DE1448725C - Arrangement for suppressing seismic reverberation components - Google Patents

Description

Y ₂ ...

Y ₁ ...
Y ₀ ...

Ym-i Ym-2 Ym-s Ym Ym-i Yμ -2

m-2

pm + 1
¹ M + l 0 riAf +1
'M 0 j-Af + 1.
¹ MI 0 ρ M + l
¹ 1 0 _Γ Μ ₊₁

where Y ₀₁ Y ₁ ... Ym represent the autocorrelation function coefficients of the seismic record, Γ% t \, Tt ⁺¹ · · ■ Γ ¹ I ^{+1 are} the relative magnitudes of the electrical potentials,. / ^ J} is a predetermined known value , B _{M + 1 is} determined uniquely by solving the matrix equation and M is an integer.

2. Arrangement according to claim 1, characterized in that the delay device contains M + l outputs (a, b ... M + I) , of which M outputs (b ... M + I) the entered seismic recording (/ ( t)) with respect to an output (α) delayed by a different multiple m of a fixed time period τ, where m = 1, 2... M is shown.

3. Arrangement according to claim 1 or 2, characterized in that the control device (4) has a data processing Establishment is.

The invention relates to an arrangement for suppressing the adjacent components of the Primary reflections in a seismic record contained reverberation components with a A large number of delay devices reproducing recordings that have been shifted in time, with an autocorrelation function generator that generates a large number of autocorrelation function coefficients of the seismic recording supplies, with a control unit, that from the supplied autocorrelation function coefficients a large number of electrical control potentials generated as filter weights and which in turn the seismic recording and the temporally shifted seismic recordings modified in their amounts, as well as with a die actual recording and the device composing the time-shifted records., ..

In marine seismology, in which an explosive charge is detonated underwater near the coast, it is common practice to detect the seismic disturbance that occurs and to record seismic curves in the form of a seismogram. Each seismic curve contains useful information about subterranean formations, but most of this information is obscured by undesirable characteristics of the curve. For example, the primary reflections contained in the seismic curve, by means of which the formations lying perpendicular to one another can be assessed, are covered by multiple reflections, so that the primary reflections become unrecognizable. One of these undesirable characteristics contained in the seismic curves is called water echo; This is to multiple reflections, ^v caused by strong near-surface layers or reflectors. These reflectors are the interface between air and water and the interface between water and the seabed. A trap forms between these separating surfaces, which causes a pulse generated inside the trap or entering the trap from below to be reflected several times in succession between the two separating surfaces The decay of the amplitude is directed towards the reflection coefficients of the separating surfaces acting as reflectors. As a result, a seismic curve exhibiting water echo characteristics contains primary reflections that are obscured by numerous multiple reflections with decaying amplitudes. The interaction between the impulse or the seismic wave and the strong neighboring surfaces acting as reflectors is therefore referred to here as the echo effect. Further details on the water echo problem in marine seismology can be found on pages 223 to 261 of the publication Geophysics, "Water Reverberation-Their Nature and Elimination", Vol. XXIV, No. 2, April 1959, by MM

B a ck u s.

The reverberation or echo problem is most noticeable in marine seismology, however it is not limited to this area. For example, the echo problem can also occur with seismic Investigations on land occur when the area under investigation has strong near-surface reflectors contains. A seismic curve recorded under such circumstances contains an echo characteristic analogous to the water echo characteristics.

In the following, the term "seismic curve" denotes an electrical signal that is a continuous Time function (analog), as it is the case with an electrical signal that the output

a seismometer is taken, which is sensitive to seismic waves, or it refers to one or more electrical signals that digitally represent the continuous function of time. The digital representation of an analog signal requires the analog signal to be sampled at successive points of the analog signal, these points being separated by time intervals corresponding to the sampling interval A t . The sampled values are then digitally encrypted so that a digitally reproduced seismic curve is obtained.

From US Pat. No. 2,794,965 it is known to associate a function measured in a certain area with the seismic recordings measured in another area, for example by means of a deconvolution filter. The way this deconvolution filter works depends on the amount of noise in a given recording. If then in a seismic. Recording reflection components (no noise components) are present, then an error display appears. The filter effect in this arrangement is ■); therefore rests on the fact that a noise component must be present in the recording. In this arrangement, precise values can then be set with the aid of potentiometers, which do not change when a recording is applied to the deconvolution filter. The main aim of the invention is therefore to eliminate the echo characteristics or the reverberation components in a seismic curve as far as possible and thus to improve the evaluability of the curve.

In an arrangement of the type described at the outset for suppressing the components in addition to the of the reverberation components contained in a seismic record will be achieved according to the invention in that the autocorrelation function generator with the control unit is linked in such a way that filter weights can be derived from the large number of electrical control potentials, their The size relationship is given by the following matrix equation:

Y ₁

To
Yi

Y ₂ --- Ym
Y ₁ ... Y ^ ₁

Yo ■ ■ ■ Ym-2

pm + l ^ m + 1 pm + 1
¹ st 0 Pm ⁺ A 0 ^ ₊ I 0 , If ⁺¹ 0

Y V V

¹ JVf-2 ^r M-3 ¹ I.

Ym-I Ym-2 Yo

where Y ₀ , Y ₁ ... Y _{M represent} the autocorrelation function coefficients of the seismic recording, rfyXl, Γ $ ⁺¹ ... If ^{+1 are the} relative sizes of the electrical potentials, f ^ t * is a previously determined known value, B _{M + 1} uniquely determined by solving the matrix equation and M is an integer.

The adjustability of the weights of the individual delayed reproductions of the seismic recording thus leads to a variable weighting filter. A continuous input time function, as shown in the seismic recording, is converted in a weighting filter into a continuous output time function, which is composed of several values of the input function, each of which is offset in time and weighed differently. In the case of the arrangement according to the invention, autocorrelation function coefficients can also be specified for the point m = 0. Since the control potentials of the control unit and thus the individual filter weights are based on the autocorrelation function of the seismic recording, any number of seismic recordings can be made with the arrangement according to the invention after one-time dimensioning of the control unit, which is possible through calculation or experiments

be treated. ''

The invention and individual fundamentals for their easier understanding are below on a Embodiment explained with reference to the drawings.

F i g. 1 shows a seismic record treated with the arrangement according to the invention can be;

F i g. 2 is a block diagram of that part of the arrangement with which the control potentials for the Filter weights are generated;

F i g. 3 shows the filtering delay device with the adjustable weights;

F i g. 4 is a graph following that of the seismic record according to FIG. 1 after suppression of the periodicities.

With the arrangement according to the invention for suppressing the echo characteristics or the reverberation components a linear filter is used in a seismic recording whose impulse response, d. H. its output time function as a response to a unit pulse on the input side as follows is designed so that its frequency characteristic of the> echo characteristic is inverse. As mentioned above, one can also call such a filter "inverse" because of its relation to the mathematical convolution theorem Call the convolution filter «.

The seismic curve or signal detected during the time interval during which a reflection from a deep layer is expected has a repetitive waveform (periodicity) that is partly due to the echo effect and additionally due to the behavior of the entire seismic system (Seismometer, amplifier, recorder, etc.). The seismic recording can therefore be viewed as a function f (t) , which arises from the impulse response g (t) folded under the surface with the reverberation effect k (t) and the function h {t) of the entire seismic system.

Assuming that the near-surface reflectors are characterized by a parallel bedding, and that the response h (t) of the entire seismic system has a minimal phase, then the linear filter is used to suppress the reverberation effect and to reduce the influence of the seismic system according to the invention is determined solely by the autocorrelation function of the seismic record. This applies not only when the subterranean formation comprises only a single deep layer, but also when the deep layers follow one another at random, which comes close to the actual conditions when using reflection seismology.

It was assumed that the eigenfunction of the entire seismic system has a minimal phase. If this is not the case, the known influence of the seismic system can optionally be eliminated by the usual inverse filtering before the autocorrelation function of the record is derived. If the function / i (i) of the system is neglected, the filter to be used to suppress the echo characteristic has an impulse function k '(i), where the convolution of k' (t) with / c (i) to a Dirac delta function < 5 (i) leads. So it is

= J

fc (r) k '(t - τ) di.

If the function h (t) has a minimum phase, it is eliminated by the function of the corresponding filter.

The seismic signal / (i), convoluted with the impulse function of the filter, gives an output signal with which the underground formation can best be estimated, the time function resulting from the reflections under the surface through the impulse function g (t) in response to an impulse.

In order to estimate the filter function required to enable optimal assessment of the subterranean formations, the autocorrelation function of the seismic signal is used along the time interval within which primary reflections are expected. The term “autocorrelation” is used here in the same sense as in equation (0.424) on page 5 of the publication entitled “Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications by Norbert Wiener (1949); for real data the autocorrelation function applies as follows: ti + τ

y (mr) = y J / (i) / (t-mr) dt. (1)

Il

Y (mr) is the autocorrelation function, Il to (ti + T) is the time interval of the seismic signal f (t) in which primary reflections of interest are to be expected, τ the sampling interval of the autocorrelation function, m = 0, 1, 2 .. .M, ie the number of sampling points, Μτ the maximum delay time in the correlation function, which is usually less than 0.10T.

Once the autocorrelation function is established for a particular seismic signal, one can generate a unique set of filter weights, which weights describe an a {M + I) -point delay line filter that has the desired momentum function fc '(i). The filter weights are given by the following matrix equation:

Here Y ₀ , Y ₁ ... Y _{m are} the autocorrelation

function coefficients defined by equation (1) for m = 0, 1 ... M; the indices of the autocorrelation function coefficient correspond to the respective values of m;

pM + l ttM + 1 j-Λί + Ι pM + 1

¹ M + l) ¹ M J- "JW-I · ■ ·· ■« 1

are the filter weights, and the subscript M + 1 indicates that there are M + 1 weights and that the Matrix an M + 1 square matrix of the autocorrelation function coefficients is;

ΓμΧ \ = 1, B _{M + l} is part of the solution of the matrix equation (2) and physically corresponds to the mean energy of the output signal generated by the filtering f (t) , where the M + 1 point delay line filter is the one defined by the matrix equation ( 2) has the weights described.

The unknown quantities in equation (2) are the filter weights

7-1M + I rAf + l rAf + l ¹ M » * ■ MI> ¹ I

and the output power B _{M + 1} . However, these quantities are clearly defined by equation (2), and solving this equation identifies these quantities.

The filter weights defined by equation (2) are derived assuming that the momentum function g (i) subsurface over the period E ₁ to (I ₁ + T) is essentially "white," meaning that in the subterranean Formation itself does not have a strong periodicity and that the predominant cause of the echo characteristic is to be found in the seismic signal in the stratification near the surface. Therefore, the autocorrelation function is used to derive the filter weights required to "recover" the subsurface momentum function or response g (t) from the seismic signal f (t).

With the help of the following herbal equations, the matrix equation (2) can be converted into a small fraction the time that can be solved using the usual methods of solving matrix equations would need.

ri = i

B ₁ = Y ₀

for m = O,

for m = 1, 2, 3 ... M,

rim + 1 pm 'ι rtm + I rim

G - - * ff - 1 ~ Γ - ¹ I ^J m

Y ₁ Y ₂ Y ₁ Yo Y ₁ Y ₂ Y ₁ Y ₀

Ym-i Ym-3 ■ · ■ Y ₁ Ym-i Ym-x · · ■

^ m i-Af + l
¹ M + l • #M + 1 rAf + l
^y M O rAf + l
^ M-I O If ⁺¹ O pm + i O

for m = 1, 2 "'.. .M and g = 2, 3 .. .M + 1,'
Γ / = 0 for s = 1, 2.:. M + 1,

(2) B _m = M _M _, (1 - (ΓΓ) ² ) for m = 2, 3. . ·: M +. 1. (8)

The preceding set of equations (3) through (8) describes a recursive process by which the filter weights p ^ ^{+ i} ... · Γ ^ ΧΙ in a staircase from

η η

Equations (3) through (8) describe the mathematical operations to obtain the desired ones Weights. These operations are performed as follows:

First "one chooses T ₁ ¹ = 1, where B ₁ = Y ₀ .

Then set m = 1 and apply equation (5):

¹ st r-M + i. . .
¹ M + l ... m = M, M + 1 level rl η ... m = 2 η ... m = 1 second level ... m = 0 first level

T * -

From equation (6) one obtains

if according to equation (7)

7 8. ,

Starting point T ₁ ¹ = 1 can be built up from. This "build-up" process is shown schematically below.

change by a constant value while maintaining the desired relationship.

In a preferred embodiment of the invention, the recursive process described above is carried out with the aid of a digital computer in order to determine the filter weights. The autocorrelation function coefficients Y ₀ , Y ₁ .... Y _{M are} fed to the digital computer as input data. Since the values of -T ₁ ¹ and B _{1 are} fixed, they do not need to be added to the input of the computer, but they are incorporated into the computer program. The computer is programmed to perform the mathematical operation described by equations (3) through (8) on the data supplied to the computer.

After the (M + 1) weights have been determined, they are put into a delay line filter of the type shown in Fig. 3 is realized. The weights are shown as resistors 7, their resistance values according to the values of the weights

i-iM + l rM + l njf + l

¹ II ¹ I. · ■ ■ 1 M + l

are related to each other. Therefore, the weights describe the relative amplitude scale values applied by the filter to the seismic signal / (£). In the example dealt with here, the weights are normalized with respect to the weight TmX ₁ , since this is equal to 1 by definition.

The filter according to FIG. 3, the analog seismic signal / (i) is supplied as an input signal, and An analog signal appears at the output of the filter, which has been freed from the echo characteristic.

According to FIG. 3, the delay line filter comprises a delay line 5 with sampling points α, 6 ... M + l. These sampling points are separated by distances. There is a at each sampling point Resistance? connected, which in turn is connected to a summing network 6. The resistance values the resistances? are on top of each other according to the weights

= 0.

15th

20-

25th

T ₁ ² and ri are defined as the weights of the second level and serve to define the weights of the third level, as shown above at (9).

Then we set m - 2 and obtain from equation (5)

- 3 _ - ^Σ 1 = 1 ^Ύ 9 ^Γ \

B ₂ results from equation (8) as follows:

. B ₂ = B ₁ (1 - (Γ ² ) ² ).
Now Γ ^{3 is} defined. From equation (6)

you get

T ₂ ³ = Γ ² + Γ ³ Γ ²

35

40

r ³ r ₀ ² == i

Herein T ₀ ² = 0.

It can be seen that weights Γ / with the same upper and lower indices are always equal to 1, ie F ₅ ⁵ = 1.

The weights T ₁ ³ , T ₂ ³ and T ₃ ^{3 of} the third level are now determined and used to determine the weights of the fourth level. The process continues in accordance with equations (3) through (8) until the M 4-1 weights are constructed as shown at (9).

Equation (8) gives the mean output power B _{M + 1 of} the signal which is generated with the aid of the delay filter which is given the weights described by equation (2), the distances τ being present between the sampling points of the filter.

If the output power Β _{Μ + 1} indicates that the amplitude of the output signal is not large enough to allow a visual indication, one can amplify the output signal, or alternatively one can multiply each weight with a positive value A , whereby the output signal with the Factor A is amplified. The weight Γ $ t ί is the reference weight to which the other weights

45

50 riAf + l rAf. + L ¹ I ' ⁱ 2 j

M + l

i + l

pM + l γτΜ

and therefore all weights can be obtained. The delay line 5 can be be a set of electrical delay circuits, each of which has a delay τ occurs between the sampling points, or a magnetic drum can be used on which the seismic signal / (t) is recorded. One such Delay line filter which can be suitably used in the context of the invention is shown in FIG F i g. 3 of the publication entitled Geophysics, "Magnetic Delay Line Filtering Techniques", BdXX, No. 4, October 1955, § 745 to 765 of Jones et al. shown.

Referring to Fig. 2, where is a functional block diagram the device for obtaining the filter weights discussed above is shown,

209 640/54

9 ίο

an explosive charge is detonated at 1, at the point at which m - 2, etc. In the mention of a seismic US patent in the area under investigation, however, an auto-correct fault is not to be caused. The mechanical vibration at which m = 0. This coefficient is obtained with the aid of a linear arrangement 5, that the device according to FIG. 4 detected by seismometers and changed accordingly by converting an additional channel into electrical signals. It should be noted that applies in such a way that the output signal of an individual seismometer 102 at the location of each seismometer multiplies by itself, integrates meter or a group of seismometers is present and can then appear as a further point in table 113, to be taken from the relevant location. In this way, one obtains the generation of a speaking single seismic curve. Equation (1) of the present description and below

Before deriving the autocorrelation function, use the modified device of FIG. 4th

of a seismic signal, it is expedient to use a set of M + 1-

Remove noise components from the signal. Autocorrelation function coefficients for the se-

For this purpose, the seismic fault is mixed with 15 signal / (i).

With the aid of a linear seismometer arrangement according to the autocorrelation radio output signal and shown in FIG. 2 with the aid of the aggregation generator 3, a gats 2 is thus processed, so that a single seismic set of autocorrelation function coefficients, the noise-free signal / (i), is generated. In the case of the aggregate described by equation (1),
gat 2 is a well-known multi-channel 20. The digital computer 4, by means of which the filter processing device for seismic data, which weights it can be determined, can be one; the noises or the noise to act digital computer of the type IBM 7074 that switch. an IBM 1401 peripheral computer for generating

It is elsewhere a method already described includes the program for the computer IBM 7074, has been that allows the noise by ₂₅ For the input data zugezu suppress the IBM computer that seismic wave trains with leads are, it is the with the aid of the generator 3 scanned with the aid of a linear seismometer arrangement and that the output signal is a noise-free correlation function coefficient. The program seismic signal is generated, the effect according to the IBM computer is obtained by reacting seen by a valve provided in the middle of the assembly ₃₀ equations (3) to (8) in the advancing edge language down seismometer "" will. It should be noted that writing and placing the results on IBM cards 866 424 other methods of generating one which can then be applied to the IBM peripheral computer noise-free seismic signal are supplied 1401 to generate the program, including the single-channel processing. The digitally encrypted values of the I \ and B ₁ processing method. It should also be noted that the uses 35 are also included in the program, a processing device for turning off the signal. In this way, the IBM computer 7074 serves to extract noise components from the signal / (i) before the one defined by equation (2) Determine filter weights deriving the autocorrelation function of the signal.

for the invention without critical importance, but it should be mentioned that one also other

is desired. . 40 digital computers can use to set the filter weights

The noise-free seismic signal / (i), which has to be determined, e.g. B. the IBM computer 704, the IBM using the known method is obtained, 'computer 1620, the computer 225 of General Electric recorded on a magnetic tape and the input or digital computer 1604 of the company Control gang of the autocorrelation function generator 3 to- Data. The procedures for programming this are guided. ₄₅ calculators for performing the arithmetic operations

In addition, in the case of the seismic signal, rations according to equation (2) or according to the equations supplying the signal / (i) to the input of the steps (3) to (8) are known to anyone skilled in the art. Generator 3 in particular if the overall The invention has so far not been described in connection with function h (t) of the seismic system has an analog seismic signal f (t) , minimum phase, a reciprocal filter 50 that a seismometer output or a Applying a magnet to the effect of the function h (t) of the tape record is taken, taking from the-. System to eliminate. sem signal the associated autocorrelation function

A suitable generator 3 for obtaining the de-autocorrelation function of the seismic signal / (£) with the aid of the aforementioned modified device is wound. However, there must be no restriction to this, as described in US Pat. No. 2,794,965. ₅₅ , because the analog seismic signal of the aforementioned USA patent, to which reference can be made here with the aid of an analog-digital converter, is shown in FIG. 4 describes a device, converted in digital form, on a magnetic tape by means of which the autocorrelation function can be determined > recorded and then be used as an input signal; a description of the device is in? ' Digital computers are supplied, e.g. B. the IBM column 6, lines 15 to 66 given. The seismic 60 calculator 7074 so that the autocorrelation function signal is recorded as a reproducible record 100 coefficients Y can be determined. Recorded here, and the autocorrelation function- is the seismic coefficients used as input signal are shown in the form of table 113- signal is a digital signal, or it is a. The distances between the detectors 102, several digital signals, the seismic waves represent 103 etc. determine the sampling interval τ. With regard to 65 sent, which are verified at the location of a seismometer of equation (1) of the present description.

the detector 102 is at the point when the seismic signal / (i) is digitally represented

which m = 1; the detector 103 is located, this is loaded in the analog-to-digital converter

used sampling interval denoted by Λ t , and the number of sampling points along the signal is equal to N; In this way, the seismic signal time interval t _x to J ₁ + I) is defined as N t. The sampling interval τ of the autocorrelation function is usually a whole multiple of Λ t.

The digitally encrypted signal for the autocorrelation function coefficients Y appearing at the output of the IBM computer 7074 can then be fed to the input of the computer using the program already mentioned in order to determine the filter weights Γ. After these filter weights have been determined, they can also be added to the computer program in order to process the digitally encrypted signal / (i) shown as an input signal, as shown in FIG. 3 is represented functionally by the delay line filter.

In Fig. 1 an analog seismic signal / (i) reproduced, which was processed using the well-known multi-channel method. About the noise components To eliminate it, an apparent reciprocal velocity pass width of 0 + 2 msec became Slope / line used.

The time interval for the signal (J ₁ to C ₁ + T) is about 1.5 seconds. In the following table I the autocorrelation function coefficients Y are given, which were derived from the signal over its time interval for the sampling interval of τ = 4 milliseconds, where M corresponds to a number of 79 sampling points.

Table I.

Autocorrelation Function Coefficients 12

Table I, continued

m Y / Jl Y 5 52 141410 66 -196431 53 54428 67 -135854 54 -36449 68 8184 IO 55 9633 69 50090 56 143517 70 -38540 57 178493 71 -117865 58 10165 72 -42623 T C , 59 -249512 - ' 73 154985 ¹ D 60 -340807 74 272186 61 · -144048 75. 150471 62 181764 76 · -135900 63 346811 ■ 77 -327589 20th 64 219701 78 ■ -241088 : 65 -46337 79 34090

m Y m Y 0 422751 26th -99953 1 240392 27 102567 2. -99730 28 284328 3 -307561 29 231811 4th -233407 30th -47989 5 -14287 31 -310206 6th 107900 32 ■ -308715 7th 53250 33 -55972 8th -47741 34 197326 9 -25690 35 237250 10 130508 36 81046 .11 236924 37 -66233 12th 121459 .38 -62922 13th -163893 '39 37312 14th -363490 " 40 64175 15th -261084 41 · -63718 16 60077 42 -223476 .. / 17 309990 43 -206247 18th 279583 44 33869 19th 39980 45 ' , 309868 20th -152734 46 347179 21 -144892 47 95770 22nd -13796 48 -217906 23 53267 49 -321381 24 -25999 50 -160386 25th -134422 51 64256

Table II below lists the filter weights derived from those given in Table I. Autocorrelation function coefficients were obtained.

³⁰ Table II

Filter weights

~ m p »+ l
'M + lm IJl j-iM + 1
¹ st + lm 0 ' 1.00000 '26 -0.00355 1 -0.11310 27 . 0.00183 2 0.27616 28 0.03451 3 0.57477 29 0.03382 4th 0.40749 '. 30th -0.00736 5 0.21105; 31 0.01605 6th 0.25461 ' 32 0.01187. 7th 0.21366 33 -0.04832 8th 0.06538 34 -0.01936 9 0.06867 35 -0.05082- 10 -0.01256 36 0.02193 11th -0.17926 37 ' -0.05829 12th -0.16559. 38 -0.00801 13th -0.06648, 39 0.02350 14th 0.16009 40 0.01868 15th -0.03030 4L, 0.04488 16 -0.05891 42 0.10760 17th 0.03455 43 0.01262. 18th 0.03152 44 0.08599 19th 0.08702 45 -0.13443 20th 0.01140 46 ' -0.08410 21 -0.05173 47. *. -0.00346 22nd 0.04488 48 -0.00416 23 0.02752 49 -0.02421 24 -0.01333 50 -0.05605 ' 25th -0.06476 51 , 0.03529

Table II, continued

m r * f + l
* M + I -m m / \ V + 1
'Af + 1 - tu 52 0.04478 66 0.01337 53 · 0.02506 67 0.01439 • ⁵⁴ 0.03492 68 0.00396 55 0.02544 69 0.03859 56 0.02098 70 -0.00975 57 0.03422 '71 -0.00846 58 -0.06302 72 -0.00507 59 -0.00761 73 0.03088 60 -0.03625 74 0.01169 61 -0.04458 75 -0.03446 62 -0.01225 76 -0.00420 63 0.01382 77 0.01719 64 0.00600 78 0.01201 65 0.00510 79 0.01389

The negative weights given in Table II mean that the polarity of the signal at which the weight in question is applied, reversed before being fed to the summing network will.

The sample points and the corresponding weights, i.e. H. the values from the two columns of Table II, in the delay line filter of FIG. 3 as follows in an appropriate manner be realized:

The resistors according to FIG. 3 are adjustable potentiometers, and 6 in the summation network it can be a Philbrick P-2 differential summing amplifier trade with a positive and a negative input.

A sinusoidal voltage corresponding to a steady state is fed to the input of the delay line filter; this input is labeled / (1) in FIG. 3. A low-frequency alternating voltmeter is connected to the resistor labeled Γ ^ Xi? connected to measure the voltage across this resistor. The magnitude of the input voltage is chosen so that the voltmeter reading is equal to a suitable predetermined multiple of the actual desired weight, which in this case is the same. According to Table II, the sampling point channel α corresponds to the expression m = 0 and the weight is equal to 1. Then the voltmeter is connected to the resistor ini sampling point channel b corresponding to m = 1 in Table II. This resistance is adjusted until the voltage to be read directly on the voltmeter scale has reached the predetermined value. Multiples of 0.11310 is set. All other weights

riM + 1 r> M + l pM + l

■■ * Af-I ' ² MZ · · · * ■ 1

are set by adjusting the resistance concerned and reading the voltmeter, until the reading equals the predetermined multiple of the absolute values of the weights in Table II.

Each sampling point channel is made according to the specifications

in the weight column of Table II a positive

Assigned to 5 or negative polarity. The positive channels are connected to the positive input of the Differential summing amplifier and the negative channels to the negative input of this amplifier connected.

The gain factor corresponding to the aforementioned predetermined multiple can be adjusted by setting the gain of the differential summing amplifier can be eliminated or adjusted.

The foregoing has been a method of establishing the desired predetermined relationship between the weights of the delay line filter. However, it is also possible to do this for each sample point channel to calculate the required resistance values.

F i g. 4 shows the seismic output signal of the filter according to FIG. 3, while the input signal f (t) in FIG. 1 is shown; the filter weights Γ are given in Table II and the sampling interval τ is 4 milliseconds.

A comparison between Figs. 1 and 4 shows that the echo characteristic has been attenuated. this will especially clear when several output signals from a seismometer arrangement form a seismogram be united:

If the linear filter described by equation (2) is applied to the input signal f {t) , the resulting output signal has an energy spectrum in which the amount of energy is approximately constant as a function of frequency. This means that the energy sensitivity of the filter is inversely proportional to the energy spectrum of the input signal f (t) . Hence, one can estimate the energy spectrum of signal / (i) by finding the reciprocal energy function of the linear filter described by equation (2). In this connection it should be noted that the output of the digital computer 4 according to FIG. 2 can use weights taken to determine the energy spectrum of the seismic signal / (t). This can be expressed mathematically as follows:

1 ^ e = I ⁷ * ^{e IA71} S} T

Here P (f) is the energy spectrum as a function of the frequency of the seismic signal / (i) along the time interval tj to (t _x + 7), τ is the sampling interval of the autocorrelation function, B _{M +1 is} the mean energy of the output signal, which is obtained by filtering is obtained from f (t) if the (M + 1) -point delay line filter has the weights Γ described by the matrix equation (2), F ^ ⁺¹ the (M + D weights) described by the matrix equation (2), ■■ / frequency that varies over the frequency range of seism ica signal f (t), g = 1, 2, 3- M + l, i Y ^ Y.

1 sheet of drawings

Claims (1)

Patent claims: 1. Arrangement for suppressing the next to the components of the primary reflections in one seismic recording contained reverberation components with a multitude of each other Time-shifted recordings reproducing delay device, with an autocorrelation function generator, which provides a plurality of autocorrelation function coefficients of the seismic record, with one Control unit that generates a large number of electrical Control potentials are generated as filter weights and in turn the seismic recording and modified the amounts of the time-shifted seismic records, as well with a composite of the actual recording and the time-shifted recordings Device, characterized in that the autocorrelation function generator (3) is linked to the control unit (4) in such a way that from the multitude of electrical control potentials Filter weights can be derived, their size relationship by the following matrix equation given is: