FREQUENCY ANALYSIS FOR GRAVITY AND MAGNETIC INTERPRETATION
FREQUENCY ANALYSIS FOR GRAVITY AND MAGNETIC INTERPRETATION
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作者：
W. Dean
重磁解释中的二阶导数、解析延拓、平滑、去除残差或区域等操作在数学上类似于电路的滤波作用。两者之间的主要区别在于，电滤波器作用于一个变量（时间）的函数，而地球物理滤波器必须作用于两个空间变量（x和y）的函数。本文发展了重磁解释的线性滤波理论。作为该理论的一个应用，对向下延拓进行了较详细的讨论。向上延拓的频率响应是随频率增加而减小的指数函数。向下延续的逆过程具有作为向上延续响应的倒数的频率响应。本文讨论了用系数集匹配频率响应的方法，并举例说明了向下延拓的一些固有困难。最后一个例子
The operations of second derivative, analytic continuation, smoothing, the removing of residuals or regionals, and others in gravity and magnetic interpretation are analogous mathematically to the filtering action of electric circuits. The main difference between the two is that electrical filters act on functions of one variable (time), whereas the geophysical filters must act on functions of the two space variables (x and y). This paper develops linear filter theory for gravity and magnetic interpretation. As an application of the theory, downward continuation is discussed in some detail. The frequency response of upward continuation is an exponential function decreasing with increasing frequency. The inverse process of downward continuation has a frequency response which is the reciprocal of the upward continuation response. This paper discusses a method of matching frequency responses by coefficient sets and shows by examples some of the inherent difficulties in downward continuation. A final example ...