Y y H y rr y y

— (y, a) j(a - a) = (ra, a - a), where ry and rx are elements of spaces Y and A respectively; A is a set of admissible values of a. From here and from (6.1.3)—(6.1.6) it follows that

where

In geophysical applications another formula for VR being a consequence of the relation (6.1.9) is generally used, namely,

adjoint to (6.1.5). Equation (6.1.5') is named the adjoint equation of sensitivity and, together with (6.1.5), it can be utilized to evaluate the variance of the functional R in terms of the variance of the parameter a.

Detailed information about sensitivity can be obtained if the Green's functions g(x, x') and g*(x, x') of operators ôG/dy and (dG/dy)* are known. The solutions to the problems are connected with the Green's functions by relations

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