基于粘弹性球体地球模型的震后位移与重力变化计算软件

A User-Friendly Code for Calculating Post-Seismic Displacements and Gravity Changes on a Symmetric Viscoelastic Spherical Earth

在考虑地球曲率、成层结构、可压缩性与自重的前提下,Tanaka等[1-2]提出一套较为完备的粘弹性球体位错理论,可计算全球任意位置由地震产生的同震与震后形变(含位移、重力变化、大地水准面变化)。Gao等[3]给出了与上述理论相匹配、界面友好的计算软件,能计算30个震后时间点对应的震后形变。本研究针对Gao等的软件进行改进,可计算震后任意时间点对应的震后形变。新软件由3个部分组成:1)与32个震后时间点相对应的32套离散格林函数数值框架;2)格林函数插值计算程序,可针对上述32套格林函数数值框架进行插值运算,输出任意震后时间点对应的格林函数数值结果;3)积分计算程序,调用上述格林函数数值结果,计算任意类型地震在地表任意位置产生的同震与震后形变。一般情况下,使用者只需按要求准备辅助文件,提供发震断层模型和观测站位置信息,以及震中周围地区地幔粘滞性因子,先后运行格林函数插值计算程序和积分计算程序,即可计算出目标地震在地表任意位置产生的同震与震后形变。本文基于粘弹球体位错理论与弹性球体位错理论,分别计算2011年日本MW9.0地震引起的远场同震位移,2套结果的高度一致性证明了新程序的正确性。最后,介绍需要注意的若干事项,便于使用者掌握该软件。

Tanaka proposes spherical dislocation theories in a spherically symmetric, self-gravitating visco-elastic earth model. Gao presents user-friendly software that utilizes Tanaka＇s theory, which can be used to calculate the post-seismic deformations for 30 time points after the event. Based on the work of Gao, we introduce an updated code to compute post-seismic deformations, including geoid and gravity changes caused by an arbitrary seismic source at any position, for an arbitrary time that passes after an event. The code consists of three parts. The first part is 32 set of the numerical frames of the dislocation Green function （DGF）. Each frame contains a set of two-dimensional discrete numerical frames of DGFs on a symmetric earth model, according to a time point after the event. The second part is an interpolation program. Based on the above 32 sets of the numerical frame of DGF, the pro- gram can be used to calculate a set of DGF, according to an arbitrary time point after the event, as well as the mantle viscosity around the epicenter. The third part is an integration function, which per- forms hi-quadratic spline interpolation operations on the calculated frame of DGFs. The inputs of the integration function are the information about the seismic fault models and the observation points. Af- ter the user prepares the inputs in a file with a given format, the code will automatically compute the post-seismic deformations. Then, we calculate the co-seismic displacements caused by the 2011 To- hoku-Oki Mwg. 0 earthquake using the visco-elastic and full-elastic spherical dislocation theory, re- spectively. The two sets of results agree with each other very well. This verifies the correction of our new codes. Finally, we discuss several issues that require attention when using the code, which should be helpful for users.