passband of recorded signals

Info

Publication number: WO1998036293A1
Application number: PCT/FR1998/000246
Authority: WO
Inventors: Eric De Bazelaire; Didier Rappin
Original assignee: Elf Exploration Production
Priority date: 1997-02-13
Filing date: 1998-02-09
Publication date: 1998-08-20
Also published as: EP0894273A1; NO984762D0; FR2759459B1; NO984762L; CA2250355A1; FR2759459A1

Abstract

The invention concerns a method for the automatic analysis of frequency passband of recorded signals, characterised in that it consists in: a) applying a Fourier transform on at least one of the signals to obtain an amplitude spectrum of said signal; b) producing a mean spectrum of said amplitude spectrum; c) analysing said mean spectrum so as to produce a spectral component representing said signal; d) determining, on the basis of the representative spectral component, the minimum (Fmin) and maximum (Fmax) frequency values for which the amplitude of said spectral component is equal to half (Amax/2) of the maximum amplitude (Amax). The invention is particularly useful for determining the passband of seismic signals.

Description

Method for automatic frequency bandwidth analysis of recorded signals

The present invention relates to a method for automatic analysis of frequency bandwidth of recorded signals and more particularly of seismic signals recorded as a function of time.

The processing of seismic data sometimes requires knowing the frequency width of the passband of the signals propagating in a given medium and from which said seismic data are obtained. Indeed, the bandwidth defines the separating power of seismic events, that is to say the smallest distance that can exist between two signals and such that we can discern the two signals and not the result of their interference. The determination of the bandwidth is therefore necessary to avoid aliasing problems in the representation of the analysis spaces.

In the seismic processing technique known as POLYSTACK, developed by Eric de BAZELAIRE and based on the analysis of the curvatures of indicatrices, a new parameter called t _p is used which is the development depth time and which depends on the bandwidth B of the recorded signals constituting the traces of the recordings.

There are several methods for calculating the bandwidth of recorded signals, but none of them is automatic, regardless of the form of the recorded signals. In fact, the methods of determining the bandwidth of the prior art have limitations and cannot therefore be used for processing the collections of traces usually produced. Among the collections of traces very widely used in seismic processing, one can cite those which are called point of fire collections, point or geophone point collections, point medium collections, with or without dynamic corrections. In addition, the methods of the prior art are only reliable if a large number of traces are available.

The object of the present invention is to propose a method for analyzing a bandwidth of signals or traces which can be implemented. works automatically, regardless of the number of available traces since it can take into consideration a single trace or even a portion of a trace, the estimate then being valid for the defined portion.

Another object of the present invention is to implement the method on collections of seismic traces, whatever the nature of the collection of treated traces, firing point, midpoint or other, or even sum or migrated section.

An object of the present invention is a bandwidth analysis method which is characterized in that it consists in: a) applying a Fourier transform on at least one of the signals, so as to obtain an amplitude spectrum of said signal, b) producing an average spectrum of said amplitude spectrum, c) analyzing said average spectrum, so as to produce a spectral component representative of said signal, and d) determining, from the representative spectral component, the minimum frequency values F _m j _n and maximum F _max for which the amplitude of said spectral component is equal to half A _max / 2 of the maximum amplitude A _max .

Another characteristic according to the invention is that the analysis of the average spectrum can be carried out, for example, by filtering or a statistical analysis of said average spectrum.

Another characteristic according to the invention is a method characterized in that a set of seismic signals recorded in the form of traces is analyzed. Another characteristic according to the invention is a method characterized in that the signals to be analyzed are pretreated beforehand.

Another characteristic according to the invention is a method characterized in that the Fourier transform is applied to the preprocessed signals. Another characteristic according to the invention is a method characterized in that the amplitude spectra are filtered by means of a filtering capable of obtaining amplitude spectra centered around the zero value. Another characteristic according to the invention is a method characterized in that the envelopes of the centered amplitude spectra are produced.

Another characteristic according to the invention is a method characterized in that it also consists in carrying out an explicit smoothing on at least part of the centered spectra of amplitude, so as to obtain a smoothed average spectrum.

Another characteristic according to the invention is a method characterized in that another Fourier transform is applied to the average spectrum so as to obtain a transformed spectrum.

Another characteristic according to the invention is a method characterized in that the position of the β barycenter of the transformed spectrum is determined.

Another characteristic according to the invention is a method characterized in that it also consists in filtering the average spectrum by means of a low-pass filter.

Another characteristic according to the invention is a method characterized in that the low-pass filter is limited by an upper slope which extends from 2β to 4β. Another characteristic according to the invention is a method characterized in that the preprocessing of the signals consists of an initial filtering of said signals and in that the initial and low-pass filtering are combined so as to obtain a spectral component representative of said signals . Another characteristic according to the invention is a method characterized in that it also consists in determining on the spectral component representative of the signals, the amplitude A _max then the minimum values F _m i _n and maximum frequency F _max for which the amplitude is equal to half A _max / 2 of the maximum amplitude. Another characteristic according to the invention is a method characterized in that it also consists in determining the frequency position of the barycenter of the spectral component representative of said signals, so as to calculate the carrier frequency F _p of the signals.

Another characteristic according to the invention is a method characterized in that it also consists in determining, from the values ^F min> ^F max> ^B = ^F max - ^F min * ^{the value of} the spectral eccentricity E using the formula:

E = t mm 't n - 2 F,

B

Other advantages and characteristics of the present invention will emerge more clearly on reading the description of an embodiment as well as the appended drawings in which:

FIG. 1 represents part of a collection of seismic traces ordered in common medium point (PMC),

FIG. 2 schematically represents the amplitude spectra of some of the traces of the collection of FIG. 1,

- Figure 3 represents the amplitude spectra of Figure 2 but refocused, - Figure 4 shows the envelopes of the amplitude spectra refocused of Figure 3,

FIG. 5a represents the smoothed envelopes of the refocused amplitude spectra of FIG. 4,

FIG. 5b represents the average spectrum of the smoothed envelopes of FIG. 5a,

FIG. 6 represents the amplitude spectrum of the Fourier transform applied to the average spectrum of FIG. 5b,

FIG. 7a represents the low frequency component of the envelope of the mean spectrum of FIG. 5b, FIG. 7b represents the spectral component representative of the signals selected and processed from the PMC collection of FIG. 1,

In FIG. 1, part of a collection of seismic traces sorted in common medium point (PMC) is represented, but it goes without saying that any other collection of traces could be used such as a collection point of fire, point of reception, or even a sum cut or migrated time. On the abscissa, the trace numbers 1 to 47 are indicated, as well as the offsets between the transmitter-receiver pairs that generated said traces, the transmission-reception device (or recording) not being shown because it is well known to specialists. On the ordinate, the times in ms of the arrivals of the seismic events represented on the traces are indicated, some of which only were selected for the implementation of the method according to the invention. In what follows, the processed traces will be identified by their serial number and / or by the corresponding offset because in a collection of PMC traces, each trace can be identified by the midpoint X _Q and the offset h. Likewise, when reference is made to signals, these are the signals received, after crossing the medium to be studied, having been recorded on the receivers, the corresponding recordings also being called traces.

When we want to analyze the bandwidth of the recorded signals, we seek to determine the frequency characteristic corresponding to the width at half-height of the amplitude spectrum of the source of the transceiver device. Unfortunately, the source function is not available directly and it must therefore be sought in the recorded signals in which it is convolved by the impulse response of the medium and disturbed by various noise and parasites. If we simply apply a Fourier transform or another similar operation, the Fourier transform obtained reflects the same complexity as that observed on the records. Complexity means only the complex character, that is to say, the combination of several different elements which are difficult to distinguish or separate.

According to at least one known method, a Fourier transform is applied to the positive part of the amplitude spectrum of the recordings or traces to be analyzed. Indeed, the amplitude spectrum of a recorded signal is contained in the amplitude spectrum of the source function which generated said signal. The two amplitude spectra. (signal and source) different from each other by a modulation representing the participation of all the information generators in the environment (underground) such as interfaces, faults, diffracting points. A certain number of physical phenomena (attenuation, conversion of waves, multiple rebounds, diffusion, etc.) modify the amplitude spectrum of the signal by their contribution. This results in a character of increased complexity. Apart from the dispersion phenomenon, of negligible importance in the practice of oil seismic acquisition, the components linked to the source remain within the limits of the amplitude spectrum of the source function. The curve sought is that which best corresponds to the amplitude spectrum of the apparent source function that we assimilate to that of the real source. This is the unmodulated amplitude spectrum and therefore the low frequency component of the amplitude of the spectrum of the signal to be analyzed. Obtaining the desired function by passing a curve through all of the amplitude maxima, as in the known methods, is not satisfactory since these methods are too sensitive to the presence of frequency peaks of high amplitude linked to parasites and not to the source function. The subsequent calculation of the amplitude spectrum envelope of the recorded signal does not solve the problem because the modulus of the spectrum is positive. A first step of the method according to the invention consists in preprocessing, preferably, the signals recorded before sorting into PMC collection, by performing for example the following operations:

- amplitude recovery because attenuation is a very low frequency phenomenon which filtering destroys if it is not compensated, - bandpass filtering to eliminate very low frequencies (around zero) and high frequencies around of the Nyquist frequency.

It should be noted in passing that the number of traces to be treated has no incidence and that it is not necessary to apply a particular treatment beforehand such as dynamic correction, deconvolution or antimultiple treatment insofar as the characteristics of the function source are present and not distorted in the recorded signals (recordings or traces). If a deconvolution has been carried out, the characteristics of the equivalent source function will be estimated. A second step is to. calculate the set of Fourier transforms, from which the amplitude spectra are determined for the traces taken together for the analysis.

In FIG. 2, the amplitude spectra have been represented, after the Fourier transform, of traces whose serial number is between 1 and 45 with the corresponding offsets between 75 m and 2275 m. The amplitude spectra obtained are characterized by the parts set to zero by the frequency filtering which is necessary for the elimination of specific noises which can pollute the edges of the frequency space (calibration error of the amplitude of zero, low frequency noise, time aliasing). As it can result in a continuous component which would disturb a new frequency analysis, we perform, in a third step, a filtering of the frequency peaks. The filtering called "filtering τ" is applied to the amplitude spectrum which is then considered as a new signal, with fixed characteristic parameters totally determined by a sampling step time past and the time limits of the input signal (recorded signal ). The filtering τ is carried out by means of a bandpass filter which is applied in the Fourier transformed space of the amplitude spectra and with the BLACKMAN function. The minimum frequency used is, for example, ten times the sampling step δt of the input signal. The other frequencies are deduced therefrom so as to present attenuation slopes on an octave at each limit (low and high), in order to avoid any disturbance due to the filtering τ. The result of the filtering τ is shown in FIG. 3, in which one can observe "signals" comparable to signals of seismic traces. In reality, these are amplitude spectra centered around the zero value. The refocused amplitude spectra are non-zero over the entire range of the associated Fourier space, said range having approximately 5 and 65 Hz limits in the case of the example shown. In a fourth step, the envelopes of the refocused amplitude spectra are calculated, in the sense of the analytical signal. The envelopes of the centered amplitude spectra are shown in Figure 4.

Steps 1, 3 to 4 are steps for conditioning the spectral amplitude which make it possible to stabilize the results of the following steps. But it should be noted that they are not essential since one could directly use the amplitude spectra of the recorded signals obtained after application of the Fourier transform, for the implementation of the sixth step.

A fifth step which is preferred but not essential, consists in carrying out a first explicit smoothing on the envelopes of the centered amplitude spectra of FIG. 4. An explicit smoothing is obtained by performing for the whole of a signal a calculation of the value samples by means of a weighting function of a predetermined number of values of the samples surrounding the sample to be calculated. In the exemplary embodiment according to the invention, the smoothing is done for example by average in sliding window on a predetermined number of samples representative of the input signals to be processed, so as to obtain smoothed envelopes, as shown in FIG. 5a.

A sixth step consists in producing from the smoothed envelopes of FIG. 5a, an average smoothed spectrum. This is obtained by statistical analysis at constant frequency from the collection of amplitude spectra in Figure 2. Several statistical analyzes can be used including the arithmetic or quadratic mean, the median, the modal, such a list being nonlimiting and far from be exhaustive. In this way, an estimated average spectrum such as that shown in FIG. 5b is obtained.

At this stage, it is necessary to eliminate the residual irregularities from the average spectrum of FIG. 5b so as to avoid that a residual modulation greater than a half does not cause a false measurement. For this purpose and in a seventh step, a second Fourier transform is applied to the average spectrum of FIG. 5b. We thus obtain a spectrum, like that of FIG. 6, which represents the amplitude of the Fourier transform in time space and centered on time zero.

To estimate the smoothing parameters, the width of the spectrum in FIG. 6 is defined by the position of its barycenter β. Any energy located beyond twice the value obtained is neglected because it is not representative, as in the case of Gaussian representations or functions of L ² . Indeed, the theory of distributions of the Gaussian type or of L ² standards shows that the energy representative of a signal is contained, with sufficient precision in the sense of information, in a subspace extending over two times a characteristic statistical quantity which can be the standard deviation or the barycenter according to the criteria and the probability distribution of the entity to be studied, in this case a set of consecutive samples belonging to the same signal and in particular to the same seismic trace.

In another step, the average spectrum of FIG. 5b is filtered (filtering τ ') by a low-pass filter limited by an upper slope extending from 2β to 4β because an octave is used to go from 100% to 0% . The amplitude at 100% is therefore maintained up to 2 and the transition to 0% on an octave gives the value 4β. The result of this operation is shown in Figure 7a. We thus obtain a low-frequency component of the average envelope or better a spectral component representative of the signals of entry. We could, if desired, stop the method at this stage and determine the bandwidth since its limits and characteristics can be determined directly from the spectral component of Figure 7a, especially when the input signals are not preprocessed . All the preceding operations were carried out over the entire extent of the spectral range. However, it is necessary to take into account the limits linked to the initial preprocessing filter and applied to the input signals. The combination of the two filterings (initial and τ 'of the average spectrum) produces a spectrum as represented in FIG. 7b and considered as being the real spectral component and representative of the input signals analyzed.

On the spectral component of FIG. 7b, the maximum value A _max of its amplitude is determined. It is located at 15 Hz. Then we calculate A _max / 2 (dotted line) and we calculate or determine the smallest value F _mm and the largest value F _max of frequency for which the amplitude is equal to A _max / 2. For the spectrum considered in Figure 7b we find F _mjn = 7.4 Hz and F _max = 50.8 Hz. The bandwidth B of the input signals is therefore 50.8 - 7.4 = 43.4 Hz.

The carrier frequency F _p of the input signal, also considered to be the pseudo-period of said signal, is obtained by determining the frequency position of the barycenter G of the amplitude of the spectrum representative of FIG. 7b (energy center of gravity of the function). The determination of the barycenter G is carried out, in a conventional manner, directly on the spectral component representative of the signals, by calculating the overall energy (mathematical integral from frequency 0 to the Nyquist frequency) then by identifying the frequency separating said spectral component in two parts of equal energy. Frequency deviations between the carrier frequency

F _p and the limits F _m j _n and F _max of the passband B define the spectral excess E. At the end of the analysis, we therefore have the value of the carrier frequency F _p , of the frequency F _m j _n , the frequency F _max , the bandwidth B = F _max - F _min and the offset E = (F _min + F _max -

2F _p ) / B.

It should be noted that, like the filtering τ, the filtering τ 'also applies in the Fourier transformed space of the amplitude spectra and with the same function (BLACKMAN function). The filtering τ 'could be replaced by another means. For example, it would be possible to perform a statistical form analysis of the mean spectrum function, looking in particular for the parameters describing a given function beforehand, a Gauss curve is often chosen, which best adjusts (usually in the least squares sense) the curve to be analyzed over an interval [ 0.2α] where α is the statistical length chosen for the analysis and which, in the embodiment of the invention, is the barycenter.

Claims

1. Method for automatic analysis of frequency bandwidth of signals recorded as a function of time, of the type consisting in applying a Fourier transform on at least one of the signals, so as to obtain an amplitude spectrum of said signal, characterized in that that it further consists in: a) producing an average spectrum of said amplitude spectrum, b) analyzing said average spectrum, so as to produce an average spectral component representative of said signal, and c) determining, from the spectral component mean, the minimum (F _m j _n ) and maximum (F _max ) frequency values for which the amplitude of said mean spectral component is equal to half

(A _max / 2) of the maximum amplitude (A _max ).

2. Method according to claim 1, characterized in that the analysis of the average spectrum is carried out by means of filtering or a statistical analysis of said average spectrum.

3. Method according to claim 1, characterized in that a set of seismic signals recorded in the form of traces is analyzed.

4. Method according to claims 1 and 3, characterized in that the signals to be analyzed are pretreated beforehand.

5. Method according to claims 1 and 4, characterized in that the Fourier transform is applied to the pretreated signals.

6. Method according to one of claims 1 to 5, characterized in that the amplitude spectra are filtered by means of a filtering capable of obtaining amplitude spectra centered around the zero value.

7. Method according to claim 6, characterized in that the envelopes of the centered amplitude spectra are produced.

8. Method according to claim 6 or 7, characterized in that it also consists in carrying out an explicit smoothing on at least part of the centered spectra of amplitude, so as to obtain a smoothed average spectrum.

9. Method according to claim 1 or 8, characterized in that another Fourier transform is applied to the average spectrum so as to obtain a transformed spectrum.

10. Method according to claim 9, characterized in that the position of the β barycenter of the transformed spectrum is determined.

11. Method according to claim 1 or 8, characterized in that it also consists in filtering the average spectrum by means of a low-pass filter.

12. Method according to claims 9 and 10, characterized in that the low-pass filter is limited by an upper slope which extends from 2β to 4β.

13. Method according to claims 3 and 11 or 12, characterized in that the preprocessing of the signals consists of an initial filtering of said signals and in that the initial and low-pass filtering are combined so as to obtain a representative spectral component of said signals.

14. Method according to claim 13, characterized in that it also consists in determining on the spectral component representative of the signals, the amplitude (A _max ) then the minimum (F _m i _n ) and maximum (F _max ) values. frequency for which the amplitude is equal to half (A _max / 2) of the maximum amplitude.

15. Method according to one of claims 1, 11 to 14, characterized in that it also consists in determining the frequency position of the barycenter of the spectral component representative of said signals, so as to calculate the carrier frequency (F _p ) signals.

16. Method according to claim 15, characterized in that it also consists in determining, from the values F _ra i _n , F _max , B • = F _max - F _mjn and F _p , the value of the offset spectral (E) using the formula: