CA1051099A - Method and apparatus for the determination of start time difference and overall phase shift between two signals - Google Patents
Method and apparatus for the determination of start time difference and overall phase shift between two signalsInfo
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- CA1051099A CA1051099A CA250,827A CA250827A CA1051099A CA 1051099 A CA1051099 A CA 1051099A CA 250827 A CA250827 A CA 250827A CA 1051099 A CA1051099 A CA 1051099A
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- signals
- phase shift
- signal
- residual phase
- slope
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-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/02—Generating seismic energy
- G01V1/04—Details
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- Life Sciences & Earth Sciences (AREA)
- Acoustics & Sound (AREA)
- Environmental & Geological Engineering (AREA)
- Geology (AREA)
- General Life Sciences & Earth Sciences (AREA)
- General Physics & Mathematics (AREA)
- Geophysics (AREA)
- Geophysics And Detection Of Objects (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
- Investigating Or Analyzing Materials By The Use Of Magnetic Means (AREA)
Abstract
METHOD AND APPARATUS FOR THE DETERMINATION
OF START TIME DIFFERENCE AND OVERALL PHASE
SHIFT BETWEEN TWO SIGNALS
(D#71,200-DTA117 -F') ABSTRACT OF THE DISCLOSURE
Apparatus and method determines the time shift and total phase difference between two alternating current signals. A value ?(f) corresponding to the phase relation-ship between the two signals is determined for each fre-quency f contained in the two signals. A slope A and an ordinate section D of the best fitting straight line g(f)=Af + B through the totality of the values ? (f) so obtained is determined. The phase shift ? o=B modulo (2.pi.) is determined from the ordinate section B and the time shift ?; = A/2.pi. from the slope A.
I
OF START TIME DIFFERENCE AND OVERALL PHASE
SHIFT BETWEEN TWO SIGNALS
(D#71,200-DTA117 -F') ABSTRACT OF THE DISCLOSURE
Apparatus and method determines the time shift and total phase difference between two alternating current signals. A value ?(f) corresponding to the phase relation-ship between the two signals is determined for each fre-quency f contained in the two signals. A slope A and an ordinate section D of the best fitting straight line g(f)=Af + B through the totality of the values ? (f) so obtained is determined. The phase shift ? o=B modulo (2.pi.) is determined from the ordinate section B and the time shift ?; = A/2.pi. from the slope A.
I
Description
~Sl~g~
BACKGROUND OF TH~ LNVENTION
Field of the Invention The present invention relates to the determination of relationships between two alternating current signals, and, more particularly, to the phase shift and time shift relationship between the two sigrlals.
STATEMENT OF THE INVENTION
Apparatus and method determines the time shift~and total phase difference between two AC signals. A value ~ ~-(f), representative of the phase relationship between the ~;~
two signals, is determinèd for each f~equency f contained in ~;
the two signals; g signals, corresponding to the ~ values, are provided in accordance with the determination and corr-esponding f signals. A slope A and an ordinate intercept B
of a best-itting straight line gt) = Af~B through the ` `
totality of the values ~ are determined in accordance with ~ :;
the g and f signals and a slope signal and an intercept signal are provided accordingly. A signal T, corresponding to the time shift, is provided in accordance wLth the slope signal and the equation T - A/2~r . A~signal ~, corres-~ ; ,.
ponding to the total phase shift, in accordance with the `~`
intercept signal and the equation ~ o = B modulo(27r~. ;
The objects and advantages of the invention willappear more fully hereinafter ~rom a consideration of the detailed description which follows, taken together with the accompanying drawings wherein one embodiment of the in-vention is illustrated by way of example. It is to be expressly understood, however, that the drawings are for illustrative purposes only and are not to be construed as ~ ;
:
defining the limits of the invention. ;~ -: ~ .
- , . - ,., , : . ...
~ [) 5109 ~ !
DESCRIPTION OF THE DRAWINGS
Figure 1 is a simplifled block diagram of appara-tus, constructed in accordance with the present invention, ~:
for the determination of the phase shift and the time shift between two signals.
;~, .
' , ' ' ~ ' ''' la ~L~S~g ~
Figures 2 and 3 are graphical representations of waveforms occurring during the op~ation of the apparatus of Figure 1.
DESCRIPTION OF THE INVEN~ION
The inventlon relates to a method and apparatus for the determinatlon of start time difference and overall phase shift between two signals. It is particularly, but not exclusively, intended for testing of the similarity of vibrators for the generation of seismic signals. Such vibrators are, ~or example, employed in the seismic method ~
known under the name "Vibroseis"~ In this exploration ;
method signals of several seconds length, essentially constant amplitude and within a certain frequency range -. . .
monotonously increasing or decreasing frequency are trans-mitted into the subsurface in form of elastic waves. A
portion of this signal is reflected from changes in the `
elastic parameters of the subsurface, which are frequently ~ `
.
~ related to boundaries of geological formations. These , ~ . . .
reflected signals are detected at the earth's surface by ~ ~-means of a plurality of geophones and recorded on magnetic tape in ~orm o~ a seismogram. Owing to their length, sig-nals reflected in different depths~ and therefore arriving at different times, overlap. In order to separate signals arriving at different times, and therefore reflected in ~ `
dlfferent depths, the long signals have to be compressed to short, impulse-like ones. Thls can 7 for example, be achieved by correlating the recorded seismogram with the ~ ;
seismic signal. Usually, three toseven synchronously operating vlbrators are employed in order to increase the a~ount of useful seismic energy transmitted into the sub-surface, In this connection, the term synchronous means _2-~s~9~
that the motion of the base-plate of each vibrator has a fixed phase relation to a so-called pilot signal. This fixed phase relation between the motion of the base-plate of each vibrator and the pilot signal guarantees that the signals transmitted into the subsurface by all the vib-rators add up coherently. If the phase relationship bet-ween base~plate motion and pilot signal is determined in such a way that the phase of the emitted seismic signal is approximately equal to that of the pilot signal, this ~' latter signal rather than the (not recorded') seismic sig- ~
:
nal can be used for correlating the recorded seismogram. ' `
Therefore, a successful use of vibrators for the generation of the seismic signals requires not only in-.
phase operation of the vibrator~ but also that the motionof their respective base~plates has a fixed, pre-defined relation to the pilot signal.
This fixed phase relationship is provided by a phase lock circuit which detects the phase difference hetween base-plate motion~and pilot signal and which, ~20 ~ upon deviation from~the pre-set value~ actuates a phase shift network to correct, for this deviation. ' Usua].ly the motion Or the base-plate is recorded ' - by means of an accelerometer attached to the base-plate ' ~
structure. The output signal of the accelerometer is ~ ' heavily distorted by harmonics and must therefore be ' ' smoothed. This is usually done by two-fold integration '~
and subsequent amplitude compensation. Thls smoothing causes a slight ph~ase shift and delay of the accelero-meter signal, which, for the sake of comparison with the pilot sign'al~is compensated by passing the latter signal ~ ;
through filters providing the same phase shift. In a ' ~ , . ~ ,.: .: : ... .
9 : ~
particular phase lock circuit the filtered pilot signal is ~hase-shifted by 90Q prior to comparison with the smoothed base~plate signal.
In vie~ of the importance o~ phase control for the generation of strong seismic signals~ and, ~or the ~ ;
successful contraction of the lon~ reflected signals in the seismogram, similarity tests of the vibrators are per-formed at regular intervals. In these tests proper func-tio~ing o~ the phase detection circuit~ the phase shift network and the accelerometer is checked.
A standard procedure for checking the phase lock ;~
circuit is to record the two signals applied to the cir-cuit, i.e. the smoothed base~plate accelerometer signal ;
and the filtered pilot signal, and to inspect play-backs -of the recordings for indications of phase shifts and start time differences. Start time differences in the order of milliseconds and phase shifts of a few degrees ~ ~
;are, however, difficult ~o detect on usual play-backs. It `
ls~particularly~difficult if there exists a specified phase difference of 90 between the two signals. In this case, a sufficiently~accurate optical similarity control ; as described above can hard:Ly be performed.
In principle~ Lissa~ous pattern.s could be used for determination of the phase relation between the two signals. But due to harmonics still present in the smoothed accelerom~ter signal no regular stable ellipse (with circle and straight~line as extreme cases) appears, but rather a distorted bean-l~ike figure which furthermore changes its posltion in~case there is a signific~nt time shift between the two signals. -: ' ~' _4_ ~
~S~ 9 The accelerometer and the electronlc circuits passed by the accelerometer signal on its way to the phase ~
lock circuit can best be checked by means of an independent ;
measurement of the base-plate motion, e.g. by means of a second test accelerometer attached to the base plate struc-ture close to the first accelerometer (in the following termed system accelerometer). Of course the output signal of this test accelerometer is to a large degree dlstorted by harmonics and, in general~ not fit for a comparison of the signals supplied to the phase lock system. It has to be smoothed as well. Upon comparison of play-backs of the ~;~
two smoothed accelerometer signals the problem recurs that ~;
time and phase shifks are dif~icult to detect with su~fi cient accuracy.
The advantages are also inherent in the method and apparatus ~or control of vibrators as described by Landrum ;;
(U.S.Patent No. 3,863,202). In his method play-backs of traces have to be lnspected for phase shifts and start time differences as well.
The sub~ect of this invention is there~ore a method and apparatus ~or automatic determination and digital ;~ `
display of start time difference and phase shift between two signals. This method can furthermore be used to dis-play the oscillations of the phase of one of the signals .
about the phase of the other signal after accounting for start time dlfference and overall phase shift (in the ~ollowing the term residual phase shift is used for these oscillations). It is thus possible to display in form of a curve how, after accoùnting for start time difference and overall phase shift, the phase of the one signal leads the phase of the other signal at certain frequencies and lags it at other frequencies.
; 5 The essential advantage of this method as com-pared with the tedious comparison of traces as presently required in vibrator similarity tests is that two clearly defined numeric values for start time difference and over~
all phase shift are obtained and that the oscillation of -~
the phase of the one signal about the phase of the other signal - after accounting for start time difference and ;
,~
overall phase shift can be represented as a function o~ ~ ~
the frequency. . -Further advantages will be evident from the ~
: , .
following description.
The method underlyin~ this invention essentially `
consists of the following 5 steps:
In the first step a value ~(f) characterizing the phase relat~on between the two signals is determined ;
for each frequency f contained in the two signals.
In the second step slope A and ordinate section B are determined o~ the best (l~ast square) straight line g(f) = Af + B passing through the values ~(f), characteri zing the phase relation between the two si~nals as deter- ;
mined in the first step.
.
In the third step the start time difference between the two signals and the overall phase difference are determined according to the formulae (1) T = A/(27~: )
BACKGROUND OF TH~ LNVENTION
Field of the Invention The present invention relates to the determination of relationships between two alternating current signals, and, more particularly, to the phase shift and time shift relationship between the two sigrlals.
STATEMENT OF THE INVENTION
Apparatus and method determines the time shift~and total phase difference between two AC signals. A value ~ ~-(f), representative of the phase relationship between the ~;~
two signals, is determinèd for each f~equency f contained in ~;
the two signals; g signals, corresponding to the ~ values, are provided in accordance with the determination and corr-esponding f signals. A slope A and an ordinate intercept B
of a best-itting straight line gt) = Af~B through the ` `
totality of the values ~ are determined in accordance with ~ :;
the g and f signals and a slope signal and an intercept signal are provided accordingly. A signal T, corresponding to the time shift, is provided in accordance wLth the slope signal and the equation T - A/2~r . A~signal ~, corres-~ ; ,.
ponding to the total phase shift, in accordance with the `~`
intercept signal and the equation ~ o = B modulo(27r~. ;
The objects and advantages of the invention willappear more fully hereinafter ~rom a consideration of the detailed description which follows, taken together with the accompanying drawings wherein one embodiment of the in-vention is illustrated by way of example. It is to be expressly understood, however, that the drawings are for illustrative purposes only and are not to be construed as ~ ;
:
defining the limits of the invention. ;~ -: ~ .
- , . - ,., , : . ...
~ [) 5109 ~ !
DESCRIPTION OF THE DRAWINGS
Figure 1 is a simplifled block diagram of appara-tus, constructed in accordance with the present invention, ~:
for the determination of the phase shift and the time shift between two signals.
;~, .
' , ' ' ~ ' ''' la ~L~S~g ~
Figures 2 and 3 are graphical representations of waveforms occurring during the op~ation of the apparatus of Figure 1.
DESCRIPTION OF THE INVEN~ION
The inventlon relates to a method and apparatus for the determinatlon of start time difference and overall phase shift between two signals. It is particularly, but not exclusively, intended for testing of the similarity of vibrators for the generation of seismic signals. Such vibrators are, ~or example, employed in the seismic method ~
known under the name "Vibroseis"~ In this exploration ;
method signals of several seconds length, essentially constant amplitude and within a certain frequency range -. . .
monotonously increasing or decreasing frequency are trans-mitted into the subsurface in form of elastic waves. A
portion of this signal is reflected from changes in the `
elastic parameters of the subsurface, which are frequently ~ `
.
~ related to boundaries of geological formations. These , ~ . . .
reflected signals are detected at the earth's surface by ~ ~-means of a plurality of geophones and recorded on magnetic tape in ~orm o~ a seismogram. Owing to their length, sig-nals reflected in different depths~ and therefore arriving at different times, overlap. In order to separate signals arriving at different times, and therefore reflected in ~ `
dlfferent depths, the long signals have to be compressed to short, impulse-like ones. Thls can 7 for example, be achieved by correlating the recorded seismogram with the ~ ;
seismic signal. Usually, three toseven synchronously operating vlbrators are employed in order to increase the a~ount of useful seismic energy transmitted into the sub-surface, In this connection, the term synchronous means _2-~s~9~
that the motion of the base-plate of each vibrator has a fixed phase relation to a so-called pilot signal. This fixed phase relation between the motion of the base-plate of each vibrator and the pilot signal guarantees that the signals transmitted into the subsurface by all the vib-rators add up coherently. If the phase relationship bet-ween base~plate motion and pilot signal is determined in such a way that the phase of the emitted seismic signal is approximately equal to that of the pilot signal, this ~' latter signal rather than the (not recorded') seismic sig- ~
:
nal can be used for correlating the recorded seismogram. ' `
Therefore, a successful use of vibrators for the generation of the seismic signals requires not only in-.
phase operation of the vibrator~ but also that the motionof their respective base~plates has a fixed, pre-defined relation to the pilot signal.
This fixed phase relationship is provided by a phase lock circuit which detects the phase difference hetween base-plate motion~and pilot signal and which, ~20 ~ upon deviation from~the pre-set value~ actuates a phase shift network to correct, for this deviation. ' Usua].ly the motion Or the base-plate is recorded ' - by means of an accelerometer attached to the base-plate ' ~
structure. The output signal of the accelerometer is ~ ' heavily distorted by harmonics and must therefore be ' ' smoothed. This is usually done by two-fold integration '~
and subsequent amplitude compensation. Thls smoothing causes a slight ph~ase shift and delay of the accelero-meter signal, which, for the sake of comparison with the pilot sign'al~is compensated by passing the latter signal ~ ;
through filters providing the same phase shift. In a ' ~ , . ~ ,.: .: : ... .
9 : ~
particular phase lock circuit the filtered pilot signal is ~hase-shifted by 90Q prior to comparison with the smoothed base~plate signal.
In vie~ of the importance o~ phase control for the generation of strong seismic signals~ and, ~or the ~ ;
successful contraction of the lon~ reflected signals in the seismogram, similarity tests of the vibrators are per-formed at regular intervals. In these tests proper func-tio~ing o~ the phase detection circuit~ the phase shift network and the accelerometer is checked.
A standard procedure for checking the phase lock ;~
circuit is to record the two signals applied to the cir-cuit, i.e. the smoothed base~plate accelerometer signal ;
and the filtered pilot signal, and to inspect play-backs -of the recordings for indications of phase shifts and start time differences. Start time differences in the order of milliseconds and phase shifts of a few degrees ~ ~
;are, however, difficult ~o detect on usual play-backs. It `
ls~particularly~difficult if there exists a specified phase difference of 90 between the two signals. In this case, a sufficiently~accurate optical similarity control ; as described above can hard:Ly be performed.
In principle~ Lissa~ous pattern.s could be used for determination of the phase relation between the two signals. But due to harmonics still present in the smoothed accelerom~ter signal no regular stable ellipse (with circle and straight~line as extreme cases) appears, but rather a distorted bean-l~ike figure which furthermore changes its posltion in~case there is a signific~nt time shift between the two signals. -: ' ~' _4_ ~
~S~ 9 The accelerometer and the electronlc circuits passed by the accelerometer signal on its way to the phase ~
lock circuit can best be checked by means of an independent ;
measurement of the base-plate motion, e.g. by means of a second test accelerometer attached to the base plate struc-ture close to the first accelerometer (in the following termed system accelerometer). Of course the output signal of this test accelerometer is to a large degree dlstorted by harmonics and, in general~ not fit for a comparison of the signals supplied to the phase lock system. It has to be smoothed as well. Upon comparison of play-backs of the ~;~
two smoothed accelerometer signals the problem recurs that ~;
time and phase shifks are dif~icult to detect with su~fi cient accuracy.
The advantages are also inherent in the method and apparatus ~or control of vibrators as described by Landrum ;;
(U.S.Patent No. 3,863,202). In his method play-backs of traces have to be lnspected for phase shifts and start time differences as well.
The sub~ect of this invention is there~ore a method and apparatus ~or automatic determination and digital ;~ `
display of start time difference and phase shift between two signals. This method can furthermore be used to dis-play the oscillations of the phase of one of the signals .
about the phase of the other signal after accounting for start time dlfference and overall phase shift (in the ~ollowing the term residual phase shift is used for these oscillations). It is thus possible to display in form of a curve how, after accoùnting for start time difference and overall phase shift, the phase of the one signal leads the phase of the other signal at certain frequencies and lags it at other frequencies.
; 5 The essential advantage of this method as com-pared with the tedious comparison of traces as presently required in vibrator similarity tests is that two clearly defined numeric values for start time difference and over~
all phase shift are obtained and that the oscillation of -~
the phase of the one signal about the phase of the other signal - after accounting for start time difference and ;
,~
overall phase shift can be represented as a function o~ ~ ~
the frequency. . -Further advantages will be evident from the ~
: , .
following description.
The method underlyin~ this invention essentially `
consists of the following 5 steps:
In the first step a value ~(f) characterizing the phase relat~on between the two signals is determined ;
for each frequency f contained in the two signals.
In the second step slope A and ordinate section B are determined o~ the best (l~ast square) straight line g(f) = Af + B passing through the values ~(f), characteri zing the phase relation between the two si~nals as deter- ;
mined in the first step.
.
In the third step the start time difference between the two signals and the overall phase difference are determined according to the formulae (1) T = A/(27~: )
(2) ~O ~ . B modulo (2~r) The abbreviation modulo 2~ is understood to mean that a multiple Or 2~r is to be added to B or to be sub-, tracted from B so that the value of ~O is 'ess than or equal to 7r and greater than or equal to (- ~ c ~ c -6_ ~:~ ' .. .. - . - . . .
``
~ ~5 In the fourth step the residual phase shift
``
~ ~5 In the fourth step the residual phase shift
(3) ~(f) = ~ (f) _ g(f) is determined. Thls residual phase shift indicates which further phase differences exist at the different frequen~
cies within the frequency range of the two signals after accounting for possible differences in start time and for an overall phase shift.
Finall,y, in a fifth step a numeric value can be .
determined which is representati~e o~ the amount of this residual phase shift, The values ~ (f3 characterizing the phase re-lation between the two signals as described in the ~irst step can be determined'in various ways.
The easiest way is to sub~ect the two signals to be compared to a Fourier transformation and to multiPly the ~ourier transform of the one signal with the complex con~
,~ugate of the Fourier transform of the other signal. ~- ;
Real and imaginary part of this product are usually de-noted by cospectrum and quadraturspectrum, respectively.
The arcustan~ent of the quotient of quadraturspectrum and cospectrum gives the desired values ~ (f) characterlzin~ `' the phase relation between the two signals at the frequency f. Equivalent values of ~(f) can also be obtained in a different way.
One can, for example, first correlate~the two signals which are to be compared and sub~ect the resulting correlation functlon to a Fourier transformation. The ;
real and imaginary part of the Fourier transform so ob-tained correspond to cospectrum and quadraturspectrum, respectivel~.
~ .
.:
~L~Sl~
A third approach to the values y(f) is to sub~ect ~ -bcth slgnals to a Fourier transformation, the difference of`
the phase spectra of the two signals is equal to ~(f) ~
possibly up to a multiple of 2 ~ due to the fact that the arcus tangent is a multivalued function.~
The principle underlying the method can be charac-: ,. :, . . .
terized as follows.
Let so(t) and sl(t) be two signals which should be compared and let So(f) and Sl(f) denote their respective Fourier transforms'(frequency spectra). These complex fre-qu~ency spectra can be represented in form of amplitude spectrum M(f) and phase spectrum ~ (f~
So(f) ~ Mo(f)eXp~i~O(f) ) ' '~ Sl(f) Y Ml(f)exP(i~ l(f) j A law well known in the theory of Four~er trans-formatlons states that the Fourier transform of two - apart from a time shift (e.g. start time difference) - identical signals.
cies within the frequency range of the two signals after accounting for possible differences in start time and for an overall phase shift.
Finall,y, in a fifth step a numeric value can be .
determined which is representati~e o~ the amount of this residual phase shift, The values ~ (f3 characterizing the phase re-lation between the two signals as described in the ~irst step can be determined'in various ways.
The easiest way is to sub~ect the two signals to be compared to a Fourier transformation and to multiPly the ~ourier transform of the one signal with the complex con~
,~ugate of the Fourier transform of the other signal. ~- ;
Real and imaginary part of this product are usually de-noted by cospectrum and quadraturspectrum, respectively.
The arcustan~ent of the quotient of quadraturspectrum and cospectrum gives the desired values ~ (f) characterlzin~ `' the phase relation between the two signals at the frequency f. Equivalent values of ~(f) can also be obtained in a different way.
One can, for example, first correlate~the two signals which are to be compared and sub~ect the resulting correlation functlon to a Fourier transformation. The ;
real and imaginary part of the Fourier transform so ob-tained correspond to cospectrum and quadraturspectrum, respectivel~.
~ .
.:
~L~Sl~
A third approach to the values y(f) is to sub~ect ~ -bcth slgnals to a Fourier transformation, the difference of`
the phase spectra of the two signals is equal to ~(f) ~
possibly up to a multiple of 2 ~ due to the fact that the arcus tangent is a multivalued function.~
The principle underlying the method can be charac-: ,. :, . . .
terized as follows.
Let so(t) and sl(t) be two signals which should be compared and let So(f) and Sl(f) denote their respective Fourier transforms'(frequency spectra). These complex fre-qu~ency spectra can be represented in form of amplitude spectrum M(f) and phase spectrum ~ (f~
So(f) ~ Mo(f)eXp~i~O(f) ) ' '~ Sl(f) Y Ml(f)exP(i~ l(f) j A law well known in the theory of Four~er trans-formatlons states that the Fourier transform of two - apart from a time shift (e.g. start time difference) - identical signals.
(4) sOtt~) and s}(t) = sO(t- ~
~o di~fer by the factor exp(~r~if (). This means that the difference (5j ~l(f)-~O(f) = 2~
of the phase spectra of the two signals as function of the frequency is a straight line through the origin with the ,slope of the straight line equal to the 2~-fold of the time shift between the two signals. On the other hand, the ourier transform of two signals of the general form ~: (6? so(tj =~cos( ~(t))~ and sltt)~= cos( ~ (t)+ ~o) i~ ;
differ only by the constant factor exp(i~O) for all fre~
quency above a lower frequency limit which depends on ~(t). For the signals considered here this lower .
9 - ~
frequency limit is as low as a few hertz. Therefore (7) ~l(f)-~o(f)= ~o The function ~(t) appearing in the argument of the cosine in equation (6) denotes an arbitrary, monotonously increa- :
sing or decreasing function of ~i.ne. For the moæt frequently used Vibroseis signal (known under the name "linear sweep" ;
to those experienced in the art)~ ~(t) has the form ~ (t) - 2/rCfot+(fl-fo)t2/(12T)J for O~t~
where fO, fl and T denote lower and upper frequency limits and length of the sweep, respective,ly.
A combination of the relation between equations (4) and (5) and between equations (6) and (7) shows that the phase spectra of the two signals (8) so(t) = cos(~ (t)), sl(t) = cos( ~(t-~+ ~o) ; are related to each other by (9) ~(f) = ~1(t)-~o(t)~= 2 ~rf+ ~O
As indicated in equation (9) the difference of the :: .
phase spectra of the two signals is the function ~'(f) de- ;
termined in the first step of the method which characterizes the phase relation of the two signals as function of the frequency Thls function~can be obtained as the phase, i.e.
the arcustangent of the quotient of imaginary and real part of the product ~
(10) Sl(f) S*(f) = Ml(f)Mo(f)exp(i[~l(f)-~o(f)]) ~- -Because of e~uation (9) the straight line fitted - e.g. in the least s~uares se~se - through the difference of ~he phase spectra of the two signals has a slope equal to the 2 ~ -fold of the start tlme difference ~ . It furthermore has, for the frequency f=0~ an ordinate section which is equal to the phase difference ~O~ Since the arcustangent is a multivalued function, the value ~O so obtained is onIy _9_ ~5~99 ~ :
~ . .
determined modulo 2~
In real cases the difference ~ Cf) i.s not exactly a stra~ght line. As an indicator or index of the amount of `~ :
residual phase shift y (.f~-g(f~ its variance or a monotonous function (.e.g. square root~ thereof may be used. Another indicator is, for example, the largest deviation of ~ Cf~
from the straight line g(f). A large value of this i.ndex . .
may give rise to the decision to have the resi:dual phase :~ .
shift displayed as function of the frequency, for example ~.
in the form of a curve on an oscillograph.
Figure 1 shows the block diagram of an implemen-tation of the method together with a possible application. :
Both Figures 2 and 3 show two Vibroseis signals recorded in a Vibroseis similarity test as well as the residual phase shift remaining after start time difference and overall :
phase shift between the two signals have been accounted for. ~ :
Figure 1 shows how the present invention is re- ~
. .
lated to already existing vibrator systems.
The Vibroseis signal generator 1 which may also . .
be a receiver of a signal transmitted from the recording ~.
truck, supplies the Vibroseis signal via the phase shift network 2 to the vibrator control means 3 of the vibrator means 4. The Vibroseis signal and the output signal of a transducer 6 attached to the base-plate 8 are supplied to :
a phase detector 5. If a deviation is detected from the ~:
specified phase relation between the filtered pilot signal and the smoothed base-plate transducer signal an error signal is transmitted to the phase shift network 2 which shl:fts the phase of the signal. controlling th.e vibration .
in such a way that the desired phase relati.onsh.ip is reestabIish.ed.
9 ~ ~
The signals ~rom the output of the vibrator elec-tronic denoted by the numerals 9-11 and the signals from the output 12 Or the test accelerometer 7 are particularly, but not exclusively, suited to check the electronic and mechanical parts of the vibrators. Any two of these out- ;puts may be connected to the two inputs 13 and 14 of the apparatus denoted by the numerals 13-26 which is an example of an implementation of the before-described invention.
These two inputs lead to an analog/digital converter and multiplexer 15. ~he multiplexed data is supplied to a Fourier transform unit 16. Typical systems available on the market are based on the fast Fourier transform (F~T) and can perform the Fourier trans~orm of two signals in real time. The first step of the method is completed in the subsequent multiplier 17 in which the Fourier transform o~ the one signal is multiplied with the complex conJugate of the Fourier transform of the other signal and in which ;~the phase spectrum Y (f) of this product is determined. A ;
slope and intercept computer 18 serves for the determina-tion of the coefficients A and B of the best straight line g(f) = Af + B
passing through the values ~ (f). If desired, the start `
time difference ~ and the overall phase difference ~ O
may be determined and displayed, e.g. by light-emitting diodes 20 which are connected to the circuit 18 by means ; ;~of the switch 19. In addition, or alternatively, the residual phase shi~t may be determined by means of a -residual phase shift computer 24 which is connected to the computer 18 by means of a switch 21. Integrating means 26 connected to computer 24 by means of sw-itch 25 is required for the determination of an index for the amount of lL05~0~9 residual phase shift. This index may be used as a criterion for the decision whether an analog display o~
the residual phase shift is required. For this purpose, ' ~
recording means 22 which performs this analog display is ~-connected to the circuit 24 by means of the switch 23.
Figure 2 shows two Vibroseis signals with fre-quency increasing linearly from 16-65 Hz which have been `
recorded during a similarity test. Because of their length they are displayed in two pieces. 'The signal denoted by R is the signal generated in the recording truck. This signal is transmitted to the vibrators by a radio and would ' '~
correspond to the signal from putput 9 in Figure 1. The second signal denoted with P is the smoothed pilot signal used for comparison with the smoothed accelerometer signal ;
and corresponds to the signal from output 10 in Figure 1.
An analysis by means of the method described before revealed ~-~
. ~.
that it is delayed by 139.2 msec with respect to the signal R and that an overall phase shift of ~7.g exists between the two signals. The largest portion, I28 msec, of this '' start time difference is due to a static delay within the vibrator electronics. The other 11.2 msec are due to the modulation/demodulation required for the radlo connection and the many filters additionally passed by the P signal.
The curve below the two Vibroseis signals is the residual phase shift remaining after the removal of the influence ~
of start time difference and overall phase shift between ~ ' ; the R and P~signal. `~
Figure 3 corresponds to Figure 2. Here the sig~
nal P is compared with 'the' acceleration of the base-plate - -recorded by means of a test acceleromet,er ~Signal B~. The large content of harmonics- in signal B manifests itself in ::
~ .
~o di~fer by the factor exp(~r~if (). This means that the difference (5j ~l(f)-~O(f) = 2~
of the phase spectra of the two signals as function of the frequency is a straight line through the origin with the ,slope of the straight line equal to the 2~-fold of the time shift between the two signals. On the other hand, the ourier transform of two signals of the general form ~: (6? so(tj =~cos( ~(t))~ and sltt)~= cos( ~ (t)+ ~o) i~ ;
differ only by the constant factor exp(i~O) for all fre~
quency above a lower frequency limit which depends on ~(t). For the signals considered here this lower .
9 - ~
frequency limit is as low as a few hertz. Therefore (7) ~l(f)-~o(f)= ~o The function ~(t) appearing in the argument of the cosine in equation (6) denotes an arbitrary, monotonously increa- :
sing or decreasing function of ~i.ne. For the moæt frequently used Vibroseis signal (known under the name "linear sweep" ;
to those experienced in the art)~ ~(t) has the form ~ (t) - 2/rCfot+(fl-fo)t2/(12T)J for O~t~
where fO, fl and T denote lower and upper frequency limits and length of the sweep, respective,ly.
A combination of the relation between equations (4) and (5) and between equations (6) and (7) shows that the phase spectra of the two signals (8) so(t) = cos(~ (t)), sl(t) = cos( ~(t-~+ ~o) ; are related to each other by (9) ~(f) = ~1(t)-~o(t)~= 2 ~rf+ ~O
As indicated in equation (9) the difference of the :: .
phase spectra of the two signals is the function ~'(f) de- ;
termined in the first step of the method which characterizes the phase relation of the two signals as function of the frequency Thls function~can be obtained as the phase, i.e.
the arcustangent of the quotient of imaginary and real part of the product ~
(10) Sl(f) S*(f) = Ml(f)Mo(f)exp(i[~l(f)-~o(f)]) ~- -Because of e~uation (9) the straight line fitted - e.g. in the least s~uares se~se - through the difference of ~he phase spectra of the two signals has a slope equal to the 2 ~ -fold of the start tlme difference ~ . It furthermore has, for the frequency f=0~ an ordinate section which is equal to the phase difference ~O~ Since the arcustangent is a multivalued function, the value ~O so obtained is onIy _9_ ~5~99 ~ :
~ . .
determined modulo 2~
In real cases the difference ~ Cf) i.s not exactly a stra~ght line. As an indicator or index of the amount of `~ :
residual phase shift y (.f~-g(f~ its variance or a monotonous function (.e.g. square root~ thereof may be used. Another indicator is, for example, the largest deviation of ~ Cf~
from the straight line g(f). A large value of this i.ndex . .
may give rise to the decision to have the resi:dual phase :~ .
shift displayed as function of the frequency, for example ~.
in the form of a curve on an oscillograph.
Figure 1 shows the block diagram of an implemen-tation of the method together with a possible application. :
Both Figures 2 and 3 show two Vibroseis signals recorded in a Vibroseis similarity test as well as the residual phase shift remaining after start time difference and overall :
phase shift between the two signals have been accounted for. ~ :
Figure 1 shows how the present invention is re- ~
. .
lated to already existing vibrator systems.
The Vibroseis signal generator 1 which may also . .
be a receiver of a signal transmitted from the recording ~.
truck, supplies the Vibroseis signal via the phase shift network 2 to the vibrator control means 3 of the vibrator means 4. The Vibroseis signal and the output signal of a transducer 6 attached to the base-plate 8 are supplied to :
a phase detector 5. If a deviation is detected from the ~:
specified phase relation between the filtered pilot signal and the smoothed base-plate transducer signal an error signal is transmitted to the phase shift network 2 which shl:fts the phase of the signal. controlling th.e vibration .
in such a way that the desired phase relati.onsh.ip is reestabIish.ed.
9 ~ ~
The signals ~rom the output of the vibrator elec-tronic denoted by the numerals 9-11 and the signals from the output 12 Or the test accelerometer 7 are particularly, but not exclusively, suited to check the electronic and mechanical parts of the vibrators. Any two of these out- ;puts may be connected to the two inputs 13 and 14 of the apparatus denoted by the numerals 13-26 which is an example of an implementation of the before-described invention.
These two inputs lead to an analog/digital converter and multiplexer 15. ~he multiplexed data is supplied to a Fourier transform unit 16. Typical systems available on the market are based on the fast Fourier transform (F~T) and can perform the Fourier trans~orm of two signals in real time. The first step of the method is completed in the subsequent multiplier 17 in which the Fourier transform o~ the one signal is multiplied with the complex conJugate of the Fourier transform of the other signal and in which ;~the phase spectrum Y (f) of this product is determined. A ;
slope and intercept computer 18 serves for the determina-tion of the coefficients A and B of the best straight line g(f) = Af + B
passing through the values ~ (f). If desired, the start `
time difference ~ and the overall phase difference ~ O
may be determined and displayed, e.g. by light-emitting diodes 20 which are connected to the circuit 18 by means ; ;~of the switch 19. In addition, or alternatively, the residual phase shi~t may be determined by means of a -residual phase shift computer 24 which is connected to the computer 18 by means of a switch 21. Integrating means 26 connected to computer 24 by means of sw-itch 25 is required for the determination of an index for the amount of lL05~0~9 residual phase shift. This index may be used as a criterion for the decision whether an analog display o~
the residual phase shift is required. For this purpose, ' ~
recording means 22 which performs this analog display is ~-connected to the circuit 24 by means of the switch 23.
Figure 2 shows two Vibroseis signals with fre-quency increasing linearly from 16-65 Hz which have been `
recorded during a similarity test. Because of their length they are displayed in two pieces. 'The signal denoted by R is the signal generated in the recording truck. This signal is transmitted to the vibrators by a radio and would ' '~
correspond to the signal from putput 9 in Figure 1. The second signal denoted with P is the smoothed pilot signal used for comparison with the smoothed accelerometer signal ;
and corresponds to the signal from output 10 in Figure 1.
An analysis by means of the method described before revealed ~-~
. ~.
that it is delayed by 139.2 msec with respect to the signal R and that an overall phase shift of ~7.g exists between the two signals. The largest portion, I28 msec, of this '' start time difference is due to a static delay within the vibrator electronics. The other 11.2 msec are due to the modulation/demodulation required for the radlo connection and the many filters additionally passed by the P signal.
The curve below the two Vibroseis signals is the residual phase shift remaining after the removal of the influence ~
of start time difference and overall phase shift between ~ ' ; the R and P~signal. `~
Figure 3 corresponds to Figure 2. Here the sig~
nal P is compared with 'the' acceleration of the base-plate - -recorded by means of a test acceleromet,er ~Signal B~. The large content of harmonics- in signal B manifests itself in ::
~ .
5~
the rapid oscillations of the residual phase shift. : : Values of the residual phase shift beyond +30 have been clipped in this representation.
~: , , , ". . . .
. .:
.':~. ' ":
.
~ ''" " ' : ,~
13- :
- ?
the rapid oscillations of the residual phase shift. : : Values of the residual phase shift beyond +30 have been clipped in this representation.
~: , , , ". . . .
. .:
.':~. ' ":
.
~ ''" " ' : ,~
13- :
- ?
Claims (15)
1. A method for determining a time shift and a total phase difference between two signals, comprising the steps of a) determining a value ? (f), representative of the phase relationship between the two signals, for each frequency f contained in the two signals;
b) providing g signals, corresponding to the values, in accordance with the determination and corres-ponding f signals;
c) determining a slope A and an ordinate inter-cept B of a best-fitting straight line g(f) = Af+B through the totality of the values ? in accordance with the g and f signals;
d) providing a slope signal and an intercept signal corresponding to the slope A and the ordinate intercept B in accordance with the next previous step;
e) providing a signal ? corresponding to the time shift in accordance with the slope signal and the following equation:
? = A/2.pi. ; and f) providing a signal ?o corresponding to the total phase shift in accordance with the intercept signal and the following equation:
?o = B modulo (2.pi.).
b) providing g signals, corresponding to the values, in accordance with the determination and corres-ponding f signals;
c) determining a slope A and an ordinate inter-cept B of a best-fitting straight line g(f) = Af+B through the totality of the values ? in accordance with the g and f signals;
d) providing a slope signal and an intercept signal corresponding to the slope A and the ordinate intercept B in accordance with the next previous step;
e) providing a signal ? corresponding to the time shift in accordance with the slope signal and the following equation:
? = A/2.pi. ; and f) providing a signal ?o corresponding to the total phase shift in accordance with the intercept signal and the following equation:
?o = B modulo (2.pi.).
2. A method as described in Claim 1 wherein the values ? (f) giving the phase relationship between the two signals are equal to the arcustangent of the quotient of co-spectrum and quadrature spectrum of the two signals.
3. A method as described in Claim 1 wherein the values ? (f) giving the phase relationship between the two signals are equal to the difference of the phase spectra of the two signals, so that a multiple of 2.pi. is added to, or subtracted from, the difference of the two phase spectra until the thus modified difference varies from the differ-ence established at the preceding frequency by less than .pi..
4. A method as described in Claim 2, further comprising the step of determining a residual phase shift ? (f)-g(f), and representing the residual phase shift ana-logically in the form of a curve dependent on the frequency.
5. A method as described in Claim 4 wherein a characteristic value for the amount of residual phase shift within the frequency range of the two signals is determined and a corresponding digital output is provided.
6. A method as described in Claim 5 wherein the absolute magnitude of the greatest residual phase shift is determined as the characteristic value for the amount of residual phase shift between the two signals.
7. A method as described in Claim 5, further comprising the steps of determining the standard deviation of the residual phase shift as a characteristic value for the amount of residual phase shift, and providing a cor-responding digital output.
8. A method as described in Claim 3, further comprising the step of determining a residual phase shift ? (f)-g(f) and is represented analogically in the form of a curve dependent on the frequency.
9. A method as described in Claim 8 wherein a characteristic value, for the amount of residual phase shift Within the frequency range of the two signals is determined and a corresponding digital output is provided.
10. A method as described in Claim 9, wherein the absolute magnitude of the greatest residual phase shift is determined as the characteristic value for the amount of residual phase shift between the two signals.
11. A method as described in Claim 10, further comprising the steps of determining the standard deviation of the residual phase shift as a characteristic value for the amount of residual phase shift, and providing a cor-responding digital output.
12. Apparatus for determining the time shift T
and the total phase difference between two signals compris-ing phase difference means adapted to receive the two sig-nals for determining a value ? (f), representative of the phase relationship between the two signals, for each fre-quency f contained in the two signals, and providing cor-responding g signals, and their associated f signals, slope and intercept means connected to the phase difference means for determining a slope A and an ordinate intercept B of a best fitting straight line g(f) = Af+B through the totality of the values ? in accordance with the f and g signals and providing signals A and B corresponding to the slope A and the ordinate intercept B; time shift signal means connected to the slope and intercept means for providing an output corresponding to the time shift T in accordance with signal A and the following equation:
T = A/2.pi. ; and total phase shift signal means connected to the slope and intercept means for providing an output ?o corresponding to the total phase shift in accordance with signal B and the following equation:
?o = B modulo (2.pi.).
and the total phase difference between two signals compris-ing phase difference means adapted to receive the two sig-nals for determining a value ? (f), representative of the phase relationship between the two signals, for each fre-quency f contained in the two signals, and providing cor-responding g signals, and their associated f signals, slope and intercept means connected to the phase difference means for determining a slope A and an ordinate intercept B of a best fitting straight line g(f) = Af+B through the totality of the values ? in accordance with the f and g signals and providing signals A and B corresponding to the slope A and the ordinate intercept B; time shift signal means connected to the slope and intercept means for providing an output corresponding to the time shift T in accordance with signal A and the following equation:
T = A/2.pi. ; and total phase shift signal means connected to the slope and intercept means for providing an output ?o corresponding to the total phase shift in accordance with signal B and the following equation:
?o = B modulo (2.pi.).
13. Apparatus as described in Claim 12 further comprising means connected to the slope and intercept means for providing an output corresponding to a residual phase shift, which is the difference between points on the best fitted straight line and their corresponding ? values, in accordance with the g signals.
14. Apparatus as described in Claim 13 in which the residual phase shift output corresponds to the absolute value of the residual phase shift.
15. Apparatus as described in Claim 13 in which the residual phase shift output corresponds to the standard deviation of the residual phase shift.
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| DE19752543294 DE2543294C3 (en) | 1975-09-27 | 1975-09-27 | Method and device for checking the synchronism of several vibrators |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1051099A true CA1051099A (en) | 1979-03-20 |
Family
ID=5957687
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA250,827A Expired CA1051099A (en) | 1975-09-27 | 1976-04-22 | Method and apparatus for the determination of start time difference and overall phase shift between two signals |
Country Status (9)
| Country | Link |
|---|---|
| JP (1) | JPS5242166A (en) |
| AR (1) | AR221815A1 (en) |
| CA (1) | CA1051099A (en) |
| CH (1) | CH621198A5 (en) |
| DE (1) | DE2543294C3 (en) |
| FR (1) | FR2325940A1 (en) |
| GB (1) | GB1548656A (en) |
| IT (1) | IT1058701B (en) |
| NL (1) | NL7603232A (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3029169C2 (en) * | 1980-08-01 | 1982-06-09 | Standard Elektrik Lorenz Ag, 7000 Stuttgart | Transmission device for a navigation system |
| JPS62278143A (en) * | 1986-05-26 | 1987-12-03 | Hoya Corp | Glass for ultrasonic delay line |
| DE19841154C2 (en) * | 1998-09-09 | 2002-11-07 | Holger Loehmer | Method and device for measuring the transit time of sound waves |
| CN106198079B (en) * | 2016-07-13 | 2019-03-26 | 广东工业大学 | A kind of rotary machinery fault diagnosis method based on margin index |
| CN114070433B (en) * | 2021-12-09 | 2023-05-09 | 中国电子科技集团公司第三十八研究所 | System and method for testing phase shift conversion time of multichannel transceiver component |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3875394A (en) * | 1973-04-20 | 1975-04-01 | Willis H Acting Admini Shapely | Correlation type phase detector |
| US3863202A (en) * | 1973-10-23 | 1975-01-28 | Amoco Prod Co | Earth vibrator tester |
| NL7504800A (en) * | 1974-04-24 | 1975-10-28 | Standard Oil Co | METHOD AND DEVICE FOR TESTING VIBRATORS FOR SEISMIC RESEARCH. |
-
1975
- 1975-09-27 DE DE19752543294 patent/DE2543294C3/en not_active Expired
-
1976
- 1976-03-16 CH CH322976A patent/CH621198A5/en not_active IP Right Cessation
- 1976-03-26 NL NL7603232A patent/NL7603232A/en not_active Application Discontinuation
- 1976-03-29 JP JP51035093A patent/JPS5242166A/en active Pending
- 1976-03-29 IT IT2169576A patent/IT1058701B/en active
- 1976-04-01 GB GB1323176A patent/GB1548656A/en not_active Expired
- 1976-04-09 FR FR7610597A patent/FR2325940A1/en active Granted
- 1976-04-09 AR AR26283376A patent/AR221815A1/en active
- 1976-04-22 CA CA250,827A patent/CA1051099A/en not_active Expired
Also Published As
| Publication number | Publication date |
|---|---|
| DE2543294A1 (en) | 1977-04-07 |
| GB1548656A (en) | 1979-07-18 |
| IT1058701B (en) | 1982-05-10 |
| FR2325940A1 (en) | 1977-04-22 |
| AR221815A1 (en) | 1981-03-31 |
| DE2543294B2 (en) | 1981-04-09 |
| DE2543294C3 (en) | 1981-11-12 |
| NL7603232A (en) | 1977-03-29 |
| FR2325940B1 (en) | 1982-10-08 |
| JPS5242166A (en) | 1977-04-01 |
| CH621198A5 (en) | 1981-01-15 |
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