Estimating the nature and the horizontal and vertical positions of 3D magnetic sources using Euler deconvolution

Abstract

We have developed a new method that drastically reduces the number of the source location estimates in Euler deconvolution to only one per anomaly. Our method employs the analytical estimators of the base level and of the horizontal and vertical source positions in Euler deconvolution as a function of the x-and y-coordinates of the observations. By assuming any tentative structural index (defining the geometry of the sources), our method automatically locates plateaus, on the maps of the horizontal coordinate estimates, indicating consistent estimates that are very close to the true corresponding coordinates. These plateaus are located in the neighborhood of the highest values of the anomaly and show a contrasting behavior with those estimates that form inclined planes at the anomaly borders. The plateaus are automatically located on the maps of the horizontal coordinate estimates by fitting a first-degree polynomial to these estimates in a moving-window scheme spanning all estimates. The positions where the angular coefficient estimates are closest to zero identify the plateaus of the horizontal coordinate estimates. The sample means of these horizontal coordinate estimates are the best horizontal location estimates. After mapping each plateau, our method takes as the best structural index the one that yields the minimum correlation between the total-field anomaly and the estimated base level over each plateau. By using the estimated structural index for each plateau, our approach extracts the vertical coordinate estimates over the corresponding plateau. The sample means of these estimates are the best depth location estimates in our method. When applied to synthetic data, our method yielded good results if the bodies produce weak-and mid-interfering anomalies. A test on real data over intrusions in the Goiás Alkaline Province, Brazil, retrieved sphere-like sources suggesting 3D bodies.

Use of a high-precision gravity survey to understand the formation of oceanic crust and the role of melt at the southern Red Sea rift in Afar, Ethiopia

“…We used a data window of 31 points and first identified the plateaus (Silva & Barbosa 2003) to arrive at the best estimates of the horizontal source positions. After identifying three distinct source positions at 290, 237 and 22 to 12 km, we then used the approach described by Melo et al (2013) to identify the best structural indices in the three regions. This was achieved by testing tentative structural indices for the three source bodies separately and computing the correlation coefficient between the complete Bouguer anomaly and the base level estimates for each of the structural indices.…”

Estimation of the total magnetization direction of approximately spherical bodies

“…18) and produces the predicted data d(ĥ) (Eq. 16) as near as possible to the observed data T o , in the L2-norm sense (Bard, 1973;Twomey, 1977;Menke, 1989;Aster et al, 2005). The least-squares estimateĥ (Eq.…”

“…Fortunately, the sensitivity of Euler deconvolution to estimating the 3-D position of magnetic sources works in the opposite direction. As shown by Silva and Barbosa (2003) and Melo et al (2013), the estimates of the source horizontal positions in Euler deconvolution are very accurate, while the depth estimates may fail. This characteristic makes Euler deconvolution a suitable technique for providing the centre of the source to be used by our method as prior information to form the matrix given in Eq.…”

Interpretation of high resolution airborne magnetic data (HRAMD) of Ilesha and its environs, Southwest Nigeria, using Euler deconvolution method

“…N is an exponential factor that corresponds to the rate at which the field falls off with distance for a source of given geometry. Processed data were subjected to Euler deconvolution operation to determine the depth to the magnetic source [16][17][18][19][20][21]. In 2011, Silva and Barbosa [22] proposed Euler deconvolution as a useful tool to calculate approximately the localities of various geologic bodies.…”