Dolerite structures such as dykes and sills are the main target for groundwater exploration in Karoo Supergroup area which is the main stratigraphy unit in South Africa. Morgenzon Farm is one of the sites in Karoo Supergroup, including a dolerite dyke, which is interested here. Magnetization/susceptibility and resistivity of dolerite dyke are significantly larger than those of encompassing sedimentary materials. Therefore, low induction number electromagnetic (EM-LIN) and magnetometry approaches may be useful to its detection. EM-LIN is composed of three techniques: EM38, EM31 and EM34, with the latter being manipulated. Since both EM34 and magnetometry inverse problems are LINear, regularized weighted minimum length solution algorithm is utilized for their inverse modeLINg, but with one main discrepancy: model weighting function for magnetometry method is attained from multiplication of depth weighting and compactness constraints, while model weighting function is only equal to depth weighting for EM34 approach. Recovered susceptibility and conductivity sections derived respectively from magnetic and EM34 data sets show high consistency. Inverted models represent a dolerite dyke in the middle of the profile with depth range of 4 to 15m.

The nonLINear Benny-LIN equation has been solved In this paper using Adomian decomposition technique (ADM ) with different initial conditions and the results shown in Figures (1-8), also by using modified Adomian decomposition technique with genetic algorithm to expound the optimal equation parameters. The proposed method (GA-ADM) guarantees that the optimal parameters will be achieved precisely regardless of the complexity and multiple values of the equation. The proposed method gives more accurate results than the ADM.

In this article we consider the stochastic restricted ridge estimation in semi-parametric LINear models when the covariates are measured with additive errors. The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates. The asymptotic normality of the resulting estimates are established. Also, necessary and sufficient conditions, for the superiority of the pro-posed estimator over its counterpart, for selecting the ridge parameter k are obtained. A Monte Carlo simulation study is also performed to illustrate the finite sample perfor-mance of the proposed procedures. Finally theoretical results are applied to Egyptian pottery Industry data set.