Abstract: The present invention relates generally to methods of enhancing seismic data and, more particularly, to methods of attenuating noise in seismic signals. The seismic data are sorted into gathers of seismic signals, and selected coherent events in each gather of seismic signals are aligned. The gathers of seismic signals are then processed so as to transform the balance of the coherent events in each gather of seismic signals into incoherent events. A two-dimensional filter is then applied to the transformed signals to attenuate incoherent events.

Abstract: Time-invariant multichannel seismic data filters are applied to seismic data traces for rejecting coherent noise signals within a time-space window. In one embodiment, these filters are applied for rejecting all signals having the same trace-to-trace slopes as the coherent noise signal. Segments of the filtered traces that are within the time-space window are added to corresponding segments of unfiltered traces outside of the time window for producing reconstituted time-variantly filtered traces. In another embodiment, these filters are applied for rejecting the coherent noise signals and passing all other signals within the time-space window and passing all signals outside of the window for producing time-variantly filtered traces.

Abstract: Seismic reflection events are enhanced by separating the events from seismic data, increasing the amplitude of the events, and adding the events back into the seismic data.

Abstract: The present invention is directed to filtering out unwanted components contained in acquired sonic well logging data, e.g., reflected wave components, converted wave components, casing arrivals, tool arrivals and/or noise. In the filtering method, the waveform components of each waveform are treated as vectors, each vector having n samples. The vectors, described in n-dimensional space, are rotated to a new coordinate system whose directions, characterized as eigenvectors, are aligned with the primary directions of the wave component vectors. The eigenvectors are ordered such that the first eigenvector represents the wave components' main direction, the second eigenvector represents the wave components' next main direction, et cetera. By projecting the waveform components onto the principal eigenvectors, the reflected wave components, converted wave components and/or noise component of each waveform is substantially eliminated. Methods are also disclosed for approximating the eigenvectors.

Abstract: A filtering system is provided for acquiring and processing signals using a sampled filter for signal separation and signal enhancement; such as for determing locations, distances, and times in a geophysical exploration system. Signature signals permit mixing and seperation with sampled filters, such as for sharing common circuitry and for increasing the amount of acquired information. A sampled filter, such as a digital correlator, is provided for generating high resolution output data in response to low resolution input data processed with low resolution computation circuits. A real-time time-domain correlator is provided with single-bit resolution computational elements to provide improved correclation filtering. A high speed real-time correlator is provided to enhance signals with copositing-after-correlation and with correlation using a plurality of correlation operators.

Abstract: A blast recorder and method for monitoring and processing vibrations from blasts, and for displaying the results in a nearly real time basis and in a manner which is easily interpreted by a relatively unskilled field worker and corresponds to a form which closely correspond to the real damage causing aspect of the blast than heretofore.

Abstract: A seismic exploration method and apparatus in which non-uniformly distributed noise signals generated by wind, machinery, or surface wave propagation and received by the sensing geophones are cancelled by the utilization of adaptive filter processing. A number of horizontally sensitive geophones are disposed along the surface of the earth to detect surface waves induced in the surface of the earth at a plurality of spaced locations throughout an entire area of investigation. Similarly, a number of wind noise and mechanical noise detectors are utilized to detect airwave and noise signals at a plurality of locations throughout the area of investigation.

Abstract: A method for separating high frequency impulse data from received signal in which it is superimposed on low frequency noise is disclosed. Median filtering is applied to the received signal to remove the impulse data therefrom. The resultant filtered signal is subtracted from the original signal; the remainder includes only the impulses from the original signal. The invention is described in connection with borehole imaging and casing collar locating logging operations, both useful geophysical tools.

Abstract: Method to process seismic data to yield useful information regarding the subsurface area explored. Generated seismic energy travels into a subsurface formation where it is distorted and attenuated. The distorted and attenuated seismic pulse is detected by a geophone or other seismic receiver and recorded. The received seismic traces are first compensated for the attenuation effects of the earth filter and the compensated seismic traces are then used to produce a close approximation of a zero-phase, band-limited output wavelet of the reflectivity of the geophysical formation under exploration.

Abstract: The filtering technique of the present invention cancels or minimizes noise in data signals found to be caused by dynamic variations in the drilling process. It has been discovered that the measurement of surface vibrations in the drill string and their effects on certain drilling equipment such as rotary table torque contains information that can be used to remove some or all of the pressure disturbance caused by these dynamic variations (vibrations). The result of removing some or all of the dynamic variation induced noise from the measurment-while-drilling (MWD) data signal yields a better signal to noise ratio (SNR) and therefore improves decoding of the MWD signal. In accordance with another important feature of the present invention, it has been found that improved SNR results from taking the first derivative with respect to time of the torque measurement. This first derivative measurement more closely resembles the actual disturbance in the standpipe pressure (SPP).

Abstract: Disclosed are improvements pertaining to measurement while drilling apparatus, methods, and systems, including: generation of mud pulse pressure variations in a regime of hydraulic shock waves; transmission of information carrying signals via mud pressure variations which include various interfering signals generally termed "noise" and employing special techniques involving digital filters for accomplishing reception of said information carrying signals; providing hydraulic means to automatically effect periodic closing of the valve means that produces the information carrying signals; providing electrical means to inhibit valve means operation in case of electrical failure in downhole apparatus; providing means which serve to greatly increase the number of satisfactory actuations of said valve means attainable without downhole battery recharge or replacement; providing unique pulse time codes which permit substantial increase in rate of information transmission and the accuracy and precision of such transmis

Abstract: Method of restoring null traces in seismic records. The seismic record is transformed from the x-t domain to the f-k domain by a series of fast Fourier transforms. The f-k transform of the seismic record is filtered to retain only coherent events and the filtered f-k transform is inverse-transformed back to the x-t domain. A first determination of the restored trace corresponding to the null trace is selected and substituted for the null trace. The first determination of the restored trace is used to determine a fully restored trace.

Abstract: An improvement in a method of treating seismic data in which predictive noise, as measured along one of the axes is discriminated and subtracted from the total signal along another of the axes recorded by geophone recording the reflection from subterranean strata of energy input from a source at the surface.

Abstract: A method of velocity filtering seismic signals and an installation for implementing the method. A two-dimensional signal g(z,t) is available built up from a set of signals .sub.i (t) for I>i>n as produced by sound wave detectors located at different depths z.sub.1, . . . z.sub.n in a borehole in response to sound waves being emitted from a source as seismic waves, with said detected signals including upgoing waves and downgoing waves. In order to reinforce the upgoing waves (or conversely the downgoing waves) in the signal g(z,t), an operator A is applied recursively to said signal, where: A=1/2[Id+.epsilon..B.H.sub.t.D.sub.z ] where: Id is the identity operator; .epsilon.=+1(or -1); B is normalization factor whose value depends on the signal g(z,t) to which the operator A is applied; H.sub.t is the one-dimensional Hilbert operator relating to the variable t; and D.sub.z is a differentiation operator relating to the variable z.

Abstract: A common bandwidth determination method for two disparate seismic datasets includes developing a weighted average of first least-squares filters assuming the data from the first dataset is the input and the data from the second dataset is the desired output, developing a weighted average of second least-squares filters assuming the data from the second dataset is the input and the data from the first dataset is the desired output, determining a first transfer function from the first weighted average filter design and a second transfer function from the second weighted average filter design, plotting respective amplitude and phase spectra using each of the first and second transfer functions, plotting the product of the amplitude spectra and the sum of the phase spectra and determining the common bandwidth where the amplitude spectra is one and the phase spectra is zero.

Abstract: Method and apparatus for producing improved synthetic velocity logs from seismic traces. The seismic traces are processed to enhance high frequency content by converting each trace to a spike trace, then filtering the spike trace with a function designed to reduce side lobes and enhance high frequency content. The processed trace is then operated on by a conventional summation process to produce a synthetic velocity log. Due to the enhanced high frequency content of the processed trace, the resulting synthetic log tends to show sharp discontinuities in the geology, much like a log taken from a well.

Abstract: In an image processing system for elimination of speckle a signal derived from a scan is passed to a statistical processor (21). An output characteristic of a statistical parameter of the local value of this image signal is passed to a comparator (4) and compared with a reference characteristic of speckle to derive a control signal for a variable bandwidth filter (6) used to enhance the image.

Abstract: Method to process seismic data to yield useful information regarding the subsurface area explored. Seismic data which is acquired from the seismic exploration is autocorrelated and the amplitude spectrums estimated, stacked and averaged to reduce the effects of nonwhite reflectivity upon the data. The amplitude spectrum is cepstral windowed a first time to reduce the effects of reflectivity leakage on the amplitude spectrum, amortized at both low and high frequencies so that the amplitude spectrum will approximate the analog wavelet and cepstral windowed a second time to eliminate any remaining rapidly varying components of the amplitude spectrum. The resultant amplitude spectrum is then used to estimate the phase spectrum for the wavelet and a two-sided least squares filter is then designed to shape the estimated seismic wavelet into a zero-phase, low sidelobe output wavelet.

Abstract: The apparatus of the present invention includes a group of at least three seismic detectors. Each seismic detector detects vibrations and provides a seismic signal in accordance with the sensed vibration. A multiplexer multiplexes the seismic signals to provide a multiplexed signal. The multiplexed signal is amplified and converted to digital signals. A memory stores the digital signals according to the detector of origin so that the stored digital signals for a detector are in effect a sample of the seismic signals from the detector. A microprocessor connected to the memory means derives a statistical reference from the stored samples. Samples that are outlying with respect to the statistical reference are discarded. The remaining samples are then combined in a predetermined manner to provide an enhanced seismic signal from the group of detectors.

Abstract: Disclosed are a method and a system for discrete transformation of measurements such as seismic data into and out of tau-p space which is both exact and practical in terms of processing time. The measurements can be filtered or otherwise processed in tau-p space in ways which are not practical or possible in their original space. Since the transformations into and out of tau-p space are exact, the filtered and transformed measurements are free of errors and distortions that perturb known approximate transforms which can be performed in a reasonable time. When the transformation process is carried out in frequency space, it is done frequency-by-frequency, and when it is carried out in the spatial domain, it can utilize a transformation matrix having a block-circulant structure. In each case, the transformation process and matrix have a structure which substantially reduces storage and processing requirements as compared with known prior art.

Abstract: The system for suppressing an ambient noise signal which comtaminates a desired signal includes a noise pickup detector for detecting the ambient noise signal. A noise discriminator processes the detected noise signal into noise data. A reference noise generator converts the noise data into a reference noise signal. The noise generator automatically adjusts the reference noise signal to correspond with changes in the noise signal as it is being detected. A filter filters the reference noise signal into an error signal which is adapted to remove the noise signal from the contaminated signal. A cross-correlator cross-correlates the contaminated signal with the reference noise signal and adjusts the filter to produce the required error signal.

Abstract: A borehole televiewer logging tool employs a transducer assembly having a transmitter of acoustic energy pulses and a receiver of acoustic energy pulses representing reflections of the transmitted acoustic energy pulses from the walls of a borehole traversing a subsurface formation. The transducer assembly is rotated within the borehole and also advanced along the borehole. The received reflection signals are corrected for amplitude modulation resulting from oblique angles of incidence of the transmitted acoustic energy pulses when the logging tool is off-center of the borehole, is in an eliptical borehole, or is tilted from the vertical axis of the borehole. The corrected reflection signals modulate an image display so that the full 360.degree. of the borehole wall can be delineated.

Abstract: In a process for obtaining seismic data relating to an exploratory well, a seismic wave transmitter and a seismic wave receiver are provided, one arranged on the surface adjacent the well and the other at a plurality of measurement points down the well, and the output of the receiver is processed in a processing installation. The measurement points are divided into at least two groups, each of which comprises a plurality of measurement points spaced apart in a distance (D.sub.z) which is less than a predetermined limit distance so as to avoid aliasing, and the groups of measurement points are separated from each other by a distance (D) greater than the limit distance. In the processing installation separation of the down-going waves from the up-going waves belonging to the same group is carried out before coherence filtration of the separated waves.

Abstract: Statistical variations in simultaneous shallow and deep investigation nuclear borehole logs are reduced using digital moving average data processing while maintaining responsiveness to formation changes, by transitioning through a combination of long and short filtered data as a function of the statistical variation of the deep log data differences of the long and short derived averages. Borehole rugosity is also indicated as a function of the difference between the shallow and the deep log indexes of the differences between their respective narrow and wide derived averages.

Abstract: A method for preparing a display of seismic data obtained from multiple-point coverage of a subterranean earth formation using an array of seismic sources and acoustic receivers. A set of seismic traces is obtained in such a manner that each trace is associated with a source-receiver pair separated by a particular offset distance, and all the traces are associated with a common subsurface reflection point. Each of the traces is filtered through a bank of band-pass filters to produce a set of filtered traces, each having a different frequency content, for each offset value. The filtered traces associated with a particular offset value are displayed in order of progressively changing frequency content, and the filtered traces associated with a particular frequency band are displayed in order of progressively changing offset value.

Abstract: A filtering system is provided for acquiring and processing signals using a sampled filter for signal separation and signal enhancement; such as for determining locations, distances, and times in a geophysical exploration system. Signature signals permit mixing and seperation with sampled filters, such as for sharing common circuitry and for increasing the amount of acquired information. A sampled filter, such as a digital correlator, is provided for generating high resolution output data in response to low resolution input data processed with low resolution computational circuits. A real-time time-domain correlator is provided with single-bit resolution computational elements to provide improved correlation filtering. A high speed real-time correlator is provided to enhance signals with compositing-after-correlation and with correlation using a plurality of correlation operators.

Abstract: A method for attenuating multiples in common depth point data whereby common depth point data is received and spike deconvolution maybe performed on the data. The data is constant velocity stacked and gap deconvolution is performed. The primary stack velocity is determined and all data having a velocity other than the primary stack velocity is muted. All scans within the constant velocity stack are composited. These composites are arranged in proper order and displayed.

Abstract: A method is disclosed for estimating the impulse response of the earth from Vibroseis data. Based on a time domain system identification approach, the earth's impulse response is estimated by operating on the seismic trace data and the vibrator pilot. Two implementations are discussed. The first is an adaptive method using a sliding data window and the uncorrelated trace data. Preferably, the process used to control the adaptation is the fast Kalman estimation (FKE) technique. This technique, based on recursive least squares, has a fast convergence rate and desirable computational requirements. The second implementation is non-adaptive. It uses the Levinson recursion technique to compute the Wiener filter solution based on the pilot autocorrelation function and the correlated trace data. Simulations demonstrate the capability of the system identification model to resolve reflection events.

Abstract: A method and apparatus for enhancing the resolution of true variations of a seismic signal amplitude as a function of range. A time-variant bandpass filter is impressed upon the seismic data having a bandpass frequency dependent upon the range between the seismic sources and the seismic receivers of a common depth point array of seismic sources and seismic receivers. A maximum bandpass frequency is derived from the maximum range between the seismic sources and the seismic receivers of a common depth point array of seismic sources and seismic receivers. The maximum bandpass frequency is adapted to accommodate time varying ranges as well as time varying stacking velocities so as to produce a seismic signal having enhanced resolution of amplitude variations of the seismic signal.

Abstract: A method for avoiding aliasing in .tau.-p transformation or "slant stacking" of seismic data is disclosed which features identification of frequency components of the data likely to be aliased during correlative summation steps and removal thereof from the data prior to summing.

Abstract: A process for better defining first break seismic energy travel times for correlated seismic return signals that consists of constructing a minimum phase bandpass filter having bandwidth narrower than the vibrational seismic return signals and convolving the filter with the return signals to convert the seismic return signals to a causal wave form.

Abstract: In seismic exploration, aliasing caused by coarse sampling along a line of exploration is corrected by trace interpolation. The interpolated traces are obtained by inserting zero amplitude traces between seismic traces. Transformation into the f-k domain and filtering of the aliased regions in the f-k domain produces properly interpolated traces when transformed to the x-t domain.

Abstract: An electronic noise filtration system for use in improving the signal to noise ratio of acoustic data transmitted from a downhole transducer in a measurement while drilling system. Signals from a pair of receiving acoustic transducers located in the mud flow path directed downhole are input to a differencing amplifier. The RMS output of the amplifier is converted from an analog to a digital signal and then processed by a computer programmed with a least mean squares technique for minimizing the signal. The input from one receiving transducer is routed through a delay line wherein a programmable clock controls the timing of the signal delay. The delay time is controlled and adjusted by the computer's calculation of the frequency with which the clock should drive the delay line to minimize the difference between the two received transducer signals. This function minimizes ambient noise in the acoustic transmission line formed by the column of drilling fluids when no data transmissions are being made.

Abstract: The invention is a method and apparatus for substantially eliminating from a seismic signal channel an interfering hiline signal in a differential mode. Differential mode and common mode components of the interfering signal are coupled from the seismic signal channel, and are correlated with each other to obtain a correlation signal. The correlation signal and the common mode signal are multiplied to obtain a correction signal that is applied to the seismic signal channel to substantially eliminate the differential mode component of the hiline interference signal. The correlation between the differential mode and common mode signals is accomplished with both in-phase and quadrature phase components of one of them so that two correlation signals actually are produced.

Abstract: A seismic exploration method is disclosed for filtering the signals produced by a detector placed at different depths in a well in response to an emission of acoustic waves from a source on the surface: the signals comprising downgoing wave components and upgoing wave components.The filtering consists in sampling from among the N signals to be processed a group of n signals s.sub.1 . . . s.sub.n detected at respective levels x.sub.1 . . . x.sub.n, in determining the propagation time t.sub.k of the acoustic waves from the level x.sub.1 to each level x.sub.k, in both advancing and delaying the signals s.sub.k by the time t.sub.k in relation to s.sub.1, in adjusting the signals for the effects of the acoustic impedance of the formation, in combining s.sub.1 and the signals s.sub.k thus shifted and adjusted to obtain a sum z.sub.1 ', in calculating a sum y.sub.1 ' of s.sub.1 and of the thus delayed and adjusted signals s.sub.k, and in generating a signal u.sub.1.sup.

Abstract: An improved duty cycle controlled filter, wherein a resistance is included in every circuit path that exists between a switch terminal and an amplifier terminal. Such improved filter produces low distortion and has been found to be especially useful in data acquisition circuits of seismic exploration systems.

Abstract: In a seismic exploration system, the waveforms provided from a plurality of seismic sources are phase shifted so as to maximize the strength of signals received by a plurality of seismic receivers and the signals output from the plurality of seismic receivers are phase shifted so as to substantially maximize the strength of the composite signal which results from the summation of the output from the plurality of seismic receivers.

Abstract: A pattern recognition system includes a filter bank, coupled via rectifying elements to integrators which are coupled via different weighting elements to the summing nodes of a summing amplifier. The filter bank, integrators, and weighting elements include switched capacitors enabling the manufacture of the filters, rectifiers, integrators and weighting elements on a monolithic integrated circuit chip. The frequencies at which the capacitors are switched are programmable enabling the system to be easily "retuned".

Abstract: A method is disclosed for editing seismic traces gathered by large multichannel collection systems using a pattern analysis of the noise spectrum of each trace. Analysis is limited to only a small time window, say the last second of the trace. In that way a minimum number of quantitative variables and mathematical manipulations are required to carry out the invention. On-site as well as off-site, processing of the traces in accordance with the method of the present invention, is contemplated.

Abstract: In seismic exploration a method for improving seismogram displays is disclosed wherein seismograms having an offset which produces poor signal power are muted and seismograms having offsets with high signal power are stacked. The signal power in a CDP set is determined as a function of different values of assumed acoustic velocity of the earth. This signal detection is repeated for successive values of travel time and offset. The maximum signal power is plotted for values of velocity as a function of travel time and for different ranges of offset to form contours of the maximum signal power as a function of time and offset.

Abstract: A method, when practiced, enhances seismic data so as to suppress noise in the seismic data. The seismic data was generated in a conventional manner by at least one receiver apparatus whose position does not substantially change. The method includes combining at least two elementary seismograms to form noise seismograms containing little or none of the desired signal. The number of different noise seismograms so derived is at least equal to the number of elementary seismograms to be combined to form a final seismogram. The probability distribution of noise is determined for each trace of the noise seismograms from the probability distributions of noise in the traces of the noise seismograms. The most probable form of the desired signals is derived from the probability distribution of noise in the traces of the elementary seismograms to provide the enhanced seismic data.

Abstract: A geophone is disclosed which includes at least two transducers having axes which are perpendicular to each other for sensing vertical and horizontal in-line components of seismic waves. In one arrangement, the geophone includes a signal processor which includes active circuit elements responsive to the transducer output for suppressing ground roll components included in the transducer outputs. At least one of transducer output signals with ground roll signal components suppressed therefrom is connected to a remote location for recording. When more than one signal is to be sent from the geophone to the remote recording location, a mulliplexer is provided at the geophone for transmission of a plurality of geophone output signals to the remote location over a single transmission path, such as a dual-conductor transmission line. Analog and digital versions of the geophone are disclosed.

Abstract: A seismic exploration method is disclosed for filtering the signals produced by a detector placed at different depths in a well in response to an emission of acoustic waves from a source on the surface: the signals comprising downgoing wave components and upgoing wave components.The filtering consists in sampling from among the N signals to be processed a group of n signals s.sub.l . . . s.sub.n detected at respective levels x.sub.l . . . x.sub.n, in determining the propagation time t.sub.k of the acoustic waves from the level x.sub.l to each level x.sub.k, in advancing the signals s.sub.k by the time t.sub.k in relation to s.sub.l and in adding s.sub.l and the signals s.sub.k thus shifted to obtain a sum z.sub.l, in calculating a sum y.sub.l of s.sub.l and of the signals s.sub.k delayed by the time t.sub.k in relation to s.sub.l, in generating a signal u.sub.l *, defined as an optimum estimation of the upgoing wave component, from the sums y.sub.l and z.sub.

Abstract: A multiple coverage seismic exploration technique provides for a plurality of seismic trace recordings along a line of exploration. From these recordings, sets of common-offset-distance traces are gathered. Initial estimates are made of the apparent dips associated with the seismic reflection signals across each set of common-offset-distance traces. These initial dip estimates are smoothed and the sets of common-offset-distance traces filtered along the apparent dips associated with the smoothed dip estimates to enhance the signal-to-noise ratio of the primary reflection signals.

Abstract: A geophysical data acquisition system is disclosed having a dynamic range larger than that achievable with typical existing systems. The range of input signals that can be accommodated by a system are limited on the lower end by the noise level of the system and at the upper end by saturation levels of the system. High amplitude input signals can be accommodated by the system if certain unneeded frequency components are filtered off at a sufficiently early point in the signal flow path. In the present invention this desirable filtering is accomplished while maintaining a high gain level in the signal flow path ahead of those components which introduce high noise levels. As a result, the system has an expanded dynamic range and the needed capability to faithfully acquire low amplitude signals.

Abstract: A method is provided for obtaining wide band seismograms made from a plurality of narrow band seismic surveys using vibrator type sources. Several different narrow frequency band seismograms are obtained using vibrator type signal sources. The narrow band seismogram having different frequency band responses are stacked, or added together, to provide a single wide band seismogram having improved signal to noise characteristics.

Abstract: This invention relates to continuous wave seismic exploration and more particularly to generating long sweep continuous seismic waves and utilizing signals resulting from detection of said seismic waves to significantly enhance the signal-to-noise ratio while simplifying the required processing.

Abstract: An apparatus and method for improving seismic resolution involving the application of scaling factors to seismic data which compensate for amplitude decay as a function of time, frequency and source-to-receiver distance (position). Each seismic trace associated with a common source-to-receiver distance is first separated into a plurality of frequency band-limited component traces. A time-variant amplitude scale factor (or its equivalent) is generated for each component trace. These scale factors are then applied to the component trace thus compensating for amplitude decay of the component trace. Upon recombination of the component traces a multidimensional amplitude scaled (MIDAS) seismic trace is recovered. The apparatus and method are particularly useful in creating a high-frequency extension of the frequency bandwidth resulting in improved resolution upon further processing or display. The method can be implemented as part of the field procedure or during subsequent computer processing.

Abstract: A method for removing an undesired surface wave from a reflected wave in a method for seismic exploration is accomplished by placing first and second detector arrays at a location on the surface of the earth in the direction of movement of the surface wave. The array has a length less than the length of the shortest wave length of the interfering wave to be eliminated. Signals from both arrays are recorded and processed by first adding the received signals to form a first output, subtracting added signals to form a second output, shifting one of the output signals by 90.degree., adjusting its amplitude and subtracting the phase shifted and adjust signal from the remaining signal thereby removing the surface wave.

Abstract: Seismic exploration on land and on ocean beds is performed by emitting vibrational acoustic signals of long time-duration within a desired frequency spectrum at one or a number of points, the signals corresponding to the waves received from the reflectors being then processed. The method further consists in forming the complex spectrum of the received signal corresponding to the emitted signal in respect of each frequency band, in forming the complex spectrum of a reference of the emitted signal in respect of each frequency band and in dividing the complex spectrum of the received signal by the complex spectrum of the reference of the emitted signal, at least an external portion of each complex spectrum being eliminated in the case of each complex spectrum.