Determination of multilayer soil parameters using Simulated Annealing algorithm
The paper presents a new method based on the Simulated Annealing Algorithm for the estimation of the parameters of multilayer soils. First the infinite integral of resistivity equation is approximated by use of complex image method. Then, Simulated Annealing Method is used to estimate the soil resistivity with the least error.
Parameter estimation of horizontal multilayer earth by complex image method
How to correctly obtain the structure parameters of earth is the precondition of grounding system design. Based on the local searching algorithm, an efficient method for estimating earth structure with any number of layers from the test data by Wenner configuration method is presented. In each iterative procedure, earth apparent resistivities are calculated by complex image method. A new method to directly obtain the partial derivatives of the earth apparent resistivities with respect to the earth parameters from the results of the complex image method is presented, which is more efficient than the conventional methods that arduously calculate the improper integrals with a Bessel's function and an infinite limit of integration. At the same time, a method to determine suitable initial earth parameters for the local searching algorithm is also proposed. The validity of the method is shown by several applications.
Examples of geoelectric surveys
The Introduction deals briefly with the general principles underlying geoelectric methods of surveying and gives a simple formula for the apparent resistivity at a given depth below the surface in a homogeneous medium. The two problems of interpreting the different kinds of curves obtained from field measurements and of determining the depth of the associated geological anomalies are discussed.In Section 1.2 the electrical equipment and field procedure are briefly described.Three particular anomalies are considered in Section 1.3. These are:(i) Parallel strata as illustrated by the boulder-clays which overlie the chalk of the Holderness Plain, East Yorkshire.(ii) Inclined strata which occur where the water-table reaches the surface on the slopes of the Mendip Hills, Somerset.(iii) A cavern in the limestone rocks at Pen Park near Filton, Bristol.In Sections 2, 3 and 4 respectively, the relevant equations, the geoelectric measurements and graphs together with their interpretations are discussed. The equation for inclined strata is deduced in a form comparable with the previously published equations for parallel strata and a spherical cavity. These latter are stated in Sections 2 and 4 respectively, and their derivation is given in the Appendix.From the graphs in Section 2 it is concluded that no ancient Humber estuary existed in the chalk beneath the boulder-clays, but the presence of an interglacial gravel separating two deposits of boulder-clays is established.In Section 3 the water-table is located and is found to emerge along a line of springs which coincides with the edge of the conglomerate deposited by the ancient Triassic sea.The deductions made from the graphs of Section 4 were verified by subsequent excavations which led to the rediscovery of Pen Park Hole.In the Appendix the derivation of the equations for a homogeneous medium, for parallel strata and for a buried sphere are given, together with theoretical relationships for calculating the depths of these particular anomalies.