分析地震波估算地壳内的应力值
AN ESTIMATION OF CRUSTAL STRESS VALUE FROM ANALYSIS OF SEISMIC WAVES
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摘要: 本文讨论了利用破裂力学理论说明地震破裂的过程, 认为地震本质上是岩石在应力作用下的低应力破裂现象.它是岩石中的裂纹不断稳态扩展、最后进入失稳扩展的结果.分析了在扩展过程中应力和位移的变化, 发现任何将要破裂的那一点的应力都要由初始应力0升高到屈服应力y 以后才破裂, 破裂后裂纹面上的点的应力降到0.在破裂前和破裂后的位移, 都可由弹性力学方程给出.在破裂的一瞬间破裂的端点产生的非弹性位移, 则不能由弹性力学方程给出.它可以由断裂力学中的裂纹滑开位移公式近似给出.根据位错模式由于计算弹性波辐射场的位错量 D(, t), 正是破裂瞬间产生的非弹性位移, 所以用弹性位移公式来计算地震位错量是错误的.我们采用了裂纹滑开位移公式来计算地震位错量, 从而导出了较合理的计算地震释放总能量的公式 ET=yDS(y 为屈服强度;D为平均位错;S 为断层面积)以及估算初始应力值0的公式:0 =[Dmax/L4y/(1-) ]1/2(L 为断层长度).用它们计算了一些地震的 Er 和0, 分别列于表1和表2.这些结果比以往的结果要更合理一些。 结果表明:(1)地震多数是在低应力作用下(即低初始应力)发生的(约100——200巴);(2)地震释放的总能量约比地震波能量大一个数量级.Abstract: In this work the process of earthquake rupture is studied by means of the theory of fracture mechanics. It is believed that the phenomenon of earthquake is essentially caused by the rupture of rock media under low shear gtress conditions. It is the result of continual development of cracks from the stable to the final unstable state. The change of stress and displacement in the process of crack development has been analysed from which one can see that the stress at any point where rupture will occur always undergo a rise from its initial value (0) to the yielding strength (y) before rupture. After rupture, the stress on the crack surface will drop to a low value near zero. The displacements before and after rupture can be calculated by the formulae of theory of elastic ity but at the instance of rupture, the inelastic displacement at the tips of crack is not given by the same formulae, which may be approximately obtained from the slide displacement formula in fracture mechanics. According to the dislocation model, it is because that the dislocation D(, t) from which elastic wave radiation field has been calculated is jusjt the inelastic displacement, at the instant of rupture. Therefore, to estimate stress drop and calculate earthquake dislocation by elastic displacement formulae will be erroneous. If the earthquake dislocation is estimated by the slide displacement formula in fracture mechanics, more adequate formulae for calculating the total energy ET(ET=yDS, y= yield strength, D= average dislocation, S = area of the fault surface) released by an earthquake andthe initial stress 0(0=[Dmax/L4y/(1-) ]1/2L=length of fault ) can be deduced.Using these formulae, the total energy ET released by some earthquakes and the initial stress To are estimated and listed in the table 1 and 2. They are more reasonable than before. They demonstrate that (1) most earthquakes take place under low initial stress, about 100-200 bars, (2) the total energy released by an earthquake is about one order of magnitude higher than the seismic wave energy.
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[1] K. Aki, Seismic displacements near a fault, J. Geophy. Res., 73, 16, 5359——5376, 1968.
[2] L. Knopoff, Energy release in earthquakes, Geopbys. J. Roy. Astro. Soe., 1, 1, 44——51, 1958.
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[7] 顾浩鼎, 陈运泰等, 1975年2月4日辽宁省海城地震的震源机制, 地球物理学报, 19, 4, 1976.
[8] K. Aki, earthquake mechanizm, Tectonophysics, 13, 1——4, 423——446, 1972.
[9] N. A. Haskell, Total energy and energy spectral density of elastic wave radiation from propagation faults, Bull. Sei.srn. Soc. Amer., 54, 6, 1811——1841, 1964.
[10] J. F. Knott, Fundamentals of fracture mechanics, London Butterworths, 1973.
[11] G. C. Sih, Mechanics of fracture, 1, 1973.
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[13] L. R. F. Rose. Recent theoretical and experimental result on fast brittle fracture, Int. J. Fract, 12, 6, 1976.[1] K. Aki, Seismic displacements near a fault, J. Geophy. Res., 73, 16, 5359——5376, 1968.
[2] L. Knopoff, Energy release in earthquakes, Geopbys. J. Roy. Astro. Soe., 1, 1, 44——51, 1958.
[3] A. T. Stan. Slip in a crystal and ?capture in a solid due to shear, Proc. Carnb. Phil. Soc., 24, 430——500, 1928.
[4] P. 0. Paris and G. l:. Sih, Stress analysis of cracks, ASTM——STP, 381, 1964.
[5] M. A. Chinnery, Theuretical fault models, Publ, Dominion. Obs., 37, 7, 211——223, 1969.
[6] V. I. Keilis——Borok, On estimation of the displacement in an earthquake source and of source dimensions. Ana. Geafis., 12, 2, 205——214, 1959.
[7] 顾浩鼎, 陈运泰等, 1975年2月4日辽宁省海城地震的震源机制, 地球物理学报, 19, 4, 1976.
[8] K. Aki, earthquake mechanizm, Tectonophysics, 13, 1——4, 423——446, 1972.
[9] N. A. Haskell, Total energy and energy spectral density of elastic wave radiation from propagation faults, Bull. Sei.srn. Soc. Amer., 54, 6, 1811——1841, 1964.
[10] J. F. Knott, Fundamentals of fracture mechanics, London Butterworths, 1973.
[11] G. C. Sih, Mechanics of fracture, 1, 1973.
[12] 陈培善等, 唐山地震前后京津唐张地区的应力场, 地球物理学报, 21, 1, 1978
[13] L. R. F. Rose. Recent theoretical and experimental result on fast brittle fracture, Int. J. Fract, 12, 6, 1976. -
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