We use a correspondence map to jointly invert surface-wave dispersion curves and magnetotelluric data for subsurface shear velocity and resistivity but also for a possible relationship between them. Our first experiments consist of inversions of synthetic data computed from models linked by first-and second-order polynomial relationships. Our methodology produces joint inversion model pairs from which 100% fit the 'observed' parameter relationship within a 5% error vs only 15% of the separate inversion pairs for the degree 1 relationship experiment. For the degree 2 relationship synthetic test, 80% of the joint inversion model pairs fit the 'observed' relationship within a 5% error while 45% of the separate inversion pairs. This reduces the number of acceptable models without compromising the data fit ('reduction of nonuniqueness'). The next experiment involves synthetic data from models of known physical properties, taken from well logs, but without a known relationship. We show how to select an appropriate polynomial degree for joint inversion when the relationship is unknown. Having validated the approach with synthetic cases, we apply our methodology to field data. We compare separate and joint inversions, and we find that the one-dimensional subsurface models retrieved from joint inversions are more similar to previous models documented in the area than the separate inversion models.