Understanding the uncertainty associated with large joint geophysical surveys, such as 3D seismic, gravity, and magnetotelluric (MT) studies, is a challenge, conceptually and practically. By demonstrating the use of emulators, we have adopted a Monte Carlo forward screening scheme to globally test a prior model space for plausibility. This methodology means that the incorporation of all types of uncertainty is made conceptually straightforward, by designing an appropriate prior model space, upon which the results are dependent, from which to draw candidate models. We have tested the approach on a salt dome target, over which three data sets had been obtained; wide-angle seismic refraction, MT and gravity data. We have considered the data sets together using an empirically measured uncertain physical relationship connecting the three different model parameters: seismic velocity, density, and resistivity, and we have indicated the value of a joint approach, rather than considering individual parameter models. The results were probability density functions over the model parameters, together with a halite probability map. The emulators give a considerable speed advantage over running the full simulator codes, and we consider their use to have great potential in the development of geophysical statistical constraint methods.