黏弹性固体中地下爆炸辐射地震波能量的演化

地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律，分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论，给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法，建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料，计算给出了地震波能量的传播特征，分析了地下爆炸辐射能量的传播衰减规律。结果表明:（1）在黏弹性介质中，某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中，某球面处流入的能量在几倍弹性半径外即可稳定到某一定值；（2）在某一固定的有限观测区域内，当观测时间足够长时，势能和耗散能均趋于某一定值，辐射动能趋于零；（3）当有限的观测区域能容纳一个完整波长的地震波时，地震波辐射动能的稳态值随波传播距离的增大而减小，总体上可以用指数函数和幂函数进行分段拟合。

Evolution of the radiated seismic wave energy of underground explosion in visco-elastic solids

The energy coupling between the underground explosion and the medium and the wave propagation mechanism in the medium are important bases for understanding the physics of the underground explosion source. In order to study the law of the propagation and attenuation for the seismic wave energy of underground explosion, the composition of the radiated energy of underground explosion in viscoelastic medium was analyzed, and the formulas for calculating inflow energy, outflow energy, radiated kinetic energy, potential energy and dissipation energy in a limited observation region were given. Based on the theory of viscoelastic spherical wave in infinite medium, the theoretical solutions of velocity, displacement, stress and strain in the Laplace domain were given by using the exponential attenuation pressure model and the generalized Maxwell viscoelastic model. The numerical solutions of velocity, displacement, stress and strain were given by using the Laplace numerical inverse method, and the inflow energy, outflow energy, radiated kinetic energy, potential energy and dissipation energy were calculated by these numerical results. The numerical results of different components of seismic wave energy are consistent with the theoretical results, and the correctness of this method is proved. Using the dry loess as typical viscoelastic material, the radial stress and particle velocity at different radii were calculated, and the relationship between the inflow energy at different radii and the wave propagation distance was obtained. The spatial distributions of the radiated kinetic energy of seismic wave were calculated by using the spatial distributions of the radial particle velocity at different times, and the propagation law of the radiated kinetic energy was obtained. The changes of the inflow energy and the radiated kinetic energy with the propagation distance in the limited observation area were analyzed, and the results show as follows: (1) In a viscoelastic medium, the energy flowing into a sphere surface decreases gradually with the increase of radius. In an ideal elastic medium, the energy flowing into a sphere surface at the elastic radius of about several times can be stabilized to a constant value. (2) The potential energy and the dissipative energy tend to constant values when the observation time is long enough in a fixed limited observation region, and the radiated kinetic energy tends to zero. (3) When a limited observation area can hold the seismic waves with complete wave length, the steady-state value of the radiated kinetic energy of seismic waves decreases with the increase of the wave propagation distance. In general, exponential function and power function can be used for piecewise fitting of the attenuation law for the steady-state value of the radiated kinetic energy of the seismic wave.