Vertical direction amplitude analysis method for ocean bottom seismograph
1. A vertical direction amplitude analysis method for an ocean bottom seismograph is characterized by comprising the following steps:
step 1: establishing a mass-spring-damping coupling model in the vertical direction based on the ocean bottom seismograph;
step 2: solving the model in the step 1 to obtain a transfer function and an amplitude in the vertical direction;
and step 3: based on the amplitude of the step 2, establishing an amplitude response model according to the actual situation;
and 4, step 4: and (3) analyzing a method for improving the system response based on the amplitude response model established in the step (3).
2. The method for analyzing the vertical amplitude of the ocean bottom seismograph according to claim 1, wherein the step 1 is specifically to establish a mass-spring-damping model based on the six factors of the gravity borne by the seismograph, the buoyancy borne by the seismograph, the seismic wave acting force borne by the seismograph, and the influence of the additional mass, the sediment layer and the background noise generated by the flow of the seawater, wherein the additional mass shows that the seismograph can move with the surrounding seawater and the sediment.
3. The method for analyzing the vertical amplitude of the ocean bottom seismograph according to claim 2, wherein the step 2 specifically comprises the following steps:
step 2.1: establishing a dynamic balance equation after the solid-liquid interface is brought into the submarine seismograph based on the influence of six factors;
step 2.2: deriving a transfer function G(s) by the dynamic equilibrium equation of step 2.1;
step 2.3: the amplitude is derived by the transfer function g(s) of step 2.2.
4. The method for analyzing the vertical amplitude of the ocean bottom seismograph according to claim 3, wherein the step 2.1 is to establish a dynamic equilibrium equation after the ocean bottom seismograph is placed at a solid-liquid interface under the influence of six factors;
wherein M iswThe quality of the drained water; msTo exclude the quality of the deposited layer;adding water mass to the system in the vibration process;adding the quality of a deposited layer in the system vibration process;is the mass of the entire system; d is an equivalent damping coefficient; k is the equivalent elastic coefficient; x is the displacement of sinking when the ocean bottom seismograph is placed on the ocean bottom sediment layer; z is a radical ofaDisplacement of the sea floor under the overall action;refers to the sum of the forces that the system is subjected to in a subsea environment; dx' is the damping force of the system; kx is the elasticity suffered by the system;is the gravitational force to which the system is subjected;is the buoyancy to which the system is subjected;the device is characterized in that water and sediment which are discharged and move together by the ocean bottom seismograph are subjected to integral acting force and are placed into the ocean bottom seismograph.
5. The method for vertical direction amplitude analysis of ocean bottom seismographs according to claim 3, wherein the step 2.2 is specifically that the transfer function g(s) is derived as follows:
in the formula ZbRepresenting Laplace transformation of seabed solid-liquid interface displacement after the seismograph is placed; zaLaplace transform representing the displacement of the seabed solid-liquid interface before the seismograph is placed; ω is the angular frequency; omega0Is the system resonance angular frequency; i represents a real number domain; c is a buoyancy factor; zeta is the damping ratio of the coupling system; the final result of the formula (2) represents the real motion situation of the seismograph along with the seabed solid-liquid interface; as long as the area in contact with the bottom does not change with the movement of the OBS, equation (2) holds; wherein:
wherein the content of the first and second substances,andthe mass of the discharged water and sediment corresponding to the static balance; rhosIs the density of the deposited layer; rhowIs the density of seawater; and S is the upper surface area of the vertical cylindrical ocean bottom seismograph.
6. The method for vertical amplitude analysis of an ocean bottom seismograph according to claim 3, wherein the step 2.3 is to make W ═ ω/ω0According to the transfer function, the corresponding amplitudes are:
7. the method for vertical direction amplitude analysis of the ocean bottom seismograph according to claim 1, wherein the step 3 specifically comprises the following steps:
step 3.1: analyzing the influence of different arrangement depths on the amplitude, and observing the relation between the change of the buried depth and the system amplitude;
step 3.2: analyzing the influence of the layout environment of different parameters on the amplitude, and observing the relation between the change of a deposition layer from soft to hard and the system amplitude;
step 3.3: and analyzing the influence of the appearance of the seismograph on the amplitude in a specific environment, and observing the relation between the height change of the cylindrical seismograph and the system amplitude.
Background
The detection of seismic waves generated by a remote source by deploying a marine seismograph at the sea floor is a good way to obtain marine information. Offshore, ocean bottom seismographs are subject to complex background noise in addition to the seismic waves they are intended to detect. The traditional ocean bottom seismograph is designed into a spherical or hemispherical shape and is arranged at a solid-liquid interface of the ocean bottom through a coupling frame, and most of a shell of the seismograph is positioned in seawater. Because the seabed interface is mostly soft silt, the signal detection effect is not obvious due to the impact of water flow or the inclination of the seismograph, and the complex background noise of the offshore environment further restricts the detection distance of the seabed seismograph. In order to improve the information acquisition capability of a long-distance seismic source, the signal detection capability of the ocean bottom seismograph needs to be improved. At present, the analysis of the signal acquisition capability of the ocean bottom seismograph is mostly judged by an actual test effect in a heuristic mode, although the reliability is high, the cost is too high, the analysis is not carried out theoretically, and a specific guideline cannot be formed. Factors influencing the detection of submarine seismic wave signals are theoretically analyzed by building a model to guide the design and layout of submarine seismographs, and the method has important significance for submarine seismic observation at present.
The existing method gives a design principle aiming at the seismograph, and does not deeply explore the problem of influence of a specific layout environment on system response; or the influence of background noise on the seismograph is neglected during modeling, and the obtained result only can represent the response of the ocean bottom seismograph under the action of seismic waves.
Disclosure of Invention
The invention provides a vertical direction amplitude analysis method for an ocean bottom seismograph, which is used for solving the problems and establishing an ocean bottom seismograph coupling model at a solid-liquid interface, and has universality in consideration of various complex conditions.
The invention is realized by the following technical scheme:
a method for vertical direction amplitude analysis of an ocean bottom seismograph, the method comprising the steps of:
step 1: establishing a mass-spring-damping coupling model in the vertical direction based on the ocean bottom seismograph;
step 2: solving the model in the step 1 to obtain a transfer function and an amplitude in the vertical direction;
and step 3: based on the amplitude of the step 2, establishing an amplitude response model according to the actual situation;
and 4, step 4: and (3) analyzing a method for improving the system response based on the amplitude response model established in the step (3).
Further, the step 1 is specifically to establish a mass-spring-damping model based on the influence of six factors, namely, the gravity borne by the seismograph, the buoyancy borne by the seismograph, the seismic wave acting force borne by the seismograph and the seawater flow, wherein the additional mass, the sediment layer and the background noise are generated, and the additional mass shows that the seismograph can move together with the surrounding seawater and sediments.
Further, the step 2 specifically includes the following steps:
step 2.1: establishing a dynamic balance equation after the solid-liquid interface is brought into the submarine seismograph based on the influence of six factors;
step 2.2: deriving a transfer function G(s) by the dynamic equilibrium equation of step 2.1;
step 2.3: the amplitude is derived by the transfer function g(s) of step 2.2.
Further, the step 2.1 specifically comprises the step of establishing a dynamic balance equation after the solid-liquid interface is placed into the ocean bottom seismograph under the influence of six factors;
wherein M iswThe quality of the drained water; msTo exclude the quality of the deposited layer;adding water mass to the system in the vibration process;adding the quality of a deposited layer in the system vibration process;is the mass of the entire system; d is an equivalent damping coefficient; k is the equivalent elastic coefficient; x is the displacement of sinking when the ocean bottom seismograph is placed on the ocean bottom sediment layer; z is a radical ofaDisplacement of the sea floor under the overall action;refers to the sum of the forces that the system is subjected to in a subsea environment; dx' is the damping force of the system; kx is the elasticity suffered by the system;is the gravitational force to which the system is subjected;is the buoyancy to which the system is subjected;the device is characterized in that water and sediment which are discharged and move together by the ocean bottom seismograph are subjected to integral acting force and are placed into the ocean bottom seismograph.
Further, in the step 2.2, specifically, the transfer function g(s) is derived by:
in the formula ZbRepresenting Laplace transformation of seabed solid-liquid interface displacement after the seismograph is placed; zaLaplace transform representing the displacement of the seabed solid-liquid interface before the seismograph is placed; ω is the angular frequency; omega0Is the system resonance angular frequency; i represents a real number domain; c is a buoyancy factor; zeta is the damping ratio of the coupling system; the final result of the formula (2) represents the real motion situation of the seismograph along with the seabed solid-liquid interface; as long as the area in contact with the bottom does not change with the movement of the OBS, equation (2) holds; wherein:
wherein the content of the first and second substances,andthe mass of the discharged water and sediment corresponding to the static balance; rhosIs the density of the deposited layer; rhowIs the density of seawater; and S is the upper surface area of the vertical cylindrical ocean bottom seismograph.
Further, in step 2.3, W ═ ω/ω is specifically set0According to the transfer function, the corresponding amplitudes are:
further, the step 3 specifically includes the following steps:
step 3.1: analyzing the influence of different arrangement depths on the amplitude, and observing the relation between the change of the buried depth and the system amplitude;
step 3.2: analyzing the influence of the layout environment of different parameters on the amplitude, and observing the relation between the change of a deposition layer from soft to hard and the system amplitude;
step 3.3: and analyzing the influence of the appearance of the seismograph on the amplitude in a specific environment, and observing the relation between the height change of the cylindrical seismograph and the system amplitude.
The invention has the beneficial effects that:
1. the invention establishes a mass-spring-damping model in the vertical direction at the solid-liquid interface, and the model considers the influence of the additional mass and the background noise and has universality.
2. The invention does not need specific earthquake wave acting force and background noise acting force forms, obtains a system transfer function and an amplitude function of the ocean bottom seismograph, and analyzes factors influencing the amplitude response of the ocean bottom seismograph system through a simulation curve.
3. According to the invention, by setting parameters, response curves of different seismograph shapes, arrangement depths and arrangement environments are compared. The conclusion obtained by the method can guide the design and layout work of the ocean bottom seismograph, and the ocean bottom seismic signal observation capability is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the system of the present invention equivalent to a mass-spring-damping model to establish a vertical coordinate system.
FIG. 3 is a schematic illustration of the position of the coupling model of the present invention.
FIG. 4 is a schematic view of the invention at different deployment depths.
FIG. 5 is a graphical illustration of the amplitude response of the present invention for different deployment depths.
FIG. 6 is a schematic amplitude response diagram of a system in a different deployment environment of the present invention.
FIG. 7 is a schematic diagram of the amplitude response of the marine seismograph of the present invention in various shapes.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
A method for vertical direction amplitude analysis of an ocean bottom seismograph, the method comprising the steps of:
step 1: establishing a mass-spring-damping coupling model in the vertical direction based on the ocean bottom seismograph;
step 2: solving the model in the step 1 to obtain a transfer function and an amplitude in the vertical direction;
and step 3: based on the amplitude of the step 2, establishing an amplitude response model according to the actual situation;
and 4, step 4: and (3) analyzing a method for improving the system response based on the amplitude response model established in the step (3).
Further, the step 1 is specifically to establish a mass-spring-damping model based on the influence of six factors, namely, the gravity borne by the seismograph, the buoyancy borne by the seismograph, the seismic wave acting force borne by the seismograph and the seawater flow, wherein the additional mass, the sediment layer and the background noise are generated, and the additional mass shows that the seismograph can move together with the surrounding seawater and sediments.
Further, the step 2 specifically includes the following steps:
step 2.1: establishing a dynamic balance equation after the solid-liquid interface is brought into the submarine seismograph based on the influence of six factors;
step 2.2: deriving a transfer function G(s) by the dynamic equilibrium equation of step 2.1;
step 2.3: the amplitude is derived by the transfer function g(s) of step 2.2.
Further, the step 2.1 specifically comprises the step of establishing a dynamic balance equation after the solid-liquid interface is placed into the ocean bottom seismograph under the influence of six factors;
wherein M iswThe quality of the drained water; msTo exclude the quality of the deposited layer;adding water mass to the system in the vibration process;adding the quality of a deposited layer in the system vibration process;is the mass of the entire system; d is an equivalent damping coefficient; k is the equivalent elastic coefficient; x is the displacement of sinking when the ocean bottom seismograph is placed on the ocean bottom sediment layer; z is a radical ofaDisplacement of the sea floor under the overall action;refers to the sum of the forces that the system is subjected to in a subsea environment; dx' is the damping force of the system; kx is the elasticity suffered by the system;is the gravitational force to which the system is subjected;is the buoyancy to which the system is subjected;the integral acting force is the whole acting force of water and sediment which are arranged and move together by the ocean bottom seismograph, is transferred to the ocean bottom seismograph after being placed in the ocean bottom seismograph, and comprises seismic wave acting force and background noiseThe acoustic force, and thus regardless of the particular form of the background noise force, is expressed as a displacement zaA function of (a); g is the acceleration of gravity;
further, in the step 2.2, specifically, the transfer function g(s) is derived by:
in the formula ZbRepresenting Laplace transformation of seabed solid-liquid interface displacement after the seismograph is placed; zaLaplace transform representing the displacement of the seabed solid-liquid interface before the seismograph is placed; ω is the angular frequency; omega0Is the system resonance angular frequency; i represents a real number domain; c is a buoyancy factor; zeta is the damping ratio of the coupling system; the final result of the formula (2) avoids the specific action effects of background noise and seismic waves, and represents the real motion condition of the seismograph along with the seabed solid-liquid interface; as long as the area in contact with the bottom does not change with the movement of the OBS, equation (2) holds; wherein:
wherein the content of the first and second substances,andthe mass of the discharged water and sediment corresponding to the static balance; rhosIs the density of the deposited layer; rhowIs the density of seawater; s isThe upper surface area of the vertical cylindrical ocean bottom seismograph.
Further, in step 2.3, W ═ ω/ω is specifically set0According to the transfer function, the corresponding amplitudes are:
further, the step 3 specifically includes the following steps:
step 3.1: analyzing the influence of different arrangement depths on the amplitude, and observing the relation between the change of the buried depth and the system amplitude;
step 3.2: analyzing the influence of the layout environment of different parameters on the amplitude, and observing the relation between the change of a deposition layer from soft to hard and the system amplitude;
step 3.3: and analyzing the influence of the appearance of the seismograph on the amplitude in a specific environment, and observing the relation between the height change of the cylindrical seismograph and the system amplitude.
Example 2
An elastic system is formed between the ocean bottom seismograph and the sea water and sediment layer, as shown in figure 2, the system comprises: sea water 1, additional mass of sea water 2, ocean bottom seismometer 3, additional mass of sediment 4, sediment 5, simplifying the system into mass 6, spring 7, damping 8. Wherein the mass comprises an additional mass 2 of sea water, a marine seismometer 3, an additional mass 4 of the sediment layer, and the spring 7 and the damping 8 are equivalent effects of the sediment layer on the mass 6. The model simplifies the seismograph into a vertical cylindrical shape, thereby neglecting the complex situation generated by the shape and the bearing area along with the change of the buoyancy and the rigidity of the bottom. The influence of the additional mass in the marine environment is considered, so that the mass of the whole system is larger than that of the seismograph, and the comprehensiveness of the consideration is increased.
As shown in fig. 3, a vertical coordinate system is established for the mass-spring-damping model, and the mechanical analysis is performed on the process. After the submarine seismograph is placed on the solid-liquid interface, the submarine seismograph can sink x displacement due to the self weight and the complex action force of the seabed.
The ocean bottom seismograph is influenced by six factors of gravity, buoyancy, seismic wave acting force, background noise acting force, additional mass acting force and sedimentary deposit acting force (the acting force is equivalent to damping force and elastic force) on the seismograph. Suppose that: mwThe quality of the drained water; msTo exclude the quality of the deposited layer;adding water mass to the system in the vibration process;adding the quality of a deposited layer in the system vibration process;is the mass of the entire system; d is an equivalent damping coefficient; k is the equivalent elastic coefficient. Establishing a dynamic balance equation when the ocean bottom seismograph is disturbed:
whereinRefers to the sum of the forces that the system is subjected to in a subsea environment; dx' is the damping force of the system; kx is the elasticity suffered by the system;is the gravitational force to which the system is subjected;is the buoyancy to which the system is subjected;the integral acting force is acted on water and sediment which are arranged and move together by the ocean bottom seismograph, the integral acting force comprises seismic wave acting force and background noise acting force, and the integral acting force is equivalent to that acted on the water and sediment which are arranged and move together by the ocean bottom seismograph after being placed into the ocean bottom seismographThis force is transferred to the ocean bottom seismometer.
Because of z ″)I=z″a-x "into the above formula:
MI *x″+Dx′+Kx=(MI-Mw-Ms)(g+z″a) (2)
the formula of the buoyancy is introduced:
when the system is in a static equilibrium state, namely no earthquake wave or background noise disturbance, the system is only subjected to gravity buoyancy and elastic force, and x ″ ═ x ═ z ″, in this casea0. Submarine seismograph sinking displacement xeSatisfies the relationship:
xe=(MI-ρwSh)g/[K+(ρs-ρw)Sg] (4)
let y be x-xeAnd the displacement variation of the ocean bottom seismograph under the integral action force is represented, and the displacement variation is obtained by the following formula:
y is relative to xeIs an infinitesimal quantity, can be omitted, so the above equation is:
corresponding toAndthe corresponding mass of water and solids displaced at static equilibrium. The above formula is written as follows:
where ζ is the damping ratio of the coupling structure, ω0And C is a buoyancy factor. The following relationship is satisfied:
the bottom positions of the ocean bottom seismographs satisfy the relation:
zI=za-x=za-y-xe (11)
the displacement of the seismograph under the combined action of the seismic waves and the background noise can be expressed as:
zb=zI+xe=za-y (12)
and then performing Laplace transformation to obtain a transfer function of the ocean bottom seismograph:
in the formula ZbRepresenting Laplace transformation of seabed solid-liquid interface displacement after the seismograph is placed; zaLaplace transform representing the displacement of the seabed solid-liquid interface before the seismograph is placed; ω is the angular frequency; i denotes the real number field. The final result of the formula avoids the specific action effects of background noise and seismic waves, and represents the real motion condition of the seismograph along with the seabed solid-liquid interface. The above equation holds so long as the area of contact with the base does not change with the movement of the OBS.
Let W be ω/ω0According to the transfer function, the corresponding amplitude:
as can be seen from equations (13) and (14), the amplitude response of the system is related to C, W, ζ. Ideally, when C is 0, the transfer function g(s) is 1, and the amplitude a is 0, which means that the seismometer completely follows the seabed solid-liquid interface under the action of the seismic wave and the background noise, and the signal transfer effect is the best, and the placement of the seismometer does not affect the propagation of the seismic wave. In order to reduce the coupling influence of the seismograph to the maximum extent possible and better capture seismic wave signals, the amplitude response should be simple and gentle.
The effect of the deployment location on the amplitude response is considered below. Assuming that the seismograph is cylindrical, the radius R of the bottom supporting circular area is 250mm, the height h is 280mm, the mass of the seismograph is about 90Kg, and the volume is about 0.05m3. The seismographs were placed at the interface of the sediment and the seawater, with the height of the sections located in the seawater being 80mm, 140mm, 200mm, respectively. As shown in the three cases of fig. 4.
Setting the density of seawater to 1000kg/m3. The relation between the elastic coefficient K and the damping coefficient D and the sediment Poisson ratio v, the shear modulus G (Lame constant G), the substrate radius R and the density rho is as follows:
the Young modulus E and the shear modulus G, the Poisson ratio v satisfy the following conditions:
E=2G(1+v) (17)
if the sediment layer is arranged in a sediment layer environment with a Poisson ratio v of 0.30, relevant parameters of the sediment layer are calculated according to the formulas (15) to (17) as shown in the table 1:
TABLE 1 deposition layer Properties
The buoyancy factors of (a), (b) and (c) are calculated to be 0.38, 0.33 and 0.29 respectively. Note that the additional mass of these three cases should be different in theory,is less thanAnd isDecreases with increasing buried depth. The response curve was observed without the actual model, the additional mass was ignored to make the damping ratio ζ of the system equal to 0.50, and the equation (14) was substituted to obtain the amplitude responses in the three cases, as shown in fig. 5, and it can be seen that when the damping ratio was constant, the coupling level was continuously increased as the placement position was deepened. When considering the additional mass actually present, since there are many factors affecting ζ, when ζ is constant, the buoyancy factor C may be lowered due to the presence of the additional mass, but the trend thereof may not be changed for the response curve, and the coupling condition in the case (C) is still better than that in the cases (a) (b). The above analysis fully illustrates that the coupling level of ocean bottom seismographs increases with increasing depth of deployment. Deployment of ocean bottom seismographs by burial in an offshore environment is proposed. Meanwhile, the submarine seismic waves are transmitted near a solid-liquid interface, so the burying cannot be too deep to influence the detection intensity of seismic wave signals.
The effect of the buried environment of the seismograph on the coupling response is explored below. Similarly, assume that the seismometer is cylindrical, with a base-supported circular region having a radius R of 250mm, a height h of 280mm, and a base area of about 0.2m2The mass of the seismograph is about 90Kg, and the volume is about 0.05m3. It is arranged in seabed sediment layers with different densities. Is provided withThe density of the seawater is determined to be 1000kg/m3The properties of the layout environment and the coupling system are derived from equation (9) and equations (15) to (17) as shown in table 2:
TABLE 2 Properties of the deployment Environment and the coupling System
The amplitude curve of the response is shown in FIG. 6 when W < 1, i.e., ω < ω0The response is relatively gentle when ω approaches ω0The response amplitude also gradually increases, which indicates that the natural angular frequency ω should be increased when designing the seismograph0And the seismic detector is far away from the working interval of the seismic detector. As can be seen from the formula (8), the seismic sensor should be arranged at a place with a large elastic coefficient, and the contact area of the bottom surface is increased, so that the overall mass of the seismic sensor is reduced, and the vertical height of the seismic sensor is required not to be too high. However, as can be seen from equation (10), ω0When the coupling coefficient is increased, zeta is reduced, but coupling is not facilitated, and comprehensive consideration should be given to design. The response curve flattens as the buoyancy factor C decreases, and according to equation (9), the seismometer mass should be reduced, the solids-displaced mass increased, and placed in dense sediment layers. The damping ratios calculated by the above equations are 0.49, 0.60, 0.61 respectively, and as the damping ratio increases, the response of the system becomes smoother and simpler (the optimal case is when the time required for the system to return from vibration to stationary is shortest in the case of critical damping). However, it should be noted that the calculation result obtained according to the formula is only a preliminary reference, various medium conditions, arrangement modes and various complex factors influence the damping ratio, and in practice, ζ should be close to 1.
The effect of seismometer size on coupling response in a particular environment is explored below. The seismograph layout environment is buried in the sediment layer (b). The seismic instrument hull is assumed to be a simple cylinder with a mass of about 90kg and a volume of about 0.05m3The corresponding buoyancy factor C is 0.15. In order not to affect the size and placement of the sensing modules of the seismometer, the height of the seismometer should not be less than 200 mm. Obtaining the earthquake according to the formula (10) and the formulas (15) to (17)The properties of the meter and coupling system are shown in table 3. The forms of the models 1-3 may be described as "short, coarse", "uniform", "intermediate".
TABLE 3 attributes of seismometers and coupled systems
The corresponding system amplitude response curve is shown in fig. 7, and it can be seen that when the mass and the volume of the seismograph are constant, the damping ratio of the system continuously rises along with the increase of the radius of the bottom surface, the response curve becomes more and more gentle, and the coupling effect is better and better. Namely, the short and thick type is superior to the thin and high type and the intermediate type.
In conclusion, the invention obtains the transfer function and the amplitude response function of the ocean bottom seismograph by establishing the mass-spring-damping coupling model, and obtains the system response related to the appearance, the arrangement position and the arrangement environment of the ocean bottom seismograph by analysis. Deducing that the contact area of the bottom surface should be increased when the seismograph is designed, and reducing the overall mass of the seismograph; the submarine seismograph cabin body with the same mass and volume is shorter and thicker than the small and tall type and the middle type; methods of burying the coupling in environments with high spring rates and high damping rates have been proposed to improve coupling capability. The model established by the invention is suitable for various complex conditions, provides a guiding guideline for the design and layout work of the ocean bottom seismograph, and has important significance for improving the ocean bottom earthquake observation capability.
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