最小曲率位场分离方法研究

位场分离是位场数据处理和解释中的重点和难点之一.本文给出了单步长非原位和原位两种最小曲率位场分离差分迭代格式,并利用Fourier频谱分析理论研究了这两种迭代格式的收敛性.通过研究表明,单步长非原位迭代格式不收敛,只有单步长原位迭代格式收敛,但单步长原位迭代格式受迭代方向选择的影响,随着迭代次数的增大其影响逐渐消失.根据单步长非原位迭代格式的频谱特点,提出了叠加步长非原位和原位迭代格式,同样利用Fourier频谱分析理论研究了叠加步长非原位和原位迭代格式的收敛性.通过研究认为,一维叠加步长非原位迭代格式收敛,但二维叠加步长非原位迭代格式不收敛;不论是一维或二维,其原位迭代格式均收敛.进一步的理论研究表明,非原位迭代格式的频率响应是一个实偶函数,而原位迭代格式的频率响应是一个复函数;单步长迭代格式的频率响应具有一定的周期性,而叠加步长迭代格式的频率响应无周期性特征;叠加步长迭代格式比单步长迭代格式的收敛性好.

The research to the minimum curvature technique for potential field data separation

Potential field data separation is one of the difficult and important problems in the potential field data processing and interpretation. Results of the potential field data separation have direct affection to the potential field data explanation. The minimum curvature technique has been widely used in the extension, blank padding and data gridding of the potential field data. We studied the frequency response and the convergence when using the minimum curvature technique for the separation of the potential field data, and take out a method for separation of the potential field data.The minimum curvature difference iteration scheme has two types: 1-D and 2-D. We used the minimum curvature basic difference iteration scheme to construct the non in situ and in situ iteration of the single step. Studied these two iteration schemes using the Fourier spectrum analysis theory, get their frequency response and studied their convergence of the iteration schemes through their frequency response feature. Popularize the Fourier spectrum analysis theory to the 2-D minimum curvature difference iteration schemes, studied the frequency response feature and the convergence of the single step non in situ and in situ iterations. Took out the superposition step non in situ and in situ iterations schemes according to the frequency response feature of the single step non in situ iteration, and studied their frequency response feature and the convergence using the Fourier spectrum analysis theory.Research of the Fourier spectrum analysis theory shows that: 1-D single step non in situ iteration cannot be used for separation of the potential field data because it has high-frequency amplification and its iteration is not convergent. But the 1-D superposition step non in situ iteration can be used for separation of the potential field data since it has good low-pass performance and its iteration is convergent. Neither single step nor superposition step, frequency response of their non in situ iteration schemes are a real even function. Frequency response of the 1-D from left to right or 1-D from right to left single step and superposition step in situ iteration are a low-pass complex function. Frequency response of the 1-D alternately iteration single step and superposition step in situ iteration are a low-pass real even function. The three types of the in situ iteration schemes are all convergent. Further theoretical study shows that when the iteration number is bigger than a bounded number, frequency response of the three types single step and superposition step in situ iteration schemes are tend to be the same. 2-D single step and superposition step non in situ iteration schemes cannot be used for separation of the potential field data because they have high-frequency amplification and their iteration are not convergent, but the convergence of the superposition step non in situ iteration is better than the single step non in situ iteration's. Frequency response of the 2-D non in situ iteration schemes are a real even function. 2-D single step and superposition step in situ iteration can be used for separation of the potential field data since they have good low-pass performance and their iteration is convergent. Frequency response of the 2-D in situ iteration scheme is a low-pass complex function. So through the comprehensive comparison, we considered that the convergence of the superposition step iteration scheme is better than the single step iteration's.We studied the frequency response of the minimum curvature difference iteration schemes for potential field data separation using the Fourier spectrum analysis theory. We get the frequency response feature and the convergence of the single step and superposition step, non in situ and in situ iteration schemes. It was proved succeed and it can be popularized to the convergence research of the other difference iteration schemes.