Abstract A subsurface volume that can be reliably interpreted in terms of geologically relevant attributes is a desirable objective for products from geophysics inversion workflows. Geophysics data contain uncertainties, however, and the solution of the inverse problem is non-unique. Some form of constraint is then required to obtain geologically reasonable outputs. Our inversions may include a priori geological information quantitatively in the regularization, e.g. to test two or more structural models for consistency with the observed geophysics data sets, updating the models accordingly. We have implemented a cross-gradient constraint for diverse geophysical data types at several geological settings for the O&G, geothermal, mining E&P community (e.g. Scholl et al 2015, 2016, Soyer et al 2018, 2021 and Mackie et al 2020). The basic application covers the familiar structural similarity objective introduced by Gallardo and Meju 2003 and 2011 - comparing the gradient fields of property volumes, e.g. velocity, resistivity, density, derived from different geophysical domains - but a distinct advantage comes when gradient control from geology (e.g. surface dip and strike data, subsurface interpreted structural models, etc.) or an ancillary geoscience property (e.g. porosity volumes as a proxy for geological structure, structural tensors extracted from PSDM, etc.) is included during single or joint domain inversions of geophysical data. In reverse, the cross gradient application may be used to de-risk competing geological or structural models, testing the consistency of the structure in each model variation – as defined by the 3D gradient field – against the observed geophysical dataset(s) (e.g. Miorelli et al 2019). A range of applications is summarized in Figure 1. The method behind our implementation and representative practical examples are discussed in the sections below.