modeling of micro-gravity data with linear regression method for inclined cylinder case study: a shaft in siahbishe region

in this paper, a new formula is applied for the calculation of gravity anomalies from a cylinder model representing a geological body. compared to conventional methods, this new development allows the cylinder to be freely oriented in space. 38 gravity forward models are produced each of which anomaly attributes are calculated. then a linear relationship is established between attributes and source parameters as a new formula. these attributes are relations which calculated from coordinates of special parts of residual gravity anomaly curve. using this linear relationship, source parameters can be then estimated by gravity anomaly attributes. linear relationship is obtained by least-square method and minimizing differences. consequently, compared to previous methods, this new development considers multiple factors that have impact on geophysical observations (some neglected in previous studies) and more variables are considered such as dip angle, strike direction, size, depth to the top, and density of the cylinder. these parameters are important for determination of the geometric of subsurface geological body. based on a series of forward modeling using the new formula, a multiple linear regression system has been developed. the multiple linear regression method relates the variations of residual gravity anomaly which is changed by variations source parameters. based on previous studies, we suppose that the shape as well the amplitude of the gravity anomaly will change with the changes of cylinder occurrence. we use the multiple linear regression to examine if there is a linear relationship between each parameter of the cylinder and a series of attributes from the gravity anomaly. actually, in this algorithm, we assessed the variability of a residual gravity anomaly as a function of the source occurrence. in previous study, seven most significant parameters of a cylinder-like body were identified, which influence the shape of the gravity anomaly as well its intensity. we build up a linear regression system that contains six linear relationships between the six most significant parameters of a cylinder-like body and seven attributes from the gravity anomaly. those equations allow the user to estimate the multiple parameters of an elongated geological body simultaneously under the constraint of gravity observations. integrating those calculations into gravity surveys helps in making a drilling decision. in this article, a shaft situated in siah bisheh dam has been considered as a case study to verify proposed formula. this case study was a part of the siah bishe pumped storage project. the project was located in the alborz mountain range, 125 km north of tehran. the site can be reached on the main chalus road, connecting tehran with the caspian sea. the project area lies in the southern part of the paleozoic- mesozoic central range of the alpine alborz mountain chain. the rock sequences in the project area consist of massive limestones, detrital series (sandstones, shales) and volcanic rocks of permian formations, triassic dolomites and jurassic formations with black shales and sandstones. several tectonic faults are crossing the project alignment. in this area, main purpose of gravity surveying was exploration of collapse zones. the gravity data used in this study come from gravity department of institute of geophysics in iran. the spatial resolution of the original gravity observations was 15 m between stations. the bouguer anomaly grid was then interpolated to a spacing of 3 m using a minimum curvature gridding algorithm. the residual bouguer anomaly is obtained after removing a first order polynomial trend to the bouguer anomaly. moreover, its engineering and geological parameters have been calculated. collapsed zone in abovementioned shaft has been determined and illustrated using microgravity data. we applied the new method to residual gravity anomaly curve of collapsed zone. finally, this zone has also been mathematically modeled using inclined cylinder.