Browsing by Author "Marobhe, Isaac M."

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Application of the Hartley Transform to the Interpretation of Magnetic Anomalies Due to Two-Dimensional Dyke Bodies
    (Elsevier, 1990) Marobhe, Isaac M.
    This study deals with the application of the Hartley transform in the inversion of total field magnetic anomalies due to a two-dimensional dyke model. The ratio of the Hartley transform to the amplitude spectrum gives the function from which the centre, magnetisation angle and dip may be determined. The depth and width of the dyke are determined from the amplitude spectrum. Tests using theoretical anomalies have shown that most of the estimates of the parameters are in agreement with parameters used to compute the anomalies. Proper scaling of the transform is required to better estimate depth and intensity of magnetisation.
  • Thumbnail Image
    Item
    Interpretation of Aerogeophysical Anomalies of Southwestern Tanzania
    (1990) Marobhe, Isaac M.
    This study deals with the interpretation of aeromagnetic data covering an approximate area of 50 000 km2 lying between 8°S to 9°30′S and 32°E to 35°E, Southwest Tanzania. The magnetic anomaly maps presented as contour maps, greytone maps, and stacked profile maps show distinct zones which match the geological units of the basement rocks. The study of magnetic lineaments has shown two prominent trends, one trending NW-SE and the second in the NE-SW. These lineaments have trends that coincide with those of structures in the rift system. Interpretation of digitized data using spectral analysis methods gave spectral depths ranging from 0.50 km to a maximum of 18 km. The shallow spectral depths were interpreted as the depths to the top of magnetic bodies. The application of singular value decomposition method in the automatic optimization of magnetic anomalies using prism, dyke and slope models was studied. The method was then used in the interpretation of prominent anomalies observed in the study area.
  • Thumbnail Image
    Item
    Optimisation of Magnetic Anomalies via Singular Value Decomposition
    (Springer, 1990) Marobhe, Isaac M.
    A study is made on the application of singular values decomposition of Jacobian rectangular matrix of partial derivatives in the interpretation of magnetic anomalies. The algorithm used in decomposing the matrix is the compact version developed by Nash. The Jacobian matrix is factorised in three matrices, one of which is the diagonal matrix containing singular values. The three matrices together with residual vector are used to calculate the parameter vector change required to account for the observed anomaly. However, tests made using theoretical and field examples have shown that such a solution needs to be smoothed with a factor having a numerical value of between 0.10 and 0.90 before being used to update the initial model parameter vector. The smoothing process was found to increase the rate of convergence and minimises the occurrence of divergences. In addition, the use of a combination of three smoothing factors varying with decrease of the objective function, results in more stable iterations than using single factors. The addition of a small number less than 1.0 on singular values as damping factor, increases the rate of convergence slightly in comparison with no damping, whereas a large factor slows the convergence rate considerably. Once divergence has occurred, the singular values are used successively as damping factors starting with the smallest. This process of overcoming divergence was found to be successful in most cases. A Turbo-Pascal program for IBM/PC’s was developed incorporating the above features to optimise six parameters for dyke and slab models and seven parameters for the prism model. The program has been used to interpret aeromagnetic anomalies observed in S.W.Tanzania of which some are presented here as examples. In some cases, initial errors with values above 20% are reduced to errors of the order of 1% within the first five iterations.
  • Thumbnail Image
    Item
    A Versatile Turbo-Pascal Program for Optimization of Magnetic Anomalies Caused By Two-Dimensional Dike, Prism, or Slope Models
    (Elsevier, 1990) Marobhe, Isaac M.
    A Turbo-Pascal program for automatic interpretation of magnetic anomalies caused by a dike, prism, or buried slope model of infinite strike length is presented. The residual between the observed and the calculated anomalies is minimized by adjusting the model parameters automatically. The change in model parameters is determined by decomposing the matrix of partial derivatives into singular values using a compact algorithm.