• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.769-774
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• 2006

In this paper, we discuss the problem of non-mutual detectability using the invariant zero. We propose a representation method for excess spaces by linear equation based on the Rosenbrock system matrix. As an alternative to the system enlargement method proposed by White[1], we propose an appropriate form of an enlarged system to make a set of faults mutually detectable by assigning sufficient geometric multiplicity of invariant zeros. We show the equivalence between the two methods and a necessary condition for the system enlargement in terms of the geometric and algebraic multiplicities of invariant zeros.

• Economic and Environmental Geology
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• v.20 no.1
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• pp.77-82
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• 1987

An analysis is made for the relative effectiveness in detecting a subsurface thin layer by four electromagnetic depth sounding systems; horizontal coplanar loops, perpendicular loops, vertical coplanar loops and vertical coaxial loops. The moduli and phases of mutual coupling ratios over a three-layered earth for the four systems are evaluated rapidly by the related convolution technique. Root mean square differences between the responses from the three-layered and the homogeneous earths are used to compare the relative effectiveness of the systems quantitatively. Comparing the all systems, it is found that the perpendicular loop system appears to be the most superior to the other systems.