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中文摘要：
为了提高重力异常导数换算的精度，真实有效地反映地质体的异常特征，提出用余弦变换计算异常导数的新方法．给出并证明了两个定理，利用它们推导出重力位余弦谱一般表达式以及重力异常各阶导数计算公式，建立了位场余弦谱分析理论．模型实验中发现，用Fourier变换计算的一阶导数与理论导数偏差很大，而余弦变换计算的导数与理论异常导数拟合效果非常好，除边界几个数据因重力异常的有限截断产生的吉布斯效应残留使误差较大外：数据的计算精度均很高，误差为一0．09％-5％．
英文摘要：
In order to improve the accuracy of derivative conversion of gravity anomalies and reflect anomaly characteristic of geologic bodies effectively, we propose a new method of calculating anomaly derivative using cosine transform. Two theorems are put forward and proved and the common expression of the cosine transform spectrum of the gravity potential field and the formula to calculate derivatives of gravity anomalies are deduced, So the theory of cosine-transform-spectrum of the potential-field is established, In model experiments, we find that the deviation of the first derivative calculated by Fourier transform is very large to comparing with the theoretical derivative, but the fitting effect of the derivative of anomalies calculated by cosine transform is very good. The calculation accuracy of data are all very high except that errors of several data on the boundary are large because of the residual Gibbus effect induced by finite truncation of gravity anomalies. Errors are -0.09% -5%.
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