局部重力场球冠谐分析中的导数计算及应用

在建立局部地区的地球重力场模型中,球冠谐分析是一种有效的方法。在球冠坐标系下建立重力场模型时,仅涉及到重力位的垂向分量,不必进行关于极角的微分运算,所以仅用单个正交基来建模,但若要在球冠坐标系下对重力场作进一步分析,如类似于平面处理的导数运算,来突出地质体的边界,要计算极角的微分,利用单个正交基表示则不易收敛,且误差较大。本文中作者采用两个正交基函数在球冠坐标系下对重力场建模,推导计算了径向导数和曲面导数模,并利用棱柱体正演模型进行检验,结果表明双基函数建模更适合曲面上的位场表示。最后计算了冲绳海槽地区卫星测高重力异常数据的曲面导数,径向导数清晰划分了东海陆架上大构造单元,曲面导数梯度带显示了东海陆架外缘隆起带,也指示了陆架盆地内的一些局部构造。这表明双基函数的球冠谐分析是一种有效的曲面位场建模方法。

DERIVATIVE CALCULATION AND APPLICATION IN SPHERICAL CAP HARMONIC ANALYSIS OF LOCAL GRAVITY FIELD

Spherical cap harmonic analysis is an effective method for modeling a local gravity field,in which only the vertical component of gravity potential is calculated,and no differentiation to pole angle is needed; therefore,only one set of orthogonal functions would be required.However,for a further analysis in detail of the internal gravity field in spherical cap coordinates,such as extracting the boundary of the geological body with derivative,as what is done in Cartesian coordinates,the model with single set of orthogonal functions converges slowly with large error,but the model with two sets can do well for the gravity field and its derivative.In this paper,two sets of orthogonal functions were applied to model the local gravity field,and to calculate radial derivative and spherical surface derivative module in spherical cap coordinates.Then a prism model was designed to verify the result.It is shown that the model with two sets of orthogonal functions is more suitable for gravity potential on sphere.Finally,using gravity anomaly data of Okinawa Trough from satellite altimetry,the derivative was calculated applying the two-set algorithm,the tectonic units of the offshore region in the East China Sea were delineated clearly by radial derivative.The spherical surface derivative module marked clearly the East China Sea uplift zone and some other local structural units in sedimentary basin on continental margin.The two-set algorithm of spherical cap harmonic analysis has been proved to be a better approach to gravity field modeling.