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在傅里叶变换的基础上,提出在只有重力异常的情况下,利用余弦变换计算重力全梯度张量,并探讨了重力异常信号中含噪声时,余弦变换法计算的梯度张量的精度问题。通过对二维无限长均匀水平圆柱体及三维“Y”型岩脉模型梯度张量的计算表明,在原始重力异常中加入噪声与否的情况下,余弦变换法的计算结果均要优于传统的傅里叶变换法,特别是从均方差上看,余弦变换法的精度提高了近2’3倍。在实际应用中,实现了对黑龙江虎林盆地的重力梯度张量计算,计算结果表明,由余弦变换获得的重力梯度张量与傅里叶变换法的结果具有较高的一致性,但余弦变换法获得的梯度张量异常更加平滑,表明其受噪声的影响更小,能够更好地反映断裂的分布特征。
On the basis of Fourier transform, this paper proposes to calculate the gravitational total gradient tensor by using the cosine transform under the condition of gravity anomaly and to discuss the accuracy of the gradient tensor calculated by the cosine transform when the gravity anomaly signal contains noise . Through the calculation of the gradient tensor of a two-dimensional infinitely-long horizontal cylinder and a three-dimensional “Y” type dyke, it is shown that the cosine transform method is better than the original gravity anomaly with or without noise In the traditional Fourier transform method, especially from the mean square error, the accuracy of cosine transform method increased nearly 2’3 times. In practical application, the gravity gradient tensor calculation of Hulin basin in Heilongjiang Province is realized. The calculation results show that the gravity gradient tensor obtained by cosine transform has a higher consistency with the Fourier transform method. However, the cosine transform The gradient tensor anomaly obtained by the method is smoother, indicating that it is less affected by noise and better reflects the distribution characteristics of the fractures.