The interpretation of the data has provided new information about the inner structure of the volcanic complex: (1) specification of the depth of post-volcanic sedimentary fill (up to ~100 m) and (2) magnetic and resistivity signs of one (or two) hidden volcanic structures interpreted as intrusions or remains of a scoria cone. (J Volcanol Geother Res 182:97–112, 2009), a multiparametric geophysical (electrical resistivity tomography, gravimetry, magnetometry, seismics) and geological/petrochemical research study had been carried out. The Mýtina maar is the first known Quaternary maar in the Bohemian Massif. In all cases the shape and depth of the buried structures are in good agreement with the actual ones. The method is applied to synthetic data with and without random errors and tested on three field examples from India, Brazil and the USA. This method can be applied to residuals as well as to the observed magnetic data consisting of the combined effect of a local structure and a second-order regional or less. The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. The computed depths are plotted against the shape factors representing a continuous monotonically increasing curve. For a fixed free parameter, the depth is determined for each shape factor. The relationship represents a parametric family of curves (window curves). The method involves using a nonlinear relationship between the depth to the source and the shape factor and a combination of observations at four points with respect to the coordinate of the source center with a free parameter (window length). Using the new formula we developed a simple and fast numerical method to determine simultaneously the depth and shape of a buried structure from second-horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths. We present in this paper a new formula representing the magnetic anomaly expressions produced by most geological structures. Thus, the final results of the different parameters are matched with those given in the published literature and from geologic results. Inversion of noise-free synthetic data, noisy synthetic data which contains different levels of random noise (5, 10, 15 and 20%) as well as multiple structures and in additional two real-field data from USA and Egypt exhibits the viability of the approach. The root mean square (RMS) error is considered as a criterion in estimating the misfit between the observed and computed anomalies. The model parameters evaluated by the present technique, generally the depth of the covered structures were observed to be in astounding concurrence with the real parameters. The model parameters deciphered here are the depth of the body, the amplitude coefficient, the angle of effective magnetization, the shape factor and the horizontal coordinates of the source. The PSO algorithm has been connected in interpreting the magnetic anomaly profiles data onto a new formula for isolated sources embedded in the subsurface. A new efficient approach to estimate parameters that controlled the source dimensions from magnetic anomaly profile data in light of PSO algorithm (particle swarm optimization) has been presented.
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