WO2004031806A2

WO2004031806A2 - Method of reducing harmonic noise in vibroseismic signals

Info

Publication number: WO2004031806A2
Application number: PCT/FR2003/002906
Authority: WO
Inventors: Julien Meunier; Thomas Bianchi
Original assignee: Compagnie Generale De Geophysique
Priority date: 2002-10-04
Filing date: 2003-10-03
Publication date: 2004-04-15
Also published as: WO2004031806A3; AU2003283491A1; MXPA05003585A; WO2004031806A8; AU2003283491A8; BR0307347A; EG24838A; FR2845483A1; FR2845483B1

Abstract

The invention relates to a method of reducing the harmonic noise in a vibroseismic signal recorded by a sensor, said vibroseismic signal corresponding to a given vibratory sequence emitted by at least one source and propagated in a subsurface in which it is reflected. The invention is characterised in that the it comprises the following steps consisting in: (a) correlating the vibroseismic signal, or part thereof, with a signal corresponding to the fundamental component of the sequence of vibrations emitted by the source (20); (b) from the correlated signal, selecting one part which corresponds to the energy of the fundamental component of the vibroseismic signal (30) and applying an estimation operator of the harmonic component of the correlated signal to said selected part (40); (c) deducing therefrom an estimation of the harmonic noise of the vibroseismic signal and subtracting said estimation from the signal (50).

Description

METHOD FOR REDUCING HARMONIC NOISE IN VIBROSISMIC SIGNALS

GENERAL AREA AND STATE OF THE ART

The invention relates to a processing method for the reduction of harmonic noise in a recorded earthquake signal.

We recall that to reconstruct images of the subsoil, geologists or geophysicists conventionally use seismic sources intended to generate waves which propagate in the subsoil and are reflected at least partially at the interfaces of the different layers of it ( reflectors). The reflected waves are recorded as a function of time by sensors which are for example of the geophone type in terrestrial seismic. The seismic traces thus recorded are processed in order to deduce therefrom information on the geology of the subsoil.

As sources, particularly in earthquake seismics, vibrators which generate vibro-seismic signals are commonly used.

Vibro-seismic signals are for example signals commonly called "sweep" by those skilled in the art, the frequency of which during a transmission sequence varies continuously so as to scan a given frequency range.

In this regard, it was proposed by H Rozemond in 1996 a seismic acquisition technique allowing the separation of vibro-seismic signals of the “sweep” type emitted by different sources and overlapping in time.

One can in particular advantageously refer to "Slip sweep acquisition" - H.J. Rozemond - SEG 1996 International Conference - Denver.

The vibrators pose problems of distortion compared to the theoretical signal that one would like to generate. The signal generated by a vibrator is in fact generally constituted by a fundamental scan and its harmonic scans, which are generally considered parasites that can affect the quality of the data.

In addition, the concern to optimize productivity leads to seeking the shortest possible time between vibrations. Under these conditions, the recordings obtained present a signal-to-noise ratio degraded compared to that which would be obtained by using the sources without overlap in time. The raw data received at the level of a sensor is in particular noised by harmonic energy due to the overlapping of the signals emitted by the different sources II methods have already been proposed intended to limit the correlation noise in vibroseismic.

In particular, the document GB 2 348 003 describes a method which applies to sets of seismograms previously processed and grouped in mirror points (so that the reflections of the same point in space are at the same point in time and in depth). These seismograms are then broken down into frequency bands on which a statistical discrimination of the signal and noise is made.

The processing described in this document however requires having seismograms recorded in parallel on several sensors. Still other methods require having several successive acquisitions over time for the same sensor. This is particularly the case of that described in document US 5,410,517. We also know from the article:

“Amplitude analysis of harmonies on vibrator generated direct waves” - EAGE 64 ^m Conference & Exhibition - Florence - May 27-30, 2002 a method for determining the amplitude relationships between the different harmonics of the source signal when the components are available harmonics of the recorded signal. To this end, it is proposed to implement wavelet transforms on these different components. The article shows that the ratios of the Fourier transforms of these wavelet transforms are independent in particular of the response of the subsoil, so that these ratios correspond to the ratios of the amplitudes of the harmonic components of the source. It should be noted, however, that there is no method proposed in this article for reducing the harmonic noise of a vibro-seismic signal.

PRESENTATION OF THE INVENTION

An object of the invention is to propose a method for reducing harmonic noise in recorded vibro-seismic data.

The method proposed by the invention has in particular the advantage of being able to be applied individually to any recording and of not requiring several successive acquisitions or several acquisitions in parallel on different sensors.

To this end, the invention proposes a method of reducing harmonic noise in a vibro-seismic signal recorded on a sensor, this vibro-seismic signal corresponding to a given vibratory sequence emitted by at least one source and propagated in a subsoil in which it is reflected, characterized by the steps according to which: a) the vibroseismic signal or a part of it is correlated with a signal corresponding to the fundamental component of the vibration sequence emitted by the source, b) a part is selected from the correlated signal which corresponds to the energy of the fundamental component of the vibro-seismic signal and an operator for estimating the harmonic component of said correlated signal is applied to the selected part c) an estimate of the harmonic noise of the vibro-seismic signal is deduced therefrom and we subtract this estimate of said signal.

As will be understood, such a method takes advantage on the one hand of the fact that the correlation of a vibro-seismic signal by the fundamental component of the sequence theoretically emitted by the source has the property of separating the energy corresponding to the part fundamental of the recorded signal from that corresponding to the harmonic part; the fundamental energy is indeed distributed around the time of origin (time of arrival on the sensor), while the energy corresponding to the harmonic part of the signal is distributed towards the negative times compared to the fundamental part of the signal, and on the other hand that it is possible d '' estimate the relationship between fundamental energy and harmonic energy independently of the knowledge of the subsoil, different methods being possible in this respect.

PRESENTATION OF THE FIGURES

Other characteristics and advantages will also emerge from the description which follows, which is purely illustrative and not limiting and should be read with reference to the appended figures among which:

- Figure 1 schematically shows the general architecture of a seismic acquisition device;

FIGS. 2a to 2c respectively illustrate a sequence of transmission of “slip sweep” signals (FIG. 2a), a recording signal resulting from the propagation and the reflection of these signals in the basement (FIG. 2b), as well as a signal which corresponds to the correlation of this recording signal by the fundamental sequence of vibrations corresponding to the signals of FIG. 2a;

- Figure 3 is a flowchart which illustrates different stages of a possible mode of implementation of the invention; - Figure 4 illustrates the decomposition of the recorded signal according to the source signal and the reflectivity of the basement;

- Figures 5a to 5c illustrate the correlation and windowing operations implemented in the context of a preprocessing for determining an operator of harmonic noise estimation.

DESCRIPTION OF ONE OR MORE EMBODIMENTS

General - Reminders FIG. 1 shows an example of a device for acquiring vibro-seismic data, which comprises a set of vibro-seismic sources Si, S ₂ , ... Sm positioned on the ground surface, as well as a set of geophones G ^ G ₂ , ... G _p also placed on the ground surface. The vibrations emitted by the sources Si, S ₂ , ... S _m (signals s ^ s ₂ , ... s _m ) propagate in the subsoil and are reflected at the interfaces of the layers of this one. The geophones G ^ G ₂ , ... G _p convert the signals they receive into electrical signals which are transmitted to a processing unit 1 where they are digitized and recorded. Seismograms thus recorded are generally processed not in the field, but in a processing center - referenced in this case by 2 - provided for this purpose.

We take the following description in the case where the signals emitted by the sources are of the “sweep” type and overlap (emission of the “slip sweep” type according to the terminology usually used by those skilled in the art).

Note however that the invention is not intended to be in any way limited to source signals of the “slip sweep” type and applies generally to the processing of any vibro-seismic signal originating from one or more source signals for which the source signals theoretically emitted.

Signals s1 (t), ... s4 (t) of the “slip sweep” type have been shown in FIG. 2a for sources S1 to S4.

As can be seen in this figure, each source emits the same vibratory sequence, the emission sequences being shifted in time from one source to another.

During a transmission sequence, the frequency of the vibratory signal varies continuously, for example according to a linear or exponential law as a function of time. In the example of Figure 2a, the frequency increases over time; laws of variations with which the frequency decreases over time are also possible.

FIG. 2a shows the duration T of a transmission sequence and the time ts which separates the transmission sequences from two sources transmitting successively over time. The time ts is less than the duration emission T, so that the vibrations generated by these two sources overlap.

The signals received at the level of geophones G ^ G _2τ ... G _p are composite signals - different from one geophone to another - which are the sum of different signals resulting from the reflection of the signals emitted by the different sources S ^ S ₂ , ... S _m. On the different reflectors in the basement.

Such a signal is for example the signal e (t) shown in FIG. 2b.

The correlation of this signal with a reference signal corresponding to the theoretically emitted vibration sequence of emission is a signal which is theoretically, in the absence of harmonic noise, a signal of the type illustrated in FIG. 2c and which presents peaks at arrival times, on the geophone considered, sequences emitted by the different sources after reflection in the basement.

Example of implementation

FIG. 3 shows different stages of a treatment in accordance with an example of possible implementation of the invention. According to this processing, a correlation is implemented on a noisy signal received on a geophone (step 10 of recovery of the input data) with a reference signal H1 which corresponds to a theoretical sequence of emission of vibrations (step 20) .

This correlation step makes it possible to highlight on the received signal the times which correspond to the arrival of reflections by the reflectors in the basement

The correlation implemented in this step 20 has in fact the property of distributing the energy of the signal recorded in the following manner:

- the energy corresponding to the fundamental part of the recorded signal is distributed around the origin time (arrival time),

- the energy corresponding to the harmonic part of the signal, in the case where the frequencies of this one increase with time, is distributed towards the negative times compared to the fundamental part of the signal. In the following presentation, we will consider a signal whose frequencies increase with time, which does not harm the generality of the method, it being understood that if the frequencies followed a descending law, the energy would be distributed towards positive times . This correlation therefore makes it possible to highlight the arrival times.

For each of the sources Sm to S2, the denoising treatment of steps 30 to 60 which will now be described is then put. It will be noted here that this processing is not necessary for the source which corresponds to the first arrival on the geophone, insofar as the noise generated by this source is rejected outside the time range retained for the rest of the processing. Steps 30 to 60 are as follows.

For a given source k (with k integer between 2 and m), a windowing including the arrival time highlighted for this source by the correlation step 20 is implemented on the recorded signal received on the geophone step 30), so as to conserve the energy of the fundamental component as much as possible.

Then the correlated signal thus filtered is convoluted with an operator op _k for estimating the harmonic component which is specific to the source k. This opki operator will have been determined beforehand during a preprocessing 70 which is described below in more detail. This convolution operation (step 40) makes it possible to supply the noise Nk which, on the correlated signal, corresponds to the harmonic components of the source k.

Once this noise Nk has been determined, it is subtracted from the correlated signal (step 50).

This provides a denoised signal with respect to the harmonics generated by the source k (step 60). A deconvolution processing makes it possible to determine the vibroseismic signal devoid of the harmonic noise corresponding to said source. Steps 30 to 50 are thus implemented successively for each of the sources Sm to S2, the correlated signal used to implement these steps for the source Sk being, when k is different from m, the denoised signal obtained in step 60 of the processing implemented for the source Sk +1.

When the processing of steps 30 to 60 has been implemented for each of the sources Sm to S2, there is then a recorded signal on which the harmonic noise has been greatly reduced.

Example of determining the operator for estimating the harmonic noise generated by a given source

We will now describe a possible example for the preprocessing of determination of the operators op _k (step 70)

1) Theoretical elements

A signal s _k emitted by a given source Sk can be modeled, as illustrated on the left part of FIG. 4, as a weighted sum of n reference signals h1 ... hn corresponding to the fundamental vibratory sequence (h1) and its harmonics (h2, ..., hn), these different reference signals being weighted by weight functions c ₁ ... c _n ,

We can therefore write:

with: hi - α - cos (lττg) h _j - α - cos (2mg) where ^* is the convolution operation, where a is an amplitude value and where g is a known function which varies as a function of time and which can be written:

^ dt (= ((where f (t) is the phase function). Furthermore, we know that in conventional vibro-seismic, the signal β _k coming from a single source S and recorded by a given geophone is considered as being able to be described as follows: e _k = (s _k * r + n ) * imp [2] where S is the signal emitted by a source S _k , r is a function representative of the coefficients of reflection of the signal s _k on the underground layers, n is a function representing a random noise, and imp is a function representing the impulse response of the acquisition chain used. If we make the assumption, which is illustrated in FIG. 4, that the non-harmonic noise is negligible and that the impulse response of the acquisition chain does not intervene, we can then consider that the recording is the convolution of the source signal s _k and the reflection coefficients r, that is to say: e _k = s _k * r [3]

2) Different stages of treatment 70

In accordance with the variant illustrated in FIG. 3, the preprocessing for determining the operators op _k of the different sources Sk can be implemented in the following manner.

This preprocessing requires the use of at least one recording obtained by making the vibration sequence sk emit by the source Sk.

When the seismogram thus recorded for a given source is available (step 701), this signal is correlated with the fundamental vibration sequence h1 and its harmonics h2, ..., hn.

Recall that the correlation with one of the harmonics or fundamental hi corresponds to a convolution with a function hdi whose amplitude spectrum is equal to the amplitude spectrum of hi and the phase spectrum is equal to the opposite of the spectrum of hi phase and that such a correlation has the following properties: the autocorrelation of hi is of zero phase and is centered around time zero; the correlation of hi and hj rejects energy at positive times when j is greater than i and at negative time when i is greater than j.

This is illustrated in FIGS. 5a to 5c which respectively represent the correlation with h1, h2 and h3 of a weighted combination signal of h1, h2 and h3.

As can be understood in these figures, the energy highlighted by these operations is mainly centered around time zero (time of arrival of the vibration sequence), the terms corresponding to correlations of hi and hj crossed (ie with i and j different) being of much lower energy.

It should be noted that only the condition relating to the phase spectrum is necessary for obtaining the targeted result.

By implementing (step 703) windowing centered around the zone where the seismogram is most energetic, that is to say around this zero time (without being necessarily necessarily centered on this, the essential being that the energy peak is in the filtering window), we then recover an approximation of the function r ^* ci ^* hi ^* hdi.

The windowing operation is for example carried out using an apodization function ap chosen to present a width perfectly covering the energy of the harmonic considered. We then have, by setting fi = ap- (e _k * hd _j ): nf = ap- (e _k * hd.) = <Τp • (r * ∑ _{C /} * h,) * hd _t f, ≈r * c, * h _i * hd _l

This equality is written in the Fourrier domain: Fi = R -C _r iHDi [5] where Fi, R, Ci, Hi and HDi correspond to the Fourier transforms of fi, r, ci, hi, hdi.

The correlation, then windowing operations therefore make it possible to determine so-called reduced weight functions CRj:

which are such as if we note in the inverse Fourier transforms of said functions CRj _. , the source signal checks: s _k = c, (b, + cr ₂ * h ₂ + cr ₃ * h ₃ + ... cr _n * h _n ) [7] After determining these coefficients (step 704), we therefore has, apart from a filter function Ci, a modeling of the signal emitted by the real source S _k .

It will be noted that in a possible implementation, to determine the functions CRi, one is limited only to the frequencies for which the values of Ci and Cj are not zero.

Also, to get a finer approximation of the functions

CRj, step 704 can be applied to several traces corresponding for example to several receivers of the same acquisition. The values of

CRj can then be calculated by doing averaging calculations or using statistical operators. 4L

Once the harmonic weight coefficients have been calculated for a source Sk considered, an operator is estimated (step 705) by means of these coefficients to estimate the harmonic noise generated by the source Sk. For a given source Sk, the harmonic noise corresponds in the frequency domain to multiplication

- the fundamental component EC _fθnC ι of the Fourïer transform of the correlated recording

EC _f - by the operator OP equal to

∑CR Hi ∑CiΗ, -

OP = i = 2 i = 2

HI CJ.HJ If we stick to equation [1], as well as to the model of equation [3], we have:

EC = R.S.HD1 = R. (∑C, .H,) .ΗD1

M and

ECfo _nd = R-C1.H1.HD1

ECarm = R. (∑C _f f,) .HD1 = OP.EC _fond

In the time domain (operator op), this operation is written as the convolution of the inverse Fourier transform of OP by the positive part of the correlated recording (which is comparable to the fundamental part of the recorded signal).

Other variants of the calculation of the harmonic weight functions Many other variants of the calculation of the harmonic weight functions can be envisaged. -

In particular, if we consider that the correlation of a vibroseismic signal by the theoretical fundamental component h1 or a harmonic hi is such that the energy corresponding to the correlation of this component or harmonic with harmonic components of higher ranks is negligible, one can describe a vibroseismic signal e on the one hand by the theoretical fundamental component and on the other hand by the various harmonic components which one wishes to consider:

c1 ^* r ^* h1 ^* hd1 = e ^* hd1

Cl ^* r ^* h1 ^* hd2 + c2 ^* r ^* h2 ^* hd2 = e ^* hd2 d ^* r ^* h1 ^* hd3 + c2 ^* r ^* h2 ^* hd3 + c3 ^* r ^* h3 ^* hd3 = e * hd3

c1 ^* r ^* h1 ^* hdn + c2 ^* r ^* h2 ^* hdn + c3 ^* r ^* h3 ^* hdn + cn ^* r ^* hn * hdn = e * hdn

There is therefore a system of n equations for determining the RC / R.C1 functions, that is to say the weight functions. It should also be noted that if there are data relating to the signature of the source, such as the force signal (weighted sum of the accelerations measured on the mass and the plate of the vibrator), the available source signal s * is advantageously used in the preprocessing of step 70 as a signal e _k , _ In this case there is no reflection and equation (3) is reduced to: e _/ ≈ s *

As will be understood, the proposed noise reduction method can be implemented either after recording the noisy data, or in real time, the recorded data then being denoised data.

Claims

1. Method for reducing harmonic noise in a vibro-seismic signal recorded on a sensor, this vibro-seismic signal corresponding to a given vibratory sequence emitted by at least one source and propagated in a subsoil in which it is reflected, characterized by the steps according to which: a) the vibroseismic signal or part of it is correlated with a signal corresponding to the fundamental component of the vibration sequence emitted by the source ^{01 * "} b) on the correlated signal is selected a part which corresponds to the energy of the fundamental component of the vibro-seismic signal and an operator for estimating the harmonic component of said correlated signal is applied to the selected part c) an estimate of the harmonic noise of the vibro-seismic signal is deduced therefrom and this estimate is subtracted from said signal .

2. Method according to claim 1, characterized in that the part of the correlated signal which is selected corresponds to:

- the energy around the time of arrival on the sensor of the propagated and reflected vibratory sequence

- and / or energy in positive times compared to said arrival time.

3. Method according to one of claims 1 or 2, characterized in that in the case where the vibratory sequence is emitted by several sources separated in space and / or in time, the vibroseismic signal is correlated with the fundamental component Theoretical vibration sequence of the transmitted vibration sequence and we deduce from this correlation the arrival times on the sensor of the emissions from the different sources after propagation and reflection in the subsoil.

4. Method according to claim 3, characterized in that part of the signal is isolated from the vibro-seismic signal around the last arrival time highlighted by the correlation with the theoretical fundamental component, it is implemented from the part thus isolated steps a) to c), and this treatment is repeated by successively raising the different arrival times, the vibro-seismic signal on which a part of the signal is isolated around the arrival time considered then being each time the denoised signal from the processing corresponding to the just preceding arrival time.

5. Method according to one of the preceding claims, characterized in that the operation corresponding to step b) is implemented in the frequency domain and corresponds to the multiplication in the frequency domain of the part of the correlated signal which corresponds to the energy of the fundamental component of the vibro-seismic signal, by an operator OP such as:

∑CR _i .H _i OP = ^ -

hl

or :

Η1 is the Fourier transform of the theoretical fundamental component of vibrations of the sequence emitted by the source,

Hi is the Fourier transform of the harmonic component of order i, and where CRi denotes a frequency function of weight associated with the harmonic of order i.

6. Method according to one of claims 1 to 4, characterized in that the operation corresponding to step b) is implemented in the time domain and corresponds to the convolution in the time domain of the part of the correlated signal which corresponds to the energy of the fundamental component of the vibro-seismic signal, by an operator which corresponds to the inverse Fourrier transform of a multiplication operator OP in the frequency domain such that:

∑CR H _i

OP = =?

HI

or :

Η1 is the Fourier transform of the theoretical fundamental component of vibrations of the sequence emitted by the source, Hi is the Fourier transform of the harmonic component of order i, and where CRi denotes a frequency function of weight associated with the harmonic of order i.

7. Method according to one of claims 5 or 6, characterized in that the operator used during step b) is determined by a pre-processing implemented on at least one recording obtained from the transmitted sequence by the source.

8 Method according to one of claims 5 or 6, characterized in that the operator used during step b) is determined by a pre-processing implemented on an estimate of the transmitted signal obtained from data acquired directly on the source ..

9. Method according to one of claims 7 or 8, characterized in that the operator thus determined in the time domain or in the frequency domain is such that:

E, H _; -HA- where ΗD1 is the Fourier transform of a function hd1 whose phase spectrum is the opposite of that of the theoretical fundamental component, HDi is the Fourier transform of a function hdi whose phase spectrum is the opposite of that of the harmonic i, and where Fi is the Fourier transform of f _ι = ap - (e * hd _l ), * being the convolution operation, "e" being a vibro-seismic signal on which the preprocessing is implemented, "ap" being a windowing function centered on centered around (an energy zone of the seismogram.

10. Method according to claim 9, characterized in that the function "ap" is an apodization function.

11. Method according to claim 6, characterized in that to determine the operator used during step b):

- a vibroseismic signal is correlated with the theoretical fundamental component h1 of the vibratory sequence and with that (s) of its harmonic components hi which one wishes to take into account,

- the correlated data are multiplied with a window excluding the energy associated with the correlation of the harmonics of a higher order than that of the component with which the vibro-seismic signal has been correlated,

- the system of linear equations thus obtained is solved in order to deduce therefrom the ratios ci / d where ci and d are weighting functions such that

s = ∑c, * h,

1 = 1

where s is the vibratory sequence emitted by the source.