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.

Citation for published item:rein keD fj¤ orn nd tegenD w rion nd woork mpD w x nd ro sD i h rd nd ghenD tin @PHIUA 9en d ptive oupling str tegy for joint inversions th t use petrophysi l inform tion s onstr intsF9D tourn l of pplied geophysi sFD IQT F ppF PUWEPWUF Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractJoint inversion strategies for geophysical data have become increasingly popular as they allow for the efficient combination of complementary information from different data sets. The algorithm used for the joint inversion needs to be flexible in its description of the subsurface so as to be able to handle the diverse nature of the data. Hence, joint inversion schemes are needed that 1) adequately balance data from the different methods, 2) have stable convergence behavior, 3) consider the different resolution power of the methods used and 4) link the parameter models in a way that they are suited for a wide range of applications.Here, we combine active source seismic P-wave tomography, gravity and magnetotelluric (MT) data in a petrophysical joint inversion that accounts Another benefit of the proposed scheme is that structural information can easily be incorporated in the petrophysical joint inversion (no additional terms are added in the objective functions) by using mutually controlled structural weights for the smoothing constraints.We test our scheme using data generated from a synthetic 2-D sub-basalt model. We observe that the adaption of the coupling strengths makes the convergence of the inversions very robust (data misfits of all methods are close to the target misfits) and that final results are always close to the true models independent of the parameter choices. Finally, the scheme is applied on real data sets from the Faroe-Shetland Basin to image a basaltic sequence reflection onsets) needs to be included.

S U M M A R YGalvanic distortion of magnetotelluric (MT) data due to small-scale surficial bodies or due to topography is one of the major factors that prevents accurate imaging of the subsurface. We present a 3-D algorithm for joint inversion of MT impedance tensor data and a frequencyindependent full distortion matrix that circumvents this problem. We perform several tests of our algorithm on synthetic data affected by different amounts of distortion. These tests show that joint inversion leads to a better conductivity model compared to the inversion of the MT impedance tensor without any correction for distortion effects. For highly distorted data, inversion without any distortion correction results in strong artefacts and we cannot fit the data to the specified noise level. When the distortion is reduced, we can fit the data to an RMS of one, but still observe artefacts in the shallow part of the model. In contrast, in both cases our joint inversion can fit the data within the assumed noise level and the resulting models are comparable to the inversion of undistorted data. In addition, we show that the elements of the full distortion matrix can be well resolved by our algorithm. Finally, when inverting undistorted data, including the distortion matrix in the inversion only results in a minor loss of resolution. We therefore consider our new approach a promising tool for the general analysis of field MT data.

SUMMARY A major step in processing magnetotelluric (MT) data is the calculation of an impedance tensor as function of frequency from recorded time‐varying electromagnetic fields. Common signal processing techniques such as Fourier transform based procedures assume that the signals are stationary over the record length, which is not necessarily the case in MT, due to the possibility of sudden spatial and temporal variations in the naturally occurring source fields. In addition, noise in the recorded electric and magnetic field data may also be non‐stationary. Many modern MT processing techniques can handle such non‐stationarities through strategies such as windowing of the time‐series. However, it is not completely clear how extreme non‐stationarity may affect the resulting impedances. As a possible alternative, we examine a heuristic method called empirical mode decomposition (EMD) that is developed to handle arbitrary non‐stationary time‐series. EMD is a dynamic time series analysis method, in which complicated data sets can be decomposed into a finite number of simple intrinsic mode functions. In this paper, we use the EMD method on real and synthetic MT data. To determine impedance tensor estimates we first calculate instantaneous frequencies and spectra from the intrinsic mode functions and apply the impedance formula proposed by Berdichevsky to the instantaneous spectra. We first conduct synthetic tests where we compare the results from our EMD method to analytically determined apparent resistivities and phases. Next, we compare our strategy to a simple Fourier derived impedance formula and the frequently used robust processing technique bounded‐influence remote reference processing (BIRRP) for different levels of stochastic noise. All results show that apparent resistivities and phases which are calculated from EMD derived impedance tensors are generally more stable than those determined from simple Fourier analysis and only slightly worse than those from the robust processing. These results show that EMD has the potential to handle noisy data. Finally, as a test on real data, we apply our processing scheme to data measured from the Costa Rica subduction zone, and obtain similar impedance estimates as the BIRRP processing method.