Application of space-wavenumber analysis in magnetic exploration

The magnetic method is a common tool in mining exploration, engineering geology andoil exploration. Depth estimation of potential field anomalies is an important step in the interpretation of the potential field data. There are various methods for depth estimation,which act in a space or wavenumber domain. Euler deconvolution is an automatic andconventional space-domain based method for depth estimation. The success of this approach depends on the choice of the two parameters, i.e. structural index and windowlength. Nowadays, wavelet transform is frequently used in geophysical data processingand interpretation. Cooper (2006) used the continuous wavelet transform of the derivative of the potential field data to estimate the depth of the potential source. This method is a qualitative approach and gives an estimate of the source depth by calculation of the similarity between the potential field data and the wavelet at different depths.The Spector and Grant method is a common approach which acts on the wavenumberdomain. Their method is based on the correlation between the wavenumber and anomalydepth. In this method, the depth of the anomaly can be estimated from the slope of thecurve fitted to the logarithm of the potential field data power spectrum. In the Spector and Grant method the power spectrum of the potential field data is calculated by a standard Fourier transform. Fourier analysis has provided important visions into the interpretation of both local and regional effect. However, there is an intrinsic disadvantage in Fourier transform the kernel of Fourier transform is a sinusoidal function extended on the whole potential filed data interval, so that it uses global oscillations to analyze local ones. Due to its global approach, the Fourier power spectral density is inherently nonlocalized in space.In this study, we used the continuous wavelet transform of the potential field data tocompute the power spectral density of data. From a mathematical point of view, thecontinuous wavelet transform analysis does not use a global-space sinusoidal function buta space-wavenumber localized function called space-wavenumber wavelet. Unlike theFourier analysis, the wavelet transform uses different wavelets and the success of theanalysis often depends on the appropriate choice of the analyzing wavelet. We used theMorlet wavelet, due to its similarity with the potential filed data. The Morlet powerspectral density is smoother than that of standard Fourier analysis and it can separate thetwo lateral and vertical anomalies.The efficiency of this method is evaluated by applying it to both synthetic and realmagnetic data. Synthetic models are considered with and without noise. The results of the synthetic example show that the space-wavenumber depth estimation method results in a more desirable estimation than the standard Fourier power spectral density. We use the mentioned methods to estimate the depth of the iron deposit of Ojat Abad located in the south of the Semnan-Damghan road.