THEORETICAL BASIS OF METHOD
OF SEISMIC OBSERVATION GROUPING (SOG)

TRƯƠNG MINH

Việt Nam Association of Geophysicists, Hà Nội

Abstract: The method of seismic observation grouping (SOG) puts forward the dynamic and kinematic solutions which divide the surface and depth factories depending on the seismic rays formed as two-ray, four-ray and six-ray groupings.

This method has the following aims:

     - To estimate the errors of dynamic and kinematic measures in seismic exploration;

     - To estimate dynamic and kinematic (static) corrections;

     - To study on changes of characteristics of reflection horizon;

     - To study the characteristics of velocity and attenuation of transmission media.

I. INTRODUCTION

To day, the seismic exploration involves handling complex tasks in the study on geology, especially in the search for and exploration of petroleum. The practical needs require that the information available in the seismic data makes the best use in order to improve the accuracy to define physical parameters of the geological media. To satisfy this requirement, a number of factors which deform the characteristics of wavelet, including those of emission, transmission media and wave receiving point must be overcome. Important task is to extract the impact of these characteristics from the observable seismic signal in order to study and assess them. By this way we can define the correction of surface condition and study on characteristics of the media. In case of identical media, we temporarily put aside the impact of the characteristics of transmission, attenuation and separation of reflection wave in the media between emissions and receiving point, the complex spectra of reflection seismic wave can be described as follow:

S(w, X, Y, Y) = m(w,X) .l (w, Y). n (w,Y).                  (1)

This shows the interdependence of the characteristics of complex spectra of the emission m(w,X), reflection  l(w,Y) and reception n(w,Y) areas; w is frequency of reflection wave, X, Y, Y are coordinates of shot point, reflection point and receiving point.

In the time domain, the signal of reflection wave is illustrated as follows:

ŋ(t,X, Y, Y) =   (2)

The time for transmission of reflection as defined as follows:

T(X, Y, Y) = t(X) + t(Y) + t(Y) + t(X,Y)            (3)

In which t(X), t(Y), t(Y) are transmission times at these zones of emission receiving, reflection and reception, t(X,Y) is the time of transmission in the seismic media.

Based on the acknowledgement of the model of the above mentioned media, the task to be solved is to extract the impact of the surface and depth conditions to study on changes of their dynamic and kinematic characteristics along the observation line.

II. METHOD OF GROUPING FOR COMMON SHOT POINT (CSP), COMMON DEEP POINT (CDP) AND COMMON RECEIVING POINT (CRP)

By gathering observation of reflection wave according to CSP, CDP & CRP, the quality of change of the surface and depth conditions can be assessed along the study line.

Suppose that at the two common reflection points Ψ1 and Ψ2 we observe signal S1 and S2 and in order to discover the change in the characteristics of their reflection, we assume coincidence or none coincidence of characteristics of the two reflection points Ψ1 and Ψ2 owing to criteria Fisher.

< F  (4)

Iin which: N1 and N2 are observation folds of CDP for each common deep point at the position of Ψ1 and Ψ2; MS and DS are mathematical expectance and dispersion respectively for the complex spectra at these two points.

Beyond the criteria F, we can conclude that the changes in the characteristics of reflection between these two points are conservable anomaly. Similarly for the common shot points and the common receiving points we can use criteria (4) to assess the change of surface conditions.

In the time domain we can use criteria Student.

< S     (5)

In which: Mŋ and Dŋ are mathematical expectance and dispersion of seismic waves.

III. SPECIAL SEISMIC OBSERVATION GROUPINGS

Based on the seismic observation groupings for shot, we can achieve the dynamic and kinematic solution which divides the surface and depth factory depending on the seismic rays to be formed as so called the two-ray, the four-ray and the six-ray groupings.

1. Two-ray seismic grouping

To illustrate this, we mark a seismic observation ray as [X, Ψ, X], where X, Ψ, Y are coordinates of emission, reflection and receiving points (see Fig. 1-3).


a. Definition of spectral characteristics of emission, reflection and receiving areas.

We mark the differential of the characteristics at two emission points in the group [, -2] and [] with fixed coordinate  (Fig. 1), as follows:

DMN (w, X, ) = ln (6)

In the group [] and [] with fixed  (Fig. 2): 

   DML (w, X, ) = ln  (7)

The differential of the characteristics at two refection points in group [,] and [-2, -1,] in fixed coordinate  (Fig. 2), as follows:

DLM (w,,) =  ln   (8)

With the fixed  (Fig. 3):

     DLN (w,,) = ln(9)

The differential of the characteristics at two receiving points in group [,,] and              [, -1, -2] with the fixed coordinate (Fig. 3), as follows:

DNL (w,, ) =  ln(10)

With the fixed  (Fig. 3):

DNM (w,,) =  ln   (11)

 = Y = 2, 4....coordinate of the emission point; = 1, 2 ....coordinate of the reflection points; ,  ~ fixed coordinates of the emission, receiving and reflection points.

b. Definition of the spectral characteristics of emission, reflection and receiving of reflection wave along lines.

Emission spectral characteristics:


m(w,x)=Exp[]                                  (12)

=Exp[]                                 (13)

Receiving spectral characteristics:

n(w,Y) = Exp [] (14)

= Exp []                                (15)

Reflection spectral characteristics:

l(w, Y) = Exp []                                      (16)

= Exp[]                                (17)

The values of ΔM(w,), DN(w,), DL(w,) for the fixed coordinates,  and  are defined as angle coefficient of the functions ΣΔMN, ΣΔNL, ΣΔML, in the equations (9)-(14).

The values of m(w, X), n(w,Y) and l(w, Y) define the complex characteristics of emission, receiving and reflection zone compared to their original values (X0, Y0, X0). Therefore, we can extract them to study frequency characteristics at the emission, receiving and reflection point independently along the observation line.

2. Four-ray seismic observation grouping SOG4.

For the group of rays [X-2, Y-1, Y], [X, Y, Y], (X, Y-1, Y-2], [X+2, Y, Y-2] (Fig. 4), the second differential of spectral characteristics of the emission area is defined as follows:



D2M(w,x)= ln               (18)

For the group of rays [X-2, Y-1, Y], [X-2, Y, Y+2], [X, Y, Y], [X, Y-1, Y) (Fig. 5), the second differential of the spectral characteristics of the receiving area: 


D2N(w,Y)= ln                (19)

For the group [X-2, Y-1, Y], [X-2, Y, Y+2], (X, Y, Y] and [X, Y+1, Y] (Fig. 6), the second differential of the spectral characteristics of the reflection area: 


D2L(w,)= ln             (20)

The spectral characteristic variation of emission m(w,x), receiving n(w,y) and  reflection  l(w,Y) along observed line are defined as follows:

M(w,x)=Exp[]                    (21)

N(w,y)=Exp[]                 (22)

L(w,Y)=Exp []               (23)

The values of DM (w, X0+2), DN (w, Y0+2) are defined as angle coefficient of the function SSD2M (w, X), SSD2N (w, Y), SSD2L (w, Y) in the equations (21), (22) and (23).

Therefore with the characteristics of m (w, x), l (w, Y) and n (w, y) we can study the spectral characteristics of emission, reflection and receiving independently by extracting each other impact along the observation line.


3. Definition of kinematic characteristics.

a. For two-ray grouping:

Handling a kinematic analysis is similar to that of dynamic task one based on the equation (3). In case of ideal media if the sloping of reflection surface is not big and after the correction NMO, the values of t(x, y) in the equation (3) are immutable based on the two-ray grouping.

We have the first differentials of the kinematics characteristics at two emission points in the group [, -2] and [] with fixed , as follows:

 (24)

Difference of the kinematic characteristics at two refraction areas :  

              (25)

Difference of the kinematic characteristics at two receiving areas Y:

         (26)

Transmission time of wave in the emission area X:

t(x) =          (27)

=     (28)

      Transmission time of wave in receiving area Y:

t(y) =   (29)

=  (30)

      Transmission time of wave in reflection area:

t(Y) =  (31)

=   (32)

The values of Δt (), Δt (), Δt () are defined as angle coefficient of the functions t(x), t(y) and t (Y) in the equations (27) - (32)

b. For four-ray grouping:

The second differentials of the kinematics characteristics at the emission, refraction and receiving areas are as follows:

D2T(x) = T(X+2, Y, Y-2) + T(X-2,Y-1,Y) - T(X, Y-1, Y-2) - T(X, Y, Y)                (33)

D2T(Y) = T(X, Y+1, Y+2) + T(X-2,Y-1,Y) - T(X, Y, Y) - T(X-2, Y, Y+2)            (34)

D2T(y) = T(X-2, Y, Y+2) + T(X,Y-1,Y-2) - T(X-2, Y-1, Y) - T(X, Y, Y)                (35)

The time characteristics of the emission t(x) receiving point's t(y) and the reflection surface t (Y) are defined as follows:

t(x)=  (36)

t(Y)=    (37)

t(Y) = (38)

The values of Δt(X0+2), Δt(Y­0+1), Δt(Y0+2) are defined as angle coefficient of the functions t(x), t(Y) and t(y) in the equations (36) - (38)

The values of t(x), t(y) are those of static corrections for emission and receiving conditions. And t(Y) is time variation of the reflection surface.

4. Criteria for controlling the dynamic and kinematic measurements of reflection wave

Based on the six-ray seismic grouping (see Fig. 7) [X-2, Y-1, Y], [X-2, Y, Y+2), [X, Y +1, Y+2], [X+2, Y, Y-2) [X+2, Y+1, Y], in the frequency domain we have correlations:

A (w, X, Y) = ln = 0      (39)

And in the time domain:

B(x,y) = T(X-2, Y-1, Y) + T(X, Y+1, Y+2) + T(X+2, Y, Y-2) -

- T(X-2, Y, Y+2) - T(X, Y -1, Y - 2) - T(X+2, Y+1, Y) = 0                (40)

While observing random noises, the characteristics of distribution and evil of their impact on the measurement values show that if there is regular wave interference the normal distribution of amplitude will be broken, the multiplicative and additional noise will have an impact on the distribution of amplitude in one way or the other. The additional noise is basically in the kinematic measurement.

It is necessary to estimate the values of systematic deformation by the impact of wave attenuation and divergence, the velocity of seismic wave and overlying formation, the anisotropic characteristics of source and the receiver on the first and second differential of the characteristics of the emission, receiving and reflection areas and the criteria for observation examination. To pay attention to that the level of distortion depends mainly on the emission interval l over the depth h of the reflection surface (L =) when L > 0.1 then the errors will be small and can be overlooked. Results of the theoretical estimates have laid the basis for the selection of the best parameters for seismic observation system in the method of seismic observation grouping.

When the criteria for examining dynamic measurement A (w, x, y) ¹ and kinematic measurement B (x, y) ¹ 0, a set of noise and errors through the process of measuring signal will be shown.

On the basic of the six-ray grouping, the errors of the measurement dynamic and kinematic values can be estimated.

;                              (41)

In which: σa and σt are the errors of separate measured values of the amplitude and time for reflection wave, σA and σB are mean square errors of the values of A(w, X, Y) and B(X, Y).

The SOG method can also estimate the errors of the separate measured values by separate factors:

σam =                (42)

σal =              (43)

σan =              (44)

σa0 =                  (45)

In which: σam, σal, σan and σa0 are the errors of separate measured values of the amplitude caused by the emission, receiving conditions and their unestimatable factors. σ2Ax, σ2AY, σ2Ay is dispersion of the values of A(x, y) at the fixed coordinates X, Y, Y correspondingly. And σA is the common dispersion of the values of A(x,y) for the whole of measured values. By the similar way will be able to analyze the errors of kinematic measured value based on the criteria B(x, y).

5. Study on the characteristics of attenuation and velocity of transmission of seismic wave by SOG method

a. Estimation of the effective attenuation coefficient

The estimation shows that the deviational values by SOG method will increase corresponding to L parameters, when L > 0.3 it is necessary to consider their effect in the data processing when using deviation effect of the second differential values D2 and the criteria for the examination A and B, the attenuation coefficient and velocity of seismic wave in the overlying formation can be estimated.

aef = -2        (46)

The effective attenuation coefficient comes also to be found by the six-ray grouping as follows:

aef =               (47)

To estimate the effective velocity:

Vef =                   (48)

In which: l is emission interval; M [D2T (Y)H)] - the mathematical expectance of second differential of the transmission time  at the reflection point Y; D2T(Y)H  - the second differential  of transmission time of reflection wave in the reflection zone Y; M[D2L(Y)H) - the mathematical expectance of the values of D2L(Y); D2L (Y)H - the second differential values of dynamic characteristics of the reflection at point Y; K(Y) - the deviation of the observation values D2L(Y) by wave diverge; A(x, y) and B(x, y) - the criteria of examining the amplitude and time; K(X, Y) - the deviation values of A(x, y) by diverge; V - an averaged velocity.

b. Experimental results and application of SOG method in practice

On the basis of SOG algorithms, a set of processing programs was set up for the purposes:

- Estimating the errors of the dynamic and kinematic measures.

- Estimating the amplitude and spectra correction for the surface conditions;

- Setting up the dynamic section;

- Estimating the effective attenuation coefficient;

- Defining the characteristics of reflector;

- Defining the static correction on the surface condition;

- Defining the effective velocity.

The method SOG has been experimented through processing seismic data in different areas of Russia and Việt Nam.

The analysis of the errors of dynamic measured values in Tiumen (Russia) shows that in a number of cases their distribution law is almost close to that of normal distribution except for a couple of special cases which are close to the Jauffret distribution. In any case, the errors of the measured values will increase normally if the emission interval increases. Basically, this has something to do with the increase of random noise level. Analyzing the erroneous factors show that the random noise has nothing to do with the shot point, but the reflection and receiving points play an important part in shaping these errors. Through the result of processing we have achieved the first and second differential values of dynamic characteristics at the study line, from which we get the values of dynamic corrections at the shot point, receiving point and the dynamic characteristics of reflection horizon.

The work of kinematic processing has been carried out on the seismic data in Astrakhan (Russia). The study of the distribution of errors for the time of transmitting reflection wave is close to the normal distribution.

The analysis of amplitude and spectra has been carried out based on seismic data available in Pricaspian basin. Through the results of processing we got dynamic correction and sections. The values of correction by separate method are well linked along the line.

In the Red River Basin (Việt Nam) the application of SOG method to study the velocity sections in different areas has brought some successes which correspond to the drilling data. The analysis of the characteristics of velocity along the axis of this basin allows us to define horizontally and vertically the laws of change in velocity of seismic wave which links to the change of thickness of overlying Neogene formations.

To study the characteristics of the attenuation of sections we have applied elective attenuation coefficient and the layered attenuation coefficient to compare these results with the logging data. The bedded attenuation coefficients are reduced in conformity with the rules once the depth is extended, while there is a big gap (up to 5.10- m) and more to the strong boundary.

IV. CONCLUSIONS

According to the SOG method we are able to find a model of appropriate seismic signal in order to research on a solution to the extraction of the impact surface and depth conditions to observe them separately; especially this method has been successfully applied for the study on dynamic characteristics (amplitude and specters) of reflection seismic waves.

The successful application of SOG method can help us to solve the following problems:

1. To estimate the errors of dynamic and kinematic measures;

2. To estimate dynamic corrections created by wave emission and receiving conditions;

3. To estimate the static corrections;

4. To study on changes of characteristics of reflection horizon concerning his structure and lithology composition;

5. To study on the characteristics of attenuation of transmission media;

6. To study on the velocity characteristics of the geological section.

The parameters of the media given by the SOG method will greatly contribute to the prediction of geological sections and in the direct search for the petroleum.

REFERENCES

1. Gurvich I.I., Truong Minh, 1971. Application of seismic observation grouping to definite the characteristics of for emission, reflection and  reception areas by seismic data. Geology and Exploration, 7. Moscow.

2. Gurvich I.I., Truong Minh, 1972. To evaluate the precision of the dynamic measure-ments by reflection seismic observation grouping. Geology and Exploration, 10. Moscow.

3. Trương Minh, 1982. Theory of seismic observation grouping applied to seismic stratigraphy. Oil and Gas J., 1. Hà Nội.

4. Truong Minh, 1987. Method of seismic observation grouping for the dynamic and kinematic analyses of the reflection wave. Dr. Sci. thesis, Nat. Libr. of SRV., Hà Nội; Nat. Libr. of R.F., Moscow.