ain is covered by clutter of man made and natural objects which significantly modify the surface impedance, in ways Q is a part of the integrand which may be considered constant in described in Causebrook (1978a). This modification can result in attenuation varying as shown in Figure 6.28 i.e. instead of a simple the interval A to be given by Equation 6.101 with quantities defined by Figure 6.29. monotonic curve, there is an initial rise and a significant dip at equal to about 100. (6.101) In practice, it is desirable to have a calculation system which allows for: The next barrier to simple solution is that A(r) is initially an unknown function. Up to a distance of 2A this presents little prob- 1. The curvature of the Earth. lem because terrain variations will not greatly modify the result. 2. A terrain which varies in height. Thus the Sommerfeld-Norton function may be used to determine 3. A surface impedance modified by clutter. attenuations A1 and A2 at distances A and 2A, respectively, by Hufford (1952) gives an integral equation which, at least in Equation 6.102. principle, provides a general solution for attenuation of radio waves. This can be written as in Equation 6.98. (6.102) A (R) = (6.98) Also, can be determined analytically by putting A(r) equal to a power series expansion of the Sommerfeld-Norton formula. Further values of I and A may be obtained by assuming that A(r) varies linearly within an interval, as in Equation 6.103 where S and In this equation R is the distance of path over which attenuation is required; is the angle in radians between the line from the receiver Rn can be derived from integrals which are amenable to analytic to the surface at range r and the tangent to the surface, at this point; solution. us is the distance between terminals subtracted from the sum of distances from terminals to surface at r, see Figure 6.29; n is the (6.103) relative surface impedance at r. The integral contains quantities which do not have 'mathemati- cally closed' forms, SO an analytical solution is unob