Joint inversion of two-dimensional magnetotelluric and ambient noise data constrained with cross gradient

We present an alternating joint two-dimensional inversion algorithm for imaging integrated magnetotelluric (MT) and ambient noise dispersion data sets. This approach is based on the limited-memory quasi-Newton method and enforced with cross-gradient constraints that seeks the geometrically similar structural features from multi-geophysical data. A classic synthetic model with same geometric boundaries has been used to test the stability and effectiveness of the joint inversion algorithm. Compared with individual MT and ambient noise tomography (ANT) inversion results, the resistivity and velocity models are captured with higher resolution, especially the electric structures below conductive units are recovered more correctly. The algorithm is also performed on another synthetic example with partial inconsistent boundaries in the resistivity and velocity models more analogous to the realistic scenario. The result demonstrates that, at the inconsistent boundaries, the resistivity model is still imaged correctly but the velocity model is constructed with some artificial structures. We suggest that, in the application of the actual case, the resistivity model obtained from joint inversion is superior and the velocity model should be evaluated comprehensively from individual and joint inversion results.