Summary Joint inversion of multiphysics data is a practical approach to the integration of geophysical data, which produces models of reduced uncertainty and improved resolution. The development of effective methods of joint inversion requires considering different resolutions of different geophysical methods. This paper presents a new framework of joint inversion of multiphysics data, which is based on a novel formulation of Gramian constraints and mitigates the difference in resolution capabilities of different geophysical methods. Our approach enforces structural similarity between different model parameters through minimizing a structural Gramian term, and it also balances the different resolutions of geophysical methods using a multiscale resampling strategy. The effectiveness of the proposed method is demonstrated by synthetic model study of joint inversion of the P-wave traveltime and gravity data. We apply a novel method based on Gramian constraints and multiscale resampling to jointly invert the gravity and seismic data collected in Yellowstone national Park to image the crustal magmatic system of the Yellowstone. Our results helped to produce a consistent image of the crustal magmatic system of the Yellowstone expressed both in low-density and low-velocity anomaly just beneath the Yellowstone caldera.

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The synthetic aperture (SA) method has recently found applications in analysis of the low frequency marine controlled source electromagnetic data. It has been shown in numbers of publications that SA method can enhance the response from an anomalous target. However, the SA method may not only 'steer' the EM field in the area of interest, but also steer the noise, thus unreasonably amplifying the noise level. In addition, the current realizations of the SA method are themselves very sensitive to the noise in the data and to the parameters of the synthetic aperture. To overcome these difficulties, we have developed a robust SA method. The synthetic model study presented here shows that this method is stable with respect to noise and has a relatively high spatial resolution.

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