保角变换在区域面波群速度反演中的应用

通过保角变换，把一个球面局部区域扩展到球面上更大的球台域，再由球台域解析延拓到整个球面域.作为约束条件，变换过程中面波速度保持不变.在变换后的球面域上用球谐函数来拟合速度函数，达到降低球谐系数阶数的目的.面波群速度的反演变成了球谐系数的线性化反演，由球谐系数计算反演分辨核以及方差.该方法的优点是计算速度快，等值线光滑，构造界限清晰，该方法同样适用于各种局部球面区域的分析.

APPLICATION OF CONFORMAL MAPPING IN REGIONALSURFACE WAVE GROUP VELOCITY INVERSION

Through conformal mapping,in which the group velocities keep unchanged,a regional spherical area can be extended to a much larger spherical segment area,and then to the whole sphere by analytical continuation. Representing velocities by spherical harmonic expansion on the sphere after transformation can greatly reduce the number of spherical harmonic coefficients needed.Thus the inversion of surface wave velocities turns into the linear inversion of spherical harmonic coefficients.The resolution kernel and the root square deviation of the inversion solution can be obtained by analyzing the spherical harmonic coefficients.The algorithm has advantages in a few aspects:fast computing speed,smooth contours,and clear tectonic boundaries.Theoretically,this method is applicable not only to the surface wave group velocity inversion,but also to various analyses of regional fields.