地球横向不均匀结构对地表以及空间固定点同震重力变化的影响

本文提出一个新算法,用来高精度计算三维不均匀地球模型中地震位错引起的地表以及空间固定点同震重力变化.具体地说,我们首先把实际三维不均匀地球分解成球对称地球模型和对应的横向不均匀增量,分别进行计算,二者对应的计算结果分别称为球对称解和三维响应.由于球对称解可直接利用球对称地球模型位错理论计算得到,本文的目标是计算三维响应即地球的横向不均匀结构对同震重力变化的影响.然后,我们把三维响应再分为震源的响应和地球横向不均匀结构的响应,它们可分别借助对震源函数的扰动以及对平衡方程式的变分求解.本文推导出六个特殊点源位错引起的地表以及空间固定点同震重力变化计算公式(一个垂直走滑位错,两个相互垂直的倾滑位错,三个开裂位错),对这些公式进行适当组合就可以计算任意位置任意类型位错产生的同震重力变化,对应的计算公式同步给出.接着,依据36阶P波速度模型,我们利用岩石试验经验关系式推导出三维S波速度模型,密度模型,位场模型以及重力模型.最后,利用上述三维模型,本文计算出三种典型类型的点源位错产生的同震重力变化,结果显示三维响应与位错类型,震源深度都有关系,其最大响应占球对称解的0.5%左右,且在所有影响因素中S波速度模型影响最大.数值结果同时表明,三维响应中震源的响应与地球横向不均匀构造的响应处于同一量级.本文给出的地表和空间固定点同震重力变化计算公式可分别高精度解析地表重力和卫星重力观测数据(GRACE、GOCE等),提高大地测量数据理论解析水平.

Effects of earth's lateral heterogeneity on co-seismic gravity changes at deformed earth surface and space-fixed point

We present new formulae to study the co-seismic gravity changes on both the deformed earth surface and the space-fixed point caused by point dislocations buried in a 3-D heterogeneous, spherical earth model. Specifically, first we express the solutions by the sum of unperturbed gravity changes on a spherically symmetric earth model and the effects of earth's laterally inhomogeneous structures (3-D effect). Because that the unperturbed solutions can be calculated directly using spherical dislocation theory for a layered earth model, the arm of this paper is to calculate the 3-D effects. Then we deliberately decompose the 3-D effects into two contributions: the effect of seismic sources and the effect of earth's laterally increments, which are obtainable respectively by perturbations of seismic source functions and equilibrium equation. Next,we present formulations for six point seismic sources: one vertical strike-slip, two vertical dip-slips perpendicular to each other, and three tensile openings on three perpendicular planes. A combination of the six dislocations is useful to compute the 3-D effect resulting from an arbitrary seismic source at an arbitrary position, which is also presented in this paper. Then, using the experience relations of rock testing we deduce density model and S-wave velocity model based on 3-D P-wave velocity model (36 degrees). We also deduce potential model and gravity model from the deduced density model. Finally, based on above 3-D models we calculate the co-seismic gravity changes resulting from three types point dislocations. Results show that the maximum 3-D effect on co-seismic gravity changes, which varies concomitantly with the dislocation types, is about 0.5% of the corresponding unperturbed solutions. Among those parameters the effect of S-wave velocity is biggest. For the 3-D effects, our numerical results show that the contributions of effect of earth's laterally increments are of the same level as those of dislocation source. The formulae presented by this paper can be used to better explain nowadays high accuracy gravity data observed by satellite gravity mission such as GRACE and GOCE, as well as those observed by gravimerty in situ on Earth's surface.