While diagnostic techniques based on the ordinary Zeeman effect (e.g. magnetograms) are almost ``blind’’ to a turbulent magnetic field with mixed magnetic polarities within the spatial resolution element, the Hanle effect is sensitive to this domain of solar magnetism. We present observational evidence that the turbulent magnetic field that fills the 99ts% of the volume between the kG flux tubes in quiet solar regions does not have a unique field-strength distribution, but the rms turbulent field strength can vary by an order of magnitude from one solar location to the next. The varying Hanle depolarization in combinations of spectral lines with different sensitivities to the Hanle effect is conspicuously evident from direct visual inspection of the spectra. To quantify these variations we have extracted the polarization amplitudes for a selection of spectral lines observed in 8 different solar regions with different turbulent field strengths, and then applied an inversion technique to find the field strengths and calibrate the selected lines. The inversion gives stable solutions for the turbulent field strengths, in the range 4–40ts G, but the field-strength scale is presently very uncertain. The inversion exercise has helped to expose a number of problem areas which need to be attended to before the differential Hanle effect can become a standard, reliable diagnostic tool. One major problem is the extraction of the line polarization when the contributions from the line and continuum are of the same order of magnitude, which is the usual case. For exploratory purposes we have applied a heuristic, statistical approach to deal with this problem here.