S U M M A R YWe present a 3-D joint inversion framework for seismic, magnetotelluric (MT) and scalar and tensorial gravity data. Using large-scale optimization methods, parallel forward solvers and a flexible implementation in terms of model parametrization allows us to investigate different coupling approaches for the various physical parameters involved in the joint inversion. Here we compare two different coupling approaches, direct parameter coupling where we calculate conductivities and densities from seismic slownesses and cross-gradient coupling, where each model cell has an independent value for each physical property and a structural similarity is enforced through a term in the objective function.For both types of approaches we see an improvement of the inversion results over single inversions when the inverted data sets are generated from compatible models. As expected the direct coupling approach results in a stronger interaction between the data sets and in this case better results compared to the cross-gradient coupling. In contrast, when the inverted MT data is generated from a model that violates the parameter relationship in some regions but conforms with the cross-gradient assumptions, we obtain good results with the cross-gradient approach, while the direct coupling approach results in spurious features. This makes the cross-gradient approach the first choice for regions were a direct relationship between the physical parameters is unclear.

[1] We present joint inversion of magnetotelluric, receiver function, and Raleigh wave dispersion data for a one-dimensional Earth using a multiobjective genetic algorithm (GA). The chosen GA produces not only a family of models that fit the data sets but also the trade-off between fitting the different data sets. The analysis of this trade-off gives insight into the compatibility between the seismic data sets and the magnetotelluric data and also the appropriate noise level to assume for the seismic data. This additional information helps to assess the validity of the joint model, and we demonstrate the use of our approach with synthetic data under realistic conditions. We apply our method to one site from the Slave Craton and one site from the Kaapvaal Craton. For the Slave Craton we obtain similar results to our previously published models from joint inversion of receiver functions and magnetotelluric data but with improved resolution and control on absolute velocities. We find a conductive layer at the bottom of the crust, just above the Moho; a low-velocity, low-resistivity zone in the lithospheric mantle, previously termed the Central Slave Mantle Conductor; and indications of the lithosphereasthenosphere boundary in terms of a decrease in seismic velocity and resistivity. For the Kaapvaal Craton both the seismic and the MT data are of lesser quality, which prevents as detailed and robust an interpretation; nevertheless, we find an indication of a lowvelocity low-resistivity zone in the mantle lithosphere. These two examples demonstrate the potential of joint inversion, particularly in combination with nonlinear optimization methods.Citation: Moorkamp, M., A. G. Jones, and S. Fishwick (2010), Joint inversion of receiver functions, surface wave dispersion, and magnetotelluric data,

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Joint inversion of different kinds of geophysical data has the potential to improve model resolution, under the assumption that the different observations are sensitive to the same subsurface features. Here, we examine the compatibility of P‐wave teleseismic receiver functions and long‐period magnetotelluric (MT) observations, using joint inversion, to infer one‐dimensional lithospheric structure. We apply a genetic algorithm to invert teleseismic and MT data from the Slave craton; a region where previous independent analyses of these data have indicated correlated layering of the lithosphere. Examination of model resolution and parameter trade‐off suggests that the main features of this area, the Moho, Central Slave Mantle Conductor and the Lithosphere‐Asthenosphere boundary, are sensed to varying degrees by both methods. Thus, joint inversion of these two complementary data sets can be used to construct improved models of the lithosphere. Further studies will be needed to assess whether the approach can be applied globally.

In this review, I discuss the basic principles of joint inversion and constrained inversion approaches and show a few instructive examples of applications of these approaches in the literature. Starting with some basic definitions of the terms joint inversion and constrained inversion, I use a simple three-layered model as a tutorial example that demonstrates the general properties of joint inversion with different coupling methods. In particular, I investigate to which extent combining different geophysical methods can restrict the set of acceptable models and under which circumstances the results can be biased. Some ideas on how to identify such biased results and how negative results can be interpreted conclude the tutorial part. The case studies in the second part have been selected to highlight specific issues such as choosing an appropriate parameter relationship to couple seismic and electromagnetic data and demonstrate the most commonly used approaches, e.g., the cross-gradient constraint and direct parameter coupling. Throughout the discussion, I try to identify topics for future work. Overall, it appears that integrating electromagnetic data with other observations has reached a level of maturity and is starting to move away from fundamental proof-of-concept studies to answering questions about the structure of the subsurface. With a wide selection of coupling methods suited to different geological scenarios, integrated approaches can be applied on all scales and have the potential to deliver new answers to important geological questions.