What is the relationship between the strength of a gravitational field and the compression of space next to this gravitational field?

Please clarify what you mean by "compression of space." Are you referring to curvature of spacetime as described by the general theory of relativity? In essence the curvature of spacetime is directly proportional to the amount of mass in the vicinity:

\mathbf{G}= \frac {8 \pi G}{c^4} \mathbf T

where G and T are both tensors - G measures curvature and T measures matter content.