GB2239950A

GB2239950A - "Acoustic signal processing using an inverse-filter"

Info

Publication number: GB2239950A
Application number: GB9014278A
Authority: GB
Inventors: Haqi Ismail Hussain Almossawi
Original assignee: Individual
Current assignee: Individual
Priority date: 1989-07-04
Filing date: 1990-06-27
Publication date: 1991-07-17
Also published as: GB9014278D0

Abstract

Physical characteristics of a material through which acoustic energy has been conducted and partly absorbed are inferred from the missing parts of the received spectrum. The signal 11, 20 is applied to an inverse filter arrangement 10, acting as a low-, high- or pass-band filter, connected to a white noise level generator 41 and the missing spectral content of the transmitted signal is built-up band-by-band. The arrangement comprises an amplifier 32, ADC 33, micro-processor 34. RAM 35. keyboard 40 and display means 36-39. The material under investigation may be an earth formation. <IMAGE>

Description

Title INVERSE-FILTER Technical Field The present invention relates to the computerised inverse-filter arrangements and to the methods of operating such arrangements.

This invention also relates to an acoustic inversefilter and to a method of operating an acoustic inverse-filter.

Background The earth material cavities are addressed as either pores between grains or joints and fractures. These cavities may be economical targets due to the accumulations of hydrocarbons or the precipitation of gold and other minerals, the size of those cavities is an important engineering parameter.

To date, the time domain and velocity of the acoustic waves have received the bulk attention of data processing and interpretation in the coal, oil and gas, civil and electrical engineering programmes. As a result, only the elastic properties of the earth materials have been addressed, leaving the inelastic properties relatively untouched.

The time domain aspects of the acoustic wave propagations have been shown to be reliable porosity indicators. The well logging programmes are recommended to be carried out to provide more accurate and reliable informations about the type of rock formations, such as porosity and permeability.

The permeability has not yet been effectively estimated from the surface survey or the well logging. Therefore, core samples are usually taken to the laboratory to evaluate the porosity and permeability, and this is a very costly method.

The prior art methods and apparatus include x-ray, ultrasonic, visual examination of non destructive techniques, or explosive and destructive techniques. The continuous signal techniques, provided for example by Proctor U.S. 3,228,232, provide limited data,and have serious shortcomings as the geometry of the object being examined becomes more complex. Works have been conducted for may years on spectral method and arrangements to measure the characteristics of the earth material through which the energy have been conducted,an example of such method or apparatus arrangement may be found in GB Pat. No. 1,521,252; GB Pat. No.

2,022,827A; GB Pat. No. 2,128,327A; and GB Pat. No. 2,208,713A.

The present invention is directed to improvements in the spectral examinations or analyses by providing an inverse-filter design An inverse-filter tends to build up frequencies in which meaningful data are virtually missing, and these filtered frequencies could be low-, band-, or high-pass frequencies. The build up of the missing; for example, acoustic; frequencies due to their filtrations in the earth material could be arranged, in use, to be valuable tool to characterise those materials.

Essential Technical Features According to a one aspect of the present invention, a computerised inverse-filter arrangement comprising computerised responsive means for input electronic signals; means for generating whi.te-noi8e-level;-means providing Central Processing Unit for calculating and build up of the missing spectra comprises signal conditioning amplifiers, ADC converter, microprocessor, RAM, serial and/or parallel ports; means responsive for indicating the output electronic signals; and operated when energised to be acted on by input electronic signals to characterise the inverse-filter of the required spectra and to build up the missing frequencies.

According to another aspect of the present invention, the inverse-filter is provided by a microprocessor unit, which unit is arranged, in use, to search rigidised mathematical modelling for computerised in-service conditions using standard mathematical techniques for processing the required spectra.

The inverse-filter operable means tend to build up low-pass inverse-filter of the missing low-pass spectra.

The inverse-filter operable means tend to build up high-pass inverse-filter of the missing high-pass spectra.

The inverse-filter operable means tend to build up band-pass inverse-filter of the missing band-pass spectra.

Operation of the inverse-filter operable means may be capable of causing the build up of the low-, band-, and highpass inverse-filter of the related missing spectra.

According to another aspect of the present invention, the white-noise-level, generated by the inverse-filter operable means, processed or added to the input spectra undergoing analysis for an inverse-filter to build up the missing data.

According to another aspect of the present invention, the inverse-filter may include an indicator, which indicator may be arranged to provide an indication of the inverse-filter of the spectral signals. The indicator may comprise signals input and output means. The signal output means include means to increase the induced signal to noise ratio,filter unwanted signals, and separate any feedback signal from the processed signals. The manually operating criteria may be remote controllable by a computerised system or operable arrangement.

The criteria carried out for a single channel may be carried out for every channel of a multi channel operable arrangement.

The inverse-filter operable means may provide a non volatile memory as well as an additional storage memory.

According to a further aspect of the present invention, a method of inverse-filter comprising reading the input spectra; search rigidised mathematical modelling for computerised inservice conditions using standard mathematical techniques for processing the required spectra; and/or adding the white-noiselevel to the processed spectra; characterising the inversefilter of the required spectra; and determining the build up of the missing frequencies and to determine the physical characteristics of the material which absorb the missing spectra based on the type and magnitude of the missing frequencies.

According to another aspect of the present invention, a method of the inverse-filter may provide rigidising mathematical modelling for computerised in-service conditions using standard mathematical techniques for processing the required spectra.

According to another aspect of the present invention, a method of providing white-noise-level arranged, in use, to be processed or added to the input spectra undergoing analysis for an inverse-filter to build up the missing data.

The method of inverse-filter tends to build up low-pass inverse-filter of missing low-pass spectral data. The method of inverse-filter tends to build up high-pass inverse-filter of missing high-pass spectral data. The method of the inversefilter tends to build up band-pass inverse-filter of the band-pass missing spectral data.

The method may include varying the frequency of the input white-noise-level over pre-selected frequency range, and determining the missing frequencies.

The method may maintain velocity (wavelength * frequency), of the output signal equivalent to the velocity of the input signal.

The method may maintain the attenuation coefficient (per unit time or frequency, as a function of the frequency), of the output signal equivalent to the attenuation coefficient of the input signal.

The required attenuations due to scattering and diffraction, and the velocity dispersion may be provided as options taking into account for the processed signals.

Fourier analyses may be provided once and/or twice, (Cepstrum), for the input and/or output signals or their windows.

According to a further aspect of the present invention, the method may comprise interpreting signals from responsive means.

The method may comprise an indicator means.The method may comprise interpreting signals from an indicator means, which signals may be indicative of the input signåls.The method may comprise techniques of obtaining the analog/digital of the input/output signals. The method may comprise techniques of energising the inverse-filter.

The method may comprise a modular construction of the electronics.

The method may comprise a technique for an electronic design.

The method may comprise rigidising the electronics for severe inservice conditions comprises using standard techniques. The signal output means may include means to filter the noise from the desired signals. The computational output means may include means to increase the signal to noise ratio. The computational output means may include means to regulate the balance between the whitenoise-level signals- and the input and the processed missing signals. The method may comprise processing or analysing the input and/or output electronic signals. The method may comprise mathematical modelling or calculations of the processed input electronic signals.The method may comprise means for calibrations of the input and/or output electronic signals.

According to yet a further aspect of the present invention there is provided apparatus substantially as herein described when used in a method substantially as herein described.

ExamPle Specific embodiments of the present invention will now be described by way of example only and with reference to the diagrammatic drawings in which : Figure 1 shows a schematic diagram of the low-pass inverse-filter.

Figure 2 shows a schematic diagram of the high-pass inverse-filter.

Figure 3 shows a schematic diagram of the inverse-filter operable arrangement.

Figure 4 shows a schematic diagram of an unknown spectral input X(Z) to a known filter B(Z) and spectral output Y(Z).

Figure 5 shows a schematic diagram of the inverse-filter A(Z), which is inverse to the filter B(Z).

Figure 6 Factoring the polynomial B(Z) breaks the filter into many two-term filters,each filter should have a bounded inverse.

Figures 1 and 2 show the inverse-filter apparatus and method arranged, in use, to demonstrate the inverse-filter of low and high pass filter, the input 11/20 and output 12/21 spectral signals are given in the time (sec) and frequency (Hz) domains.

The operable arrangement 10 is operating to inverse-filter the digital and/or analog signals of Low Frequency spectra 11 into High Frequency spectral signals 12, this process may be called the inverse-filter LHF, figure 1.

Assume that the operable arrangement 10 has given the input 11 spectra of the frequency band-width of, for example, (2-600)Hz, then the operable arrangement 10 inverse-filter the frequency band-width of the input 11 spectral characteristics up to the required limit, for example, 1.0 KHz. Therefore, the following spectra explain the process Input 11 band-width: 2 Hz to 600 Hz, Operable arrangement 10 added the missing band-width: 600 Hz to 1.0 KHz, Output 12 band-width: 2 Hz to 1.0 KHz.

The build up of frequency band-width of (600-1,000) Hz by the inverse-filter operable arrangement 10 has the same spectral characteristics of the input signal 11, and characterise the material which absorb these frequencies.

A similar approach with an opposite process is shown in a sketch diagram given in figure 2, wherein the operable arrangement 10 arranged, in use, to demonstrate the inverse-filter of High Frequency spectral signals 20 into Low Frequency spectral signals 21, this process may be called the inverse-filter HLF.

If the operable arrangement 10 has given the input 20 characteristics of the frequency band-width of, for example, (200 to 1K) Hz, then the operable arrangement 10 inverse-filter the frequency band-width of the input 20 spectral characteristics up to the required limit, for example, (2) Hz. Therefore, the following spectra explain the process Input 20 band-width: 200 Hz to 1.0 KHz, Operable arrangement 10 added the missing band-width 21 : 2 Hz to 200 Hz, Output band-width : 2 Hz to 1.0 KHz.

The build up of frequency band-width of (2 - 200) Hz by the inverse-filter operable arrangement 10 has the same spectral characteristics of the input signal 20, and characterise the material which absorb these frequencies.

In an embodiment, the inverse-filter of the required frequency range or band-width could be carried out by rigidising a mathematical modelling for computerised in-service conditions comprises using standard mathematical techniques,to extrapolate the power at those frequencies and taking into account the effects of attenuations due to, for example, scattering and diffraction, velocity dispersion, attenuation coefficient, instrumentation errors, noise, etc.

The velocity (wavelength * frequency), of the output signal is maintained equivalent to the velocity of the input signal.

The method may maintain the attenuation coefficient (per unit time or frequency, as a function of the frequency), of the output signal equivalent to the attenuation coefficient of the input signal. The required attenuations due to scattering and diffraction, and the velocity dispersion may be provided as options taking into account for the processed signals.

Then, results could be used and displayed again in the time and/or frequency domains. Fourier analyses may be provided once and/or twice, (Cepstrum), for the input and/or output signals or their windows.

In another embodiment the inverse-filter tends to build up frequencies in which meaningful data are virtually missing, so that the noise at such frequencies is decreased, and those filtered frequencies could be of low,band, or high band-width.

The white-noise-level from the generator 41 (figure 3) may be arranged, in use, inside the operable arrangement 10, processed or added to the input data 11 or 20 undergoing analysis for the inverse-filter design. The frequency of the input white-noise-level may be varied over pre-selected range, to determine the missing spectra. The addition of white-noise or what is equivalent,superimposing an impulsive function or biasing the amplitude-frequency response curve, may not limit the extent to which this can occur.

In another embodiment, an apparatus arranged,in use,to inversefilter spectra; comprises central processing unit CPU which may be needed to store permanently the required procedure, read the input data which is virtually provided in time domain, inversefilter the power of the required frequencies,store the results, and transform the results into the time domain.

The practical operable arrangement of the hard-/soft-ware may be arranged,in use, by making a card-interface operable arrangement, which arrangement comprises of a Non Volatile Memory NVM and provides the required processing soft-ware. The card-interface operable arrangement may be accommodated by a computer system or arrangement to minimise the hard-ware and aid processing.

In another embodiment, figure 3 shows the possible design and communications of the operable arrangement 10. The arrangement 10 is arranged, in use, to inverse-filter, which arrangement may comprise of signal conditioning amplifiers 32,ADC converter 33, microprocessors 34, RAM 35, serial and/or parallel port 30 to a computerised system, DAC analog relay 31, and white-noise generator 41 for the required frequency levels.

The operable arrangement 10 may be connected to , or exhibit, a keyboard 40, Cathod Ray Oscilloscope CRO 36, VDU monitor 37, plotter 38, or a printer 39. The output signals may be displayed on the units 36-39, or transferred to another computerised operable arrangement throughout the serial port 30 for a suitable storage and/or further processing.

The operable arrangement 10 may be functioning as LHF, HLF, or band-pass inverse-filter. The single or multi-channel input data (11 or 20) are fed into the apparatus 10, and these data and their inverse-filter output may be displayed on the units 36-39.

In another embodiment, to demonstrate the benefit of the inverse-filter; short pulses of vibrational energy; e.g.,figures 1 and 2; have characteristics similar to white light, they too carry spectra. Hence,spectral analyses of these pulses conducted after they have been used to interrogate the earth materials can be expected to yield results as equally as important as the data obtained by optical spectroscopy.

The inelastic properties of the earth materials as well as spectra of frequencies yield important results of the material micro-structures.For example,cavities or fractures can increase the attenuation coefficient in all mechanisms, and cause the received echo signal to be distorted due to preferential attenuation at higher frequency components of the transmitted acoustical signals. Therefore, the earth materials act as low pass filters, filtering high frequency components and the property of the filters have linear relationships with the micro-structure size.

The relationship between the band-width of the acoustical power spectra and the permeability of dry rocks is B U = K ( F ) ...

where U is the permeability, F is the cut-off frequency, K and B are constants. The relationship between the acoustical parameters and the cross sections area of cavities (A) is 2 oc = ( 2 X ) / ( TS A V ) ...

where ocis the attenuation coefficient, X and V are the wavewavelength and the velocity of the acoustic waves.

The permeability is inversely proportional to the cross section area (A), therefore C/A ...

Accordingly, from equations 2 and 3 we have 2 U = C' oL f / X = C' OL V / X ... 4 The Quality factor of the earth material is Q = TT f / ot V ... 5 From equations 4 and 5 we have 2 U = C" f / Q X ... 6 The constants C,C',C11 are described as follows C = q v (dx/dp) ... 7 C' = (TT/2) C c" = TT C' where TT is constant, q is the fluid flow, v is the viscosity, (dp/dx) is the pressure differential (dp) across the thickness (dx). The atmospheric conditions (temperature and pressure) have balanced effects on the parameters of equations 4 and 6.

This acoustic technique is expected to be valid for most physical condition.

It is obvious that the frequency (f) refers to the fundamental tone of the resonator, and may be applicable only when the wavelengths of the acoustic vibrations approach the average cavity size. The present invented spectral arrangement has an important role by inverse-filter, for example, seismic frequencies into ultrasonic frequencies which reflect the enhaced image of the micro-strucutres. The inverse-filter of ultrasonic frequencies into seismic frequencies will assist the seismic processing and interpretations.Therefore,the build up of the missing acoustic frequencies due to their filtrations in the earth materials could be arranged, in use, to be valuable tool to characterise those materials.

According to yet a further embodiment, to understand the inversefilters A(Z) for the earth materials as, for example, low pass filters B(Z), we consider that the output y of a filter b is known but t t the input x is unknown, figure 4.

t To undo the filtering operation of the filter B(Z), we must find another filter, e.g. A(Z), figures 5 and 6. To solve for the coefficients of the filter A(Z), we identify coefficients of powers of Z in [B(Z) * A(Z) = 1J. A three-term filter of B(Z) is 2 2 (a + a Z + a Z + ...) (b + b Z + b Z + ...) = 1 ... 10 0 1 2 0 1 2 the coefficients of Z are a b = 1 ... 11 0 0 a b + a b +a b + ... = 0 ... 12 k 0 k-1 1 k-2 2 Consider the example where B(Z) = 1 - Z/2, then from equations 11 and 12 and the binomial theorem, by polynomial division, or by Taylor's power series formula we obtain 2 3 A(Z) = [1/(1-Z/2)J = 1 + (Z/2) + (Z/2) + (Z/2) + ... ... 13 Equation 13 shows that there are an infinite number of filter coefficients but that they drop off rapidly in size so that approximation in a computerised apparatus presents no problem.

With the filter [B(Z)=1-2Z], we obtain 2 3 A(Z) = L1/(1-2Z)] = 1 + 2Z + (2Z) + (2Z) + ... ... 14 The outputs of the filter A(Z) depend infinitely on inputs of the infinitely distant past. Recall that the present output of A(Z) = a x + a x + ... + a x ... 15 0 t t-1 n t-n so (a ) represents memory of (n) times units earlier.

n In the general case, one may factor B(Z) into two parts B(Z) = B (Z) * B (Z) ... 16 out in where B may contain roots outside a unit circle and its inverse out is expressed as a Taylor series about the origin. The factor B in contains the roots inside, and its inverse is expressed as a Taylor series about infinity.

Claims

1. An operable arrangement of the inverse-filter, said apparatus, comprising computerised responsive means for the input electronic signals; means for generating white-noise-level; means providing Central Processing Unit to build up of the missing spectra comprises signal conditioning amplifiers, ADC converter,microprocessor,RAM,serial and parallel ports; means responsive for indicating the output electronic signals; characterising the inverse-filter of the required spectra; and operated when energised to be acted on by the input electronic signals to characterise the inverse-filter of the required spectra; determining the build up of the missing frequencies and to determine the physical characteristics of the material which absorb the missing spectra based on the type and magnitude of the missing spectra.

2. An operable arrangement of the inverse-filter as claimed in claim 1 wherein the inverse-filter is provided by a microprocessor unit, which unit is arranged to search rigidising mathematical modelling for computerised in-service conditions using standard mathematical techniques for processing the required spectra.

3. An operable arrangement of the inverse-filter as claimed in Claims 1 or 2 wherein the low-pass inverse-filter build up the missing low-pass spectral data.

4. An operable arrangement of the inverse-filter as claimed in Claims 1 or 2 wherein the high-pass inverse-filter build up the missing high-pass spectral data.

5. An operable arrangement of the inverse-filter as claimed in Claims 1 or 2 wherein the band-pass inverse-filter build up the missing band-pass spectral data.

6. An operable arrangement of the inverse-filter as claimed in Claims 1 to 5 wherein the low-,band-, or high-pass inversefilter build up the related missing spectral data.

7. An operable arrangement of the inverse-filter as claimed in Claims 1 to 6 including an indicator, which indicator is arranged, in use, to provide an indication of the inversefilter of the spectral signals.

8. An operable arrangement of the inverse-filter as claimed in Claim 7 wherein the indicator comprises signals input and output means.

9. An operable arrangement of the inverse-filter as claimed in Claims 7 or 8 wherein the signal output means includes means to increase the induced signal to noise ratio, filter unwanted signals, and separate any feedback signal from the processed signals.

10. An operable arrangement of the inverse-filter as claimed in any preceding claim wherein the white-noise-level, generated by the apparatus means, processed or added to the input spectra undergoing analysis for the inverse-filter to build up the missing data.

11. An operable arrangement as claimed in any'preceding claim, wherein the manually operating criteria are also remote controllable by a computerised system or operable arrangement.

12. An operable arrangement as claimed in any preceding claim, wherein the criteria carried out for a single channel are also carried out for every channel of a multi channel operable arrangement.

13. An operable arrangement as claimed in any preceding claim including providing a non volatile memory as well as an additional storage memory.

14. A method of the inverse-filter comprising rigidising mathematical modelling for computerised in service conditions using standard mathematical techniques for processing the required spectra; and/or adding the white-noise-level to the processed spectra; characterising the inverse-filter of the required spectra; determining the build up of the missing spectra ; and determining the physical characteristics of the material which absorb the missing spectra based on the type and magnitude of the missing frequencies.

15. A method of the inverse-filter as claimed in claim 14 providing rigidising mathematical modelling for computerised in-service conditions using standard mathematical techniques for processing and build up of the required spectra.

16. A method of the inverse-filter as claimed in claims 14 to 15 providing white-noise-level arranged, in use, to be processed or added to the input spectra undergoing analysis for an inverse-filter to build up the missing data.

17. A method as claimed in claims 14 to 16, including varying the frequency of the input white-noise-level over pre-selected frequency range and determining the missing spectra.

18. A method as claimed in any preceding claim, wherein the velocity, (wavelength * frequency), of the output signal is maintained equivalent to the velocity of the input signal.

19. A method as claimed in any preceding claim, wherein the the attenuation coefficient (per unit time or frequency, as a function of the frequency), of the output signal is maintained equivalent to the attenuation coefficient of the input signal.

20. A method as claimed in any preceding claim, wherein the required attenuations due to scattering and diffraction, and the velocity dispersion are provided as options taking into account for the processed signals.

21. A method as claimed in any preceding claim, wherein Fourier analyses are provided once and/or twice, Cepstrum, for the input and/or output signals or their windows.

22. A method as claimed in Claims 14 to 21 comprising interpreting input and/or output signals from an indicator means.

23. A method as claimed in Claims 14 to 22 comprising techniques of obtaining the analog and/or digital input signals or techniques of operating or energising the inverse-filter.

24. A method as claimed in Claims 14 to 23 comprising a modular construction of the electronics or electronic design.

25. A method as claimed in any preceding claim in which rigidising the electronics for severe in-service conditions comprising using standard techniques.

26. A method of operating inverse-filter substantially as herein described with reference to, and as shown in the accompanying representations.

27. Apparatus as claimed in any of Claims 1 to 13 when used in a method as claimed in any of Claims 14 to 26.

28. A method as claimed in any of claims 14 to 27 when using an arrangement as claimed in any of claims 1 to 13.

Amendments to the claims have been filed as follows 1. An operable arrangement of the inverse-filter, said apparatus, comprising computerised responsive means for the input electronic signals; means for generating white-noise-level; means providing Central Processing Unit to build up of the missing spectra comprises signal conditioning amplifiers, ADC converter,microprocessor,RAM,serial and parallel ports; means responsive for indicating the output electronic signals; characterising the 3D inverse-filter of the required spectra; and operated when enersised to be acted on by the input electronic signals to characterise the 3D inverse-filter of the required spectra; determining the build up of the missing frequencies and to determine the physical characteristics of the material which absorb the missing spectra based on the type and magnitude of the missing spectra.

2. An operable arrangement of the inverse-filter as claimed in claim 1 when the inverse-filter is operated, it is able to determine the build up of three dimensions of the missing frequencies and to determine three dimensions of the physical characteristics of the material which absorb the missing spectra.

4. An operable arrangement of the invrse-filter as claimed in Claims 1 or 2 wherein the high-pass inverse-filter build up the missing high-pass spectral data.

11. An operable arrangement as claimed in any preceding claim, wherein the manually operating criteria are also remote controllable by a computerised system or operable arrangement.

16. A method of the inverse-filter as claimed in claims 14 to 15 providing white-noise-level arranged, in use, to be processed or added to the input spectra undergoing analysis for an -inverse-filter to build up the missing data.

18. A method as claimed in any preceding claim, wherein the velocity, (wavelength * frequency), of the output signal is maintained equivalent-to the velocity of the input signal.