UDC 550. 348.425.4 N. I. ShishkinThe seismic energy transferred to an elastic half-space as a result of a contact explosion and a meteorite impact on a planet's surface is estimated. The seismic efficiency of the explosion and impact are evaluated as the ratio of the energy of the generated seismic waves to the energy of explosion or the kinetic energy of the meteorite. In the case of contact explosions, this ratio is in the range of 10 −4 -10 −3 . In the case of wide-scale impact effects, where the crater in the planet's crust is produced in the gravitational regime, a formula is derived that relates the seismic efficiency of an impact to its determining parameters.Introduction. Estimating the seismic energy transferred to the medium as a result of underground explosions and impacts of space bodies on the Earth is important for predictions of the seismic effect on engineering facilities, biota, the Earth's crust, and the planet as a whole.The energy of seismic motion for underground atomic explosions is determined in [1], where it is shown that the seismic efficiency (SE) k s ≡ E s /E 0 (E s is the energy of seismic waves and E 0 is the energy of explosion) has the following values: 0.1% in alluvium, 1.2% in tuff, 4.9% in rock salt, and 3.7% in granite. These data were obtained for fairly great charge depths. As the charge depth decreases, the value k s increases. As shown in [2], a decrease in the charge depth results in an increase in the SE to a value close to 10%.The seismic efficiency of a high-velocity impact was evaluated in [3][4][5][6][7][8]. From the papers cited, it follows that the value of k s was estimated with a large error (k s = E s /E 0 = 10 −6 -10 −2 , where E 0 is the kinetic energy). Its dependence on the parameters determining the seismic effect of impacts is also unclear. The value k s for contact explosions is not known.The object of the present study is to obtain the functional dependence of the seismic efficiency on the determining parameters in the cases of contact explosions and high-velocity impacts.1. Confined Explosion. The seismic effect of a confined underground explosion in rock is described using the Haskell model [1]. The longitudinal P -wave generated by an explosion is characterized by the potential ϕ(t, r) of the displacement field u(t, r) of the form Here t is the time reckoned from the time of explosion, r is the distance from the point of explosion, c P is the propagation velocity of the longitudinal waves, and f (τ ) is a function of the source equivalent in the generated P -wave to the explosion. Relation (1.1) contains three free parameters: t 0 , Φ(∞), and B, which are chosen from experiments. The physical meaning of these parameters is as follows. The parameter t 0 determines the time scale
Analytic representations are obtained for the displacement and stress fields in the Rayleigh surface wave (R-wave) generated in an elastic half-space by an internal source that produces the same seismic P -wave as an underground explosion. Oscillograms, particle trajectories, and stresses in the halfspace and on its surface are calculated. Relations for the energy flux in the R-wave are obtained. For rock salt, the fraction of the explosion energy transferred to the R-wave is estimated. It is established that this fraction can reach values of about 1% of the total explosion energy if the explosion is a contained one. As the charge depth is increased, the energy of the R-wave decreases in approximately inverse proportion to the depth.Introduction. Elastic surface Rayleigh waves (R-waves) [1] result from dynamic actions on the surface of elastic bodies. In structures of small dimensions, they are used as ultrasonic waves. Rayleigh waves are also observed in large structures and engineering constructions. In addition, R-waves are produced by explosions, earthquakes, and impacts of cosmic bodies on the planets. Seismic R-waves are used to probe the Earth's crust and to study its structure, and long R-waves are used to study the Earth's mantle. Rayleigh waves produced by explosions contain a significant fraction of the explosion energy, and at a certain distance from the epicenter, they dominate the other seismic waves. They contain information on the energy source and the properties of the medium. For example, records of R-waves from some underground nuclear explosions suggest that spall fracture of the medium occurs at the epicenters of the explosions [2]. In [3], it is shown that during impacts of cosmic bodies on the Earth, the focusing of R-waves in the antipode region (the region opposite to the site of impact) can lead to the formation of unusual geological structures such as explosion pipes or diatremes.Rayleigh waves produced by a point source in an elastic half-space were considered in [4][5][6]. Petrashen' [7] studied the Lamb problem for the case of an isotropic elastic sphere and obtained expressions for Rayleigh waves on the surface of an elastic sphere. Onis'ko and Shemyakin [8] studied the movement of the ground surface for an explosion in a half-space, and Alterman and Abramovici [9] explored the movement of the surface of an elastic sphere for a contained explosion. Brekhovskikh [10] investigated Rayleigh waves produced by a harmonious source and propagating along the curved surface of an elastic body. The present paper gives more detailed results for Rayleigh waves on both the surface of an elastic half-space and inside it for explosions at a great depth. The energy flux transferred by the Rayleigh wave is considered, and the fraction of the explosion energy converted into the R-wave energy is estimated. Such data are required to obtain more exact estimates of the damage to various engineering constructions from R-waves and describe the dynamic geological processes occurring in the regions that are ...
BackgroundAlterations in motor control systems is an inevitable consequence of space flights of any duration. After the flight, the crew-members have significant difficulties with maintaining upright balance and locomotion, which last several days following landing. At the same time, the specific mechanisms of these effects remain unclear.ObjectivesThe aim of the study was to assess effects of long-term space flight on postural control and to define the changes of sensory organization caused by microgravity.Methods33 cosmonauts of Russian Space Agency, the members of International Space Station (ISS) flights of duration between 166 and 196 days took part in this study. Computerized Dynamic Posturography (CDP) tests, which include assessment of visual, proprioceptive and vestibular function in postural stability, was performed twice before the flight and on the 3rd, 7th, and 10th days after landing. The video analysis of ankle and hip joints fluctuations was performed to investigate the basis of postural changes.ResultsExposure to long-term space flight was followed by considerable changes of postural stability (−27% of Equilibrium Score value in the most complicated test, SOT5m). Changes in postural strategies to maintain balance were observed in the tests which provide the challenge for vestibular system. In particular, increased hip joint involvement (+100% in median value and +135% in 3rd quartile of hip angle fluctuation RMS in SOT5m) into postural control process was revealed.ConclusionDecrease of postural stability after long-term space flight was associated with alterations in vestibular system and biomechanically was revealed by increased hip strategy which is less accurate, but simpler in terms of the central control.
The problem of propagation in ground of seismic waves generated by an underground explosion is usually formulated as the problem of propagation, in an elastic half-space, of waves generated by a localized source. This problem was examined in [1][2][3], where the motion of a free surface was studied. In this paper, we study displacements at internal points of the half-space and also residual displacements that occur therewith. The investigation of the motion of internal points of the medium is necessary for the analysis of elastic waves recorded upon underground explosions when the recording instruments are located inside the medium [4]. Buckling of the ground surface in an underground explosion is connected with residual displacements.1. We examine the motion that occurs in an elastic half-space as a result of a confined explosion. The explosion occurs at depth z = z0 under the free surface of the half-space related to the coordinate system OrOz with the direction of the axes shown in Fig. 1. The center of the explosion is at the point (r, z) = (0, z0). Figure 1 also shows the edges of the waves that arise: the longitudinal wave P generated by the explosion, the longitudinal wave PP reflected from the free surface, and the reflected transverse wave PS.The diverging spherical longitudinal wave generated by the explosion is described by the potential ~o*(t, r, z) of the displacement field of a source that is equivalent to the explosion:cp is the propagation velocity of the longitudinal waves, and ~(~), to, and B are the Haskell parameters that characterize the source [5]. The product ~)(oo)f(x) is called the reduced potential [~(oo) is the stationary value of the reduced potential, and f(x) is the source function].The parameter r which has the dimension of volume, can be treated as the volume introduced into the elastic medium as a result of the explosion. It is proportional to the volume of the camouflet cavity and is related to its dimensions by the approximate relation [6] ~(cx~) ..~ rc3/3, where rc is the radius of the cavity.The parameter to --the characteristic time of wave radiation --is close to the ratio rl/cp, where rl is the radius of an elastic radiator that is equivalent to the explosion, or the Sharpe radius [7]. In turn, the value of rl is close to the radius of the rupture zone near the center of the explosion. According to the estimate of Rodionov [8], rl = (E/3a.)lDrc, where E is Young's modulus and a. is the compression strength of the medium.The dimension of the camouflet cavity can be calculated from empirical relations, for example, by the Heard formula [9]: re = 16.3 Q~176176176 0"11) m [re and z0 in meters, Q in ktons, # (shear modulus) and E in megabars, and p0 is the strength of the medium in grams per cubic centimeter].The nondimensional parameter B is adjustable. It allows one to select the value of the reduced potential in accordance with the experiment. In this case, 0 ~< B <~ 0.5.The source function f(x) satisfies the conditions f(0) = f'(0) = f"(0) = fro(0) = 0, which ensure the cont...
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