Posted on :- 2020-05-17 21:47:57

- A two-layer situation is encountered often in electrical prospecting. two-layer cases were interpreted with the aid of characteristic curves.
- These theoretical curves, calculated for a particular four-electrode array, take into account the change in depth penetration when current lines cross the boundary to a layer with different

resistivity. - The electrical boundary conditions require continuity of the component of current density J normal to the interface and of the component of electric field E tangential

to the interface. - At a boundary the current lines behave like optical or seismic rays, and are guided by similar laws of reflection and refraction. For example, if u

is the angle between a current line and the normal to the

interface, the electrical “law of refraction” is

- Characteristic curves can also be computed for the interpretation of structures with multiple horizontal layers, The apparent resistivity curve for a three-layer structure

generally has one of four typical shapes, determined by the vertical sequence of resistivities in the layers. - The type K curve rises to a maximum then decreases, indicating that the intermediate layer has a higher resistivity

than the top and bottom layers. - The type H curve shows the opposite effect; it falls to a minimum then increases again due to an intermediate layer that is a better conductor

than the top and bottom layers. - The type A curve may show some changes in gradient but the apparent resistivity generally increases continuously with increasing electrode

separation, indicating that the true resistivities increase with depth from layer to layer. - The type Q curve exhibits the opposite effect; it decreases continuously along with a progressive decrease of resistivity with depth.
- Once the observed resistivity profile has been identified as of K, H, A, or Q type, the next step is equivalent to the one-dimensional inversion of the field data.
- The method assumes the equations for the theoretical response of a multi-layered ground. Each layer is characterized by its thickness and

resistivity, each of which must be determined. - A first estimate of these parameters is made for each layer and the predicted curve of apparent resistivity versus electrode

spacing is computed. - The discrepancies between the observed and theoretical curves are then determined point by point.

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