عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Gravity and magnetic methods are potential field methods and are currently used for a wide range of applications and scales in geosciences. Traditionally, they have been used for large scale investigations of geologic structures. Smaller-scale applications of gravity and magnetic methods are employed for mining exploration, environmental research, and engineering studies.
Spatial and frequency domain filtering, image processing and managing grids are essential tools in gravity and magnetic data interpretation. A potential field or image processing filter highlights different aspects of potential field data. Filters can emphasize boundaries between geological contacts, highlight deeper or shallower sources, highlight features from different angles, or reduce undesirable effects within the dataset. Filtering procedure can be undertaken in the frequency domain by means of Fourier Transform (FT) or in the spatial domain by convolution. Frequency domain filtering involves converting the dataset into the frequency domain, performing an operation on the data by applying the appropriate filter, and then transforming the data back to the spatial domain. The most commonly used frequency domain filters include reduction to pole, pseudo gravity transformation, analytical continuations, and derivative filters. Convolution methods involve convolving a filter impulse response (filter coefficients) with the dataset.
Gradient methods use the derivatives (gradients) of the field in their calculations and include the Euler deconvolution, analytic signal, and horizontal gradient. In gradient methods, the total field is measured simultaneously at two elevations by using two sensors separated by a fixed distance. The difference in magnetic intensity between the two sensors divided by the distance between them is the vertical gradient. Using a Fast Fourier Transform (FFT) in calculating the derivatives (two horizontal and one vertical) of the field makes these methods more advanced. In the early 1970s, a variety of automatic and semiautomatic methods, based on the use of the gradients of the potential field, were developed as efficient tools for determining geometric parameters, such as the locations of boundaries and the depths of the causative sources.
Researchers have proposed several methods to find the depth using infinitely extended horizontal cylinders, which represent a class of geological structures. Radhakrishna Murthy (1985) interpreted the magnetic anomaly as being caused by dikes and faults using the displacement of the midpoint of the maximum and minimum anomalies if anomalies continued to a height h. In this case, the midpoint shifted a small distance, whereas the maximum and minimum were displaced more pronouncedly than was the midpoint.
In the upward continuation process, the measured potential field is transformed into another surface further away from the source. In this paper, we introduce a method based on relationship between the maximum and minimum values of the measured anomaly and the continued anomaly in different heights.
The general expression for the magnetic anomaly (vertical, horizontal and total) observed at a point P along the x-axis due to an infinitely extended horizontal cylinder is given by
where C and Q are the amplitude coefficient and the index parameter, respectively.
Since at the maximum and minimum values of a function the first derivative is equal to zero, by differentiating equation (1) with respect to x and setting it equal to zero, the extreme points of the are determined. Subsequently, the parameter, Q, which controls the anomaly pattern, is determined. Consequently, the depth-to-top of the causative body is estimated from the parameter Q by means of the equation below:
This method has been applied successfully to synthetic magnetic data related to horizontal cylinders and to data from two magnetic profiles from magnetic anomaly No. 2 in Gol-Gohar mining areaas well. The determined depth associated with the Gol-Gohar body has a broad correlation with those determined by exploration drilling. Therefore, this method can be applied practically in depth estimation of the magnetic causative body.