* * * reflection point multiple superposition method (horizontal superposition method)

As mentioned above, the geophone combination method plays an obvious role in suppressing low apparent velocity interference such as surface wave, but the combined reflected information is the average of a small piece of reflected wave information on the interface, so there is an average effect, which reduces the lateral resolution. In addition, the suppression effect of interference waves such as multiple reflected waves is poor, or even powerless. In order to make up for the weakness of combinatorial method, Mayne (1962) proposed multi-overlapping addition. The observation system is shown in Figure 3- 19. After dynamic and static correction, superposition and other data processing, the interference wave can be suppressed and the signal-to-noise ratio can be improved. Practice has proved that this method has significantly improved the quality of seismic exploration, so it has become a widely used conventional seismic exploration method in the world.

* * * Multiple stacking of reflection points is also called multiple stacking of * * * depth points, multiple stacking of * * * center points and multiple coverage technology. Its basic idea is to repeatedly observe the geological information of a certain point underground at different observation points on the ground or in different ways, so as to ensure that the information of every point underground can be obtained even if individual observation points are disturbed.

(A) * * * central point superposition principle

This method is based on the assumption of horizontal interface (Figure 3-33). The projection of any point A on the interface on the ground is m, and it is excited at points O 1, O2, O3, … on the ground, respectively, and the reflected wave of the same point A on the interface is received at corresponding points G 1, G2, G3, …, Gn. Point A is called * * * center point or * * * depth point (CDP intersects the ground at point M through the vertical line of point A, and point M is the same center point between each excitation point and its corresponding receiving point, which is called * * * center point or * * * ground point. The time for the reflected wave from point A to reach each stack trace is t 1, t2, t3, …, tn, respectively. The data of each stack trace of * * * depth points are extracted from the original * * * gun records and gathered together to form a * * * depth point trace set. The right half of the time-distance curve corresponding to point A can be plotted with offset x as the abscissa and time t when the reflected wave reaches each stack trace as the ordinate. By exchanging the excitation point and the receiving point, the left half of the time-distance curve at point A can be obtained. To sum up, it is called * * * depth point time-distance curve, and its equation has been given in Chapter 2 (Equation (2-25)). It is also a hyperbola, which has the same form as the time-distance curve equation of the reflected wave of the cannon on the horizontal interface, but their physical meanings are different. The time-distance curve of * * gun reflected wave reflects a section of underground interface, while the time-distance curve of * * * depth point only reflects a point of underground interface. T0(x=0) on the time-distance curve of * * * depth point is the echo time of * * center point, which is equivalent to setting an excitation point at m point and receiving the observed arrival time at the same m point; It is different from the echo time of the shot point on the * * * shot point time-distance curve, and is generally called self-excitation and self-collection time. Traditionally, the offset x 1 of the first trace (the one with the smallest offset) in * * * depth gathers is called offset.

Because all traces in the * * * central point gathers record reflected waves from the same reflection point, all traces should have similar waveforms. However, due to the different offset of each channel in the gather, there is a certain phase difference between the reflected waves of each channel. Taking the self-excitation and self-collection time t0 as the reference time, the time t0 can be subtracted from the arrival time of each reflected wave in the * * * central trace set, and the time difference of each trace relative to the central trace can be obtained, which is called normal time difference. Its value is

Figure 3-33 Time-distance curve of * * center point of horizontal stratum

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Subtract the normal time difference by the arrival time of each reflected wave, and the time-distance curve of * * * central point gathers becomes a straight line with t=t0 (Figure 3-34). This process is called normal time difference correction or dynamic correction. After NMO correction, the reflected waves of * * * central point gathers not only have similar waveforms, but also have no phase difference. At this time, the reflected waves will be superimposed and enhanced. Taking the total vibration after superposition as the output of one-point self-excitation and self-collection time of the * * * center point m, multiple superposition outputs of the * * * center point are realized.

Figure 3-34 Schematic diagram of dynamic correction

When dynamically correcting the effective reflected wave time-distance curve of horizontal multilayer interface, if there are multiple reflected waves, the curvature of the multiple reflected wave time-distance curve is greater than that of the primary reflected wave time-distance curve. Therefore, the time-distance curve of multiple reflected waves after dynamic correction does not become a straight line to 0, but there is still a residual time difference, which we call the residual time difference after dynamic correction (Figure 3-35).

Figure 3-35 Residual Time Difference of Multiple Reflected Waves

Assuming that the time t0 of the primary reflection wave is the same as the time t0 of a certain multiple reflection wave, the residual time difference δTD of multiple waves after dynamic correction according to the primary reflection wave is

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In ...

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Where: Δ td is the normal time difference of multiples and Δ t is the normal time difference of reflected waves. Q is called the residual time difference coefficient of multiples. It can be seen from the formula (3-2 1) that the residual time difference of multiples is proportional to the square of offset, and the residual time difference of each stack trace is different, so it is not in-phase stacking. So the multi-wave superposition will weaken.

(b) Multiple superposition effect of * * * center points

The principle of suppressing interference waves and improving signal-to-noise ratio by multiple superposition method is discussed above, and the multiple superposition characteristics of the center point of * * * are further discussed below.

The multi-coverage observation system excited by one side is taken as an example to discuss.

Let a * * * reflection point in the underground reach the ground * * * center point M, the normal primary reflection wave is f(t0), its frequency spectrum is F(ω), the reflection waves of each channel in the * * * central point gathers are f(tk), tk = t0+δ tk, and δ tk is the normal time difference (NMO correction) of xk channel offset. According to Δ TK law, for normal primary reflected wave, Δ TK is just eliminated after dynamic correction, and the output result after superposition is as follows.

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Its frequency spectrum is

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However, when interference waves such as multiple reflections are corrected according to δTK law, there is still time difference δTK. Since the velocity of multiple waves is lower than the velocity of primary reflected wave at the same time t0, δtk is generally positive, and the output after superposition is as follows

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Its frequency spectrum is

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As can be seen from Formula (3-26), it represents the characteristics of multiple superposition. Therefore, we define it as a multiple superposition characteristic function, that is

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The superimposed output signal can be expressed as

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K(ω) can also be understood as a filtering characteristic, but its physical meaning is different. In this sense, it can be considered that multiple superposition is a linear filtering system. It has amplitude characteristics and phase characteristics. The modulus of k (Ω) is the amplitude characteristic of multiple superposition, that is

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It is obvious from Equation (3-29) that for the positive reflection wave, tk = 0 and K(ω)=n, and the amplitude of the output signal after superposition is enhanced by n times. For interference waves such as multiples, Δ tk ≠ 0 and k (ω) < N are relatively weakened after superposition.

In order to show the suppression process of multiple waves after multiple superposition relative to the normal primary reflection wave, we use the ratio of the amplitude after multiple superposition to the amplitude after primary superposition to characterize the superposition effect, including

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because

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αk is defined as the stacking parameter, which represents the ratio of the residual time difference of each stacked trace to the harmonic period, so the stacking amplitude characteristic formula is as follows.

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In order to relate the amplitude characteristics of multiple superposition with the relevant parameters of the observation system, αk is expressed by Equation (3-22) as follows

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manufacture

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Where xk is the offset of each stack trace, δx is the trace spacing in an arrangement, and α is called the unit stack parameter, that is, the stack parameter when the offset is one trace spacing, then

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This formula can be used to calculate the amplitude characteristic curve of multiple superposition. The calculation of characteristic curve is divided into the following steps:

First, determine the parameters. because

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Where μ = x1/Δ x is the number of migration tracks, and ν = d/Δ x is the number of migration tracks, which is related to the number of stacking times n and the number of instrument recording tracks n. Therefore, the parameters to be determined are the number of stacking times n, the number of migration tracks μ and the number of shot traces ν.

Secondly, the value of abscissa α can be determined according to the main frequency range of waves, the maximum possible range of track spacing and the specific situation of residual time difference coefficient Q.

Finally, taking n, μ and ν as parameters and α as variables, the superimposed amplitude characteristic curve is obtained. Figure 3-36 shows the superimposed amplitude characteristic curves of n=4, μ= 12 and ν=3.

Figure 3-36 Superimposed Amplitude Characteristic Curve

We take this diagram as an example to analyze the characteristics of the superimposed amplitude characteristic curve.

As can be seen from the figure, when α=0, P(α)= 1, that is, the amplitude of primary wave with zero residual time difference is the largest. When α increases gradually, the value of P(α) decreases rapidly. When α=α 1, P(α 1)=0.707. It is generally believed that P(α)≥0.707 means that the amplitude of superimposed waves is strengthened, and the range of 0≤α≤α 1 is called passband, α 668. With the further increase of α, P(α) is a low value area on the characteristic curve. In the range of αc≤α≤αc, the waves whose average value of P(α) falls within this range are suppressed to the maximum extent, that is, they are weakened after superposition. This low value area is called compression area. The multiple reflected waves often fall within this range, but there is also an extreme point P(α3) in the suppression area. This value affects the pressing effect, and the larger the value, the worse the pressing effect. There is a first minimum point α m near α C in the compression zone. If αm

When α increases to α2, a quadratic maximum value P(α2) appears on the characteristic curve, which is actually α >. αc and P(α) on the curve began to increase rapidly. Interference waves should not be allowed to enter this range, so it is not appropriate to use excessive track spacing.

By analyzing the characteristic curve of stacking amplitude, it can be seen that the characteristic curve will change with different stacking parameters.

If the stacking characteristic curves with different trace spacing are made with the trace spacing as the parameter (Figure 3-37), it can be seen that with the increase of trace spacing, the passband becomes narrower, which is beneficial to suppress interference waves such as multiples with similar velocity to primary waves, but it should not be too large. If Δ x is too large, it will not only affect the in-phase contrast of the wave, but also suppress the residual time difference of the primary wave. The trace spacing cannot be too small, and too small a trace spacing cannot suppress multiple waves.

Figure 3-37 superposition characteristic curve with q as abscissa

The change of offset also has a great influence on the superimposed amplitude characteristic curve (Figure 3-38). The larger the offset distance, the narrower the passband, which is beneficial to suppress regular interference waves close to the effective wave velocity. But not too big. If the offset is too large, some regular interference waves will enter the quadratic extreme value area, which will affect the effect of suppressing interference waves and lose effective waves.

Figure 3-38 Stacking Characteristic Curve Caused by Offset Change

The average value of compression band in the superposition amplitude characteristic curve is related to the superposition times. The more stacking times, the smaller the average value of compression band and the better the compression effect. Therefore, increasing the stacking times n is beneficial to improve the signal-to-noise ratio. But it can't be too big, because the higher the stacking times, the lower the production efficiency and the higher the cost.

According to the definition of phase spectrum, the formula of multiple superposition phase characteristics can be obtained from Equation (3-27).

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It can be seen from Equation (3-33) that for the primary reflected wave with residual time difference tk = 0, the phase shift of the superimposed signal is zero, that is, the phase of the superimposed signal is consistent with that of the signal at the center point m of * * *.

For multiple reflected waves. It will weaken after superposition, but sometimes there will be residual energy. According to the characteristics of superimposed phase, the in-phase axis of residual energy presents a special law, that is, the phase changes with offset and the in-phase axis is staggered. The staggered phase difference between segments decreases with the increase of times. The more times of superposition, the more the continuity of multiple events is enhanced. Therefore, when the stacking times are high, we should pay attention to whether there is a residual in-phase axis of multiple waves.

* * * The central point multiple superposition method also has a similar statistical effect to the combination method. Because the distance between stacked traces (correlation radius of multiple stacking) is greater than the combined distance of joint detection, the stacking method has better suppression effect on random interference. Its statistical effect is better than that of combination method.

The superposition method also has the function of frequency filtering, which plays the role of low-pass filtering for waves with residual time difference.

(3) Factors affecting the superposition effect of * * * center points

1. Influence of stacking speed error on stacking effect

Whether the stacking effect is good or not depends on the accuracy of dynamic correction. For the effective reflected wave, if NMO correction is correct, then NMO corrected stack gathers are corrected to t0 straight line, which can be stacked in the same phase. After stacking, the effective wave energy is greatly enhanced, and the stacking effect is good, otherwise the stacking effect is poor. Whether the NMO correction is correct or not depends on the stacking speed. If the stacking velocity is greater than the true velocity of the effective reflected wave, the amount of dynamic correction will be small, and the in-phase axis of the effective reflected wave after dynamic correction can't become a straight line to, but it is still a curve, and its in-phase axis direction is the same as that of the first break wave in the seismic record. If the stacking velocity is less than the true velocity of the effective reflected wave, the amount of dynamic correction is too large, and the dynamic correction will be over-corrected, and its in-phase axis direction is opposite to that of the first break wave. In both cases, the effective reflected waves are not superposed in the same phase, and the superposition effect will not be good. If the selected stacking speed is exactly equal to the velocity of multiples, the multiples after stacking are not suppressed, but enhanced, and the effective waves are weakened. Therefore, whether the extraction of stacking velocity is appropriate or not is directly related to the quality of stacking profile.

2. The influence of interface dip angle on the superposition effect of * * * center points.

Figure 3-39 Dispersion of * * * reflection points when the interface is inclined

(1) Overlapping of non-* reflection points: When the reflection interface under the ground is inclined, the problem of overlapping of non-* * reflection points will occur according to the horizontal multiple coverage observation system (Figure 3-39). In data processing, if the gathers are still extracted according to the law of * * * reflection gathers, then the collected gathers are no longer * * * reflection gathers. Therefore, the stack after dynamic correction is similar to the case of combination, which will inevitably affect the actual effect of stack. The dispersion distance δr between reflection points is related to the inclination angle of the interface, that is,

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Where xn and x 1 are the maximum and minimum offset distances, and the greater the inclination angle, the greater the dispersion distance of * * * reflection points, which will affect the superposition of * * * reflection points.

(2) The existence of residual time difference affects the stacking effect.

In the case of inclined interface, the * * * reflection point gathers extracted from the horizontal interface are not * * * reflection points, but * * * central point gathers. For this kind of gathers, the reflected wave time-distance curve is called * * * center point time-distance curve, and its equation is * * * center point time-distance curve equation. Using the simple geometric relationship in Figure 3-40, it is easy to establish the time-distance curve equation of * * * center reflected wave expressed by the normal depth at the center m of * * *. that is

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Where: hM is the normal depth at the center point m of * * *.

Figure 3-40 Relationship between * * * Center Point and Reflection Point of Inclined Interface

Equation (3-34) can also be written as

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Where vφ=v/cosφ is called equivalent velocity, and t0M is the self-excitation and self-collection time at the center point m of * * *.

It can be seen from (3-34) or (3-35) that when φ=0, the equation is only a * * * reflection point time-distance curve equation. Therefore, the time-distance curve equation of the center point of * * includes both horizontal interface and inclined interface.

In the case of inclined interface, the accurate dynamic correction is as follows

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or

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There is a difference between the dynamic correction amount Δ t in the case of horizontal interface and the correction amount of inclined interface, that is

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When x/2h? 1, yes

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It can be seen from Equation (3-37) that if the horizontal interface is used for dynamic correction of the inclined interface, there will be residual time difference, and in-phase stacking cannot be realized, which will affect the stacking effect, especially when the inclination angle is large.

For layered media or steep structural strata with large dip angle, DMO (Dip Time Difference) correction or migration stacking method is needed to truly stack * * * reflection points.

(4) Design principles of multi-coverage observation system

By discussing the principle of multiple superposition of * * * central points, it is easy to understand the design principle of observation system considering multiple superposition of * * * central points.

* * * The design of multiple superposition observation system of central point should follow the following principles.

(1) According to the geological, drilling and geophysical data of the work area, select the appropriate observation form according to the work tasks and equipment. The fault development area should adopt the observation form of intermediate excitation or short arrangement. This can reduce the dynamic correction error, increase the coverage density and improve the exploration accuracy.

(2) Understand the characteristics of interference waves, especially the characteristics of multiples. satisfy

αc≤αdmin≤αdmax≤αc '

Select the best characteristic curve and determine the corresponding parameters n, μ and υ. Interference waves such as multiples should fall into the suppression band of the characteristic curve as much as possible, and effective waves should enter the passband.

(3) The determination of track spacing δ x shall meet the following requirements

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Where T* is the apparent period of the interference wave.

If there are multiple regular interference waves, it should be satisfied.

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(4) On the premise of achieving good geological effect, the minimum coverage times, larger avenue spacing and longer layout should be adopted as far as possible to achieve higher production efficiency and lower cost.

(5) Carry out necessary testing work.