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9EARTH SCIENCES
ON THE METHOD OF CALCULATING STATIC CORRECTIONS IN SEISMIC MEASUREMENTS
BASED ON GRAVITY DATA
Apanovich I.
Krasnoyarsk
Abstract
Density heterogeneities of the geological section are a distorting factor in the interpretation of seismic data. To account for changes in the speed of elastic waves in the upper part of the section, gravity prospecting is used, and for calculating static corrections, the directly proportional dependence of the speed of elastic waves on the density of rocks is used. The reduction results based on the calculated corrections are often unsatisfactory, therefore, a new method for calculating static corrections based on gravity survey data has been proposed. The technique is based on a physically simple concept of the interaction of bodies moving and exchanging impulses. The efficiency of the new technique is shown by calculating corrections for the seismic profile 820411 (in the area of the Siberian platform). The new method for calculating corrections can be applied in areas where seismic surveys have already been carried out in conjunction with gravity surveys.
Keywords: static corrections, seismic prospecting, gravity prospecting, low velocity zone, movement with momentum exchange.
A seismic wave is a process of propagation of the elastic vibration energy of rocks. Any impulse can be a source of a seismic wave: earthquake, explosion, vibration, shock. The real geological environment is heterogeneous, therefore, there is always a sequential transfer of the initial impulse from one part of the rock mass (mass) to another. The final link in this chain is the seismic receiver, which records the time during which the impulse is transmitted by the moving parts of the geological section. The travel time of a seismic wave (SW) or the total time of exchange of impulses at a distance "source - receiver" depends both on the number of fragments of the formation and on the ability of rocks to transmit oscillatory motion. This ability is described by acoustic stiffness (Z). In general, the pulse rate depends on the compression modulus, shear modulus and rock density.
The most differentiated in terms of physical properties is the upper part of the section (UPS). For seismic surveys, this is a low velocity zone (LVZ). The introduction of corrections for the influence of changing elastic properties of the upper layer is necessary for reliable correlation of useful waves on seismograms. Such corrections (static) at each point represent the difference between the actual time of registration of the wave and the estimated time of its arrival, provided that the points of excitation and reception of oscillations are on a given datum line. In practice, the introduction of static corrections at the time of SW arrival is not an easy operation. The complexity is due to the presence of density inhomogeneities in the UPS located both in the LVZ and in the upper part of the underlying layer. It is
especially important to take into account the influence of such inhomogeneities when searching for oil and gas in the conditions of Eastern Siberia (in the presence of trap bodies in the upper part of the sedimentary cover). Over the past several decades, gravity prospecting has been used to calculate corrections. The static correction values are calculated from the directly proportional dependence of the P-wave propagation velocity on the density of the UPS rocks at a given point. The results of the subsequent reduction of seismic materials according to such calculations in most cases turn out to be unsatisfactory.
By definition, the speed (u) of SW propagation is the ratio of the acoustic stiffness (Z) of the rock to its density (g). Therefore, an increase in density should lead to a decrease in speed. At great depths, this condition is not met, since the acoustic stiffness increases faster than the density increases. However, for LVZ (as a very heterogeneous rock stratum), the situation may be different. Here, the constituent parts of the layer differ significantly in mass. This means that when the energy of motion is transferred, the speed is directly proportional to the momentum and inversely proportional to the mass. The less the mass of an individual body, the greater the speed of movement can impart to it an impulse of equal magnitude. This not only follows from the simple laws of dynamics, but is also confirmed by the features of the propagation of a sound wave in an inhomogeneous substance. Indeed, the data in Table 1 directly indicate the existence of an inverse relationship "speed - density" for the propagation of a sound wave in gases.
Table 1
Density and speed of sound in gases (at 20 °C and normal pressure)_
Gas Speed of sound, m/s Density, kg/m3
Hydrogen (H2) 1286 0.0916
Helium 965 0.1785
Nitrogen (N2) 334 1.2748
Air 332 1.3178
Oxygen (O2) 315 1.4567
Argon 319 1.8185
CO2 260 2.014
Thus, it is possible to use the inverse dependence of the velocity of propagation of the energy of seismic vibrations on the mass of elements of a real geological section. We can estimate the mass indirectly by the density of rocks, which directly affects the results of gravimetric measurements. Let us consider the process of propagation of the energy of elastic vibrations in more detail. The acceleration (a), with which the transfer of momentum is associated, is the ratio of the change in speed to the time (t) during which this change occurred (a = Au / t). On the other hand, acceleration is the ratio of the force acting on the component of the cut (block) to the mass of this block: a = F / m. It follows from these equalities that Au = t • F / m. The change in speed in one second is directly proportional to the magnitude of the acting force and inversely proportional to the mass of the block involved in the transfer of momentum. (The product of force and time is impulse).
However, when transmitting an impulse, the speed is proportional to the acceleration. With respect to a stationary block of dense rocks, the impulse will impart a velocity, the magnitude of which will be inversely proportional to the mass of the block. Mathematically, with an increase in mass, a decrease in the change in velocity will mean the presence of a moving object with greater mechanical inertia. Classically mechanical inertness of a body is characterized by acceleration (a). The acceleration of gravity (ag) over blocks is an indicator of the amount of matter in the block, concentrated to the density c (the mass of the rocks of this block). In practice, we can characterize the mass of a block only indirectly, by measuring the acceleration of gravity. In fact, when taking into account the influencing force (seismic impulse) and the force of interaction of the block with the mass of the planet, we must characterize the dynamics of objects by true (physical) acceleration [2]. The true acceleration a characterizes the mobility of the block, characterizes the gravitational mass as the ratio of two forces. On the one hand, it is an influencing force (seismic wave energy) imparting a "mechanical" acceleration (a) to the block. On the other hand, the force of interaction of the block with the mass of the planet, which is fixed in practice by the magnitude of the acceleration (ag): a = a / ag. The more ag, (the greater the mass of the block rocks), the less true acceleration is imparted to it by the energy of the seismic wave.
Thus, the true acceleration, which characterizes the mobility of the components of the upper part of the section, is a function of the impacting impulse of the seismic wave and the acceleration of gravity as the gravitational characteristic of local objects with different densities located in this layer. A rigorous solution to the problem requires knowledge of the magnitude of the impulse. It is problematic to calculate the amplitude of rock displacement in the volume of the seismic beam at the level of the bottom of the "target zone". This means that it is necessary to solve the problem in practice, especially since the true acceleration in our analysis turns out to be dimensionless.
For the correct calculation of static corrections, it is necessary to use a gravimetric survey in an areal version over a network, the density of which corresponds to the detail of measurements along seismic lines. Currently, there are programs that allow you to quickly solve inverse three-dimensional problems of gravity prospecting with large data sets [3]. The final product of processing is information about the distribution of local objects with different densities in the near-surface area. The selection of geological objects should be carried out for local anomalies of gravity, in which the influence of rocks of the intermediate layer with real density is taken into account, and a correction for the height with the actual (according to the measurement results) vertical gradient is introduced.
In the proposed methodology, it is recommended to calculate the corrections based on the selection in the section of two layers of different structures. The upper layer is a piecewise differentiated stratum (LVZ). The underlying rocks are the second layer containing a significant number of near-surface geological objects with different densities. Calculation of static corrections in these layers is performed according to different algorithms.
LVZ. The initial data here are the values of the density of objects, selected for local anomalies, which are maximally correlated with the sizes of the LVZ inhomogeneities. Further calculations are not difficult and consist in calculating the regression coefficient, as well as in determining the "dynamic mass" of each elementary block of the layer of the physical-geological model (PGM). Calculations can be performed both for individual profiles and for the area as a whole. The
regression coefficient is calculated from the average values of the parameters and represents the increment in the SW velocity per unit mass (the coefficient is taken with a negative sign, since the "velocity - mass" dependence is inverse). Further, determining the true SW velocity in the LVZ as the product of the regression coefficient and the dynamic mass increment at each point, and taking into account the layer thickness, it is very simple to calculate the values of the wave travel time at each point, as well as the time change (corrections).
Second layer (bedrock). It is logical to assume that the fragmentation of the rocks of the second layer (due to the influence of tectonic and exogenous processes) also exists. However, the density heterogeneities of this part of the section in this region of the Siberian Platform are not fully formed in the form of a relatively consolidated layered strata. Obviously, it is impossible to fully use the inverse "velocity-density" relationship, because this layer represents an acoustically more
homogeneous thickness. Therefore, it is proposed to take into account the gravitational influence of layer objects on the basis of calculating the acoustic stiffness of rocks, since the density of rocks affects the speed of SW propagation (Z = u • g). To calculate the corrections, the theoretical dependence of the acoustic stiffness (Z) on the density is used at a known velocity of the longitudinal seismic wave. Published data on the properties of rocks of different composition were used (a total of 11 sets of values; Table 2). According to the data in the table, a graph is constructed that represents the linear dependence of the parameters: Z = 15844.3 • g - 26929404.48 (Fig. 1).
If the density of rocks and the SW velocity in them on the study area are in the interval corresponding to the constructed dependence, we have a real opportunity to determine the acoustic stiffness from the density values from a three-dimensional array obtained by solving the inverse problem of gravity prospecting.
Table 2
Density, acoustic stiffness and P-wave velocity in rocks of different composition
Rocks Density, kg/m3 Velosity, m/s Acoustic stiffness (n103), kg/sm2
Halite 2300 4180 9614
Mudstones, marl 2400 4500 10800
Sandstone, mudstones 2500 5000 12500
Granite 2610 5600 14616
Gneiss-granite 2630 5700 14991
Limestone 2650 5500 14575
Granodiorite 2670 5950 15886
Diorite, quartz-diorite 2780 6200 17236
Dolomite 2800 6300 17640
Dolerite, diabase 2950 6500 19175
Gabbro 3020 7000 21140
An illustration of the calculation method proposed by the author is the PGM of the upper part of the earth's crust, where seismic surveys were performed (profile 820411). The geoid level (0 m) is taken as the base of the LVZ; the second layer has a thickness of 1200 m. Gravity data are represented here by areal and profile measurements. On the profiles, the survey was carried
out with a step of 50 m. In general, reliable information is known at points along a network of approximately 500 x 500 m. The initial data was corrected for the density of the rocks of the intermediate layer. (Correction for the real value of the vertical gradient of the force of gravity was not introduced due to the lack of measurements).
The original field was decomposed into components using the COSCAD-3D program. The three-dimensional problem of gravity survey was solved for a total area of 880 km2. The array of initial values is specified over a 200 x 200 m network (22321 matrix nodes). When solving the inverse problem of gravity prospecting, the selection of the values of the density of objects in the first layer of the PGM was performed with a mean square error (MSE) of ±0.021 mGal. Based on these data, corrections were calculated along the profile line with a step of 200 m. The selection
of densities for local anomalies for the second layer of our PGM was performed with an MSE of ±0.004 mGal. Further, according to the known values of Z at each point of the profile, the true SW speed, double the time of its run in a layer with a thickness of 1200 m and changes in this time relative to the average value were determined. The corrections obtained for the first and second layers are summed up with their signs and a general graph is built (Fig. 2). The results of calculations for 171 points of profile 820411 are summarized in Table 3.
Fig. 2. Seismic section and graphics of static corrections on the materials of seismic shooting and gravity shooting
Table 3
The results of calculating the static correction for the gravitational influence of rock layers from the earth's surface to the geoid level and from the geoid level to a depth of 1200 m
Parameters Limits of change Average value
LVZ
Density, kg/m3 2436 - 2504 2472
Velosity SW, m/s 2856 - 5434 4050
Travel time SW, s 0.0732 - 0.2769 0.1597
Static correction, s -0.1172 - 0.0865 Total change 0.2037
Layer from the geoid level to a depth of 1200 m
Density, kg/m3 2615 - 2682 2653
Velosity SW, m/s 5546 - 5805 5693
Travel time SW, s 0.413 - 0.433 0.4215
Static correction, s -0.0113 - 0.0082 Total change 0.0195
LVZ + layer from the geoid level to a depth of 1200 m
Static correction, s -0.1235 - 0.0944 Total change 0.218
The results of the constructions testify to the efficiency of the proposed method for calculating corrections. First, operating on the gravitational effects of the geological bodies of the real section, we obtained the amplitude of the static correction values even slightly higher than in the seismic reduction (0.218 s versus 0.190 s; see Fig. 2). Secondly, comparing the two versions of the amendments, one can more objectively judge the nature of the studied geological objects. In our example, it can be seen that a pronounced object in the lower part of the Cambrian deposits is clearly fixed by a difference anomaly (the
object is shaded in the figure). With a possible correction of the corrections (a decrease in the SW arrival time), the uplift associated with the accumulation of Cambrian salts will be even more pronounced.
A smoother form of the curve of "gravity" values of At is associated with the use of data from a sparser observation network. In real conditions of the Siberian Platform, for calculating corrections for the density inhomogeneities of the section, the observation step for individual seismic lines can be 200 m. To assess the geometric parameters of geological bodies (three-
dimensional or two-dimensional), it is necessary to carry out observations along two more parallel profiles spaced from the central one by 400-500 m. This will allow eliminating large errors when solving the inverse problem of gravity prospecting. The presence in the area of work of significant differences in the heights of the earth's surface will require measurements of the vertical gradient of the force of gravity to reduce the field Ag. Such measurements should be carried out in the areas of negative and positive anomalies Ag in a volume sufficient to plot the "Wzz - density" dependence. The probable presence of such a dependence was established by measuring Wzz in the Avacha area in 2018 [1].
REFERENCES:
1. Apanovich I.A. On the physical nature ofthe vertical gradient of the force attraction. Norwegian Journal of development of the International Science. № 25/2018. Part 1. Oslo, Norway, p. 3-8.
2. Apanovich I.A. 66 postulates and hypothesis about the device of the world. Norwegian Journal of development of the International Science. № 27/2019. Part 2. Oslo, Norway, p. 8-14.
3. Kochnev VA., Khvostenko V.I. An adaptive method for solving inverse problems of gravimetry // Geology and Geophysics, 1997, No. 7. P. 120-129.
