位场反演计算的场比值法及在宽城地区磁异常解释中的应用

在磁异常的反演计算中,为了避免由于选错了磁性体的形状而产生很大的误差,前人已研究了多种所谓自动反演的计算方法.与传统的方法不同,用这些方法,可以同时确定磁性体的几何形状和埋藏深度等参数.但是前人研究的方法需要计算磁异常的三阶导数,因此所受高频噪声干扰十分严重,以至于影响到计算结果的可靠性.因此很难用到实际资料处理中.本文提出的场比值法可以同时确定磁性体的形状和埋藏深度.场比值法通过场比值field-ratio来确定磁性体的形状,field-ratio的物理含义与Euler反褶积公式中的形状因子类似.场比值法的优点是在反演计算中只需要计算磁异常的一、二阶导数,因此比前人的方法受高频随机干扰小,可以用于实际资料的处理中.模型实验证明了场比值法的正确性,在河北省宽城地区用场比值法对磁异常反演计算,展示了方法的实用性.

The Field Ratio Method for Automatic Interpretation of Magnetic Data and its Application to the Interpretation of Magnetic Anomaliesin Kuancheng area

The analytic signal method for magnetic anomalies in two dimension (2D) was proposed by Nabighian (1972) and then improved and extended to three dimension (3D) (Roest et al., 1992; Hsu et al., 1996, 1998, 2002; Thurston et al., 1997, 2002; Smith et al., 1998; Salem et al., 2002, 2003, 2005; Keating et al., 2004). The advantage of using the absolute value of the analytic signal is that its shape over linear structures is independent of the magnetization direction of the source material. Therefore, the method does not require the knowledge of magnetization directions for anomalies caused by 2D sources.It is important to construct an appropriate model through analyzing the properties of a given magnetic anomaly and its analytic signal. Thurston et al. (1997, 2002) and Smith et al. (1998) proposed a method for determining the ap-propriate model type by using the local wavenumber. The method has been used to interpret anomalies arising from contacts, sheets, horizontal cylinders, and thick dikes as well as sloping steps. Hsu et al. (1998) proposed an algorithm recognizing the attributes of the analytic signal maxima, and constructed a criterion that discriminated between maxima from dike-like and step-like structures. Salem and Ravat (2003) presented the AN-EUL method, with which the location coordinates and the geometry of the magnetic source can be determined simultaneously.This paper suggests another method for determining an appropriate model which can obtain an estimate of the depth of the model. The proposed method allows the most appropriate model to be determined according to the field ratio, which is analogous to the structural index in the Euler equations. A disadvantage existent in several commonly-used methods is that the third derivative of the magnetic anomaly has to be calculated. These methods, therefore, are quite sensitive to noise in the data. Especially in the case of complex magnetic anomalies, high-wavenumber noise can distort the higher order analytic signal values to such an extent that the results are unreliable. The present method bases itself only on the first and second derivative fields and is therefore less af-fected by the noise. Synthetic model and real data from Kuancheng area in Hebei Province were used to determine the effectiveness of the method