The Midcontinent rift system is a 1.1‐b.y.‐old structure extending from Kansas, through the Lake Superior region, and into southern Michigan. The rift is filled with thick sequences of basaltic volcanic rocks and clastic sediments. For most of its extent it is buried beneath Paleozoic rocks but can be traced by its strong gravity and magnetic anomalies. The rocks of the rift system are exposed only in the Lake Superior region and comprise the Keweenawan Supergroup. Much of the geology of the Keweenawan is beneath Lake Superior and has only been inferred from potential field studies and seismic refraction studies and extrapolation from on‐shore geology. Seismic reflection surveys by the Great Lakes International Multidisciplinary Program on Crustal Evolution in 1986 imaged much of the deep structure of the rift beneath the lake in detail. The reflection profiles across the rift reveal a deep, asymmetrical central graben whose existence and magnitude was not previously documented. They show that, in addition to crustal sagging documented by previous investigations, normal faulting played a major role in subsidence of the axial region of the rift. A sequence of volcanic and sedimentary rocks, in places greater than 30 km thick, fills the graben. Thinner volcanic and sedimentary units lie on broad flanks of the rift outside of the graben. Near the axis, the prerift crust is thinned to about one fourth of its original thickness, apparently by a combination of low‐angle extensional faulting and ductile stretching or distributed shear. The sense of asymmetry of the central graben changes along the trend of the rift, documenting the segmented nature of the structure and suggesting the existence of accommodation zones between the segments. The location of the accommodation zones is inferred from abrupt disruptions in the Bouguer gravity signature of the rift. Uplift of the central graben occurred when the original graben‐bounding normal faults were reactivated as high‐angle reverse faults with throws of 5 km or more in places. The Midcontinent rift has some striking similarities to some younger passive continental margins. We propose that it preserves a record of nearly complete continental separation which, had it not been arrested, would have created a Middle Proterozoic ocean basin.

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A description of the theory and numerical implementation of a 3-D linearized asymptotic anisotropic inversion method based on the generalized Radon transform is given. We discuss implementation aspects, including (1) the use of various coordinate systems, (2) regularization by both spectral and Bayesian statistical techniques, and (3) the effects of limited acquisition apertures on inversion. We give applications of the theory in which well‐resolved parameter combinations are determined for particular experimental geometries and illustrate the interdependence of parameter and spatial resolutions. Procedures for evaluating uncertainties in the parameter estimates that result from the inversion are derived and demonstrated.

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The problem of recovering density‐normalized elastic moduli of a transversely isotropic anisotropic medium from data consisting of qP or qSV phase velocities measured in multiple directions is addressed. Previous studies have used linear fitting methods with approximate forms of the dispersion relation. Here, it is shown that with algebraic manipulation, and a prior estimate of the squared shear velocity along the symmetry axis (A55), it is possible to use simple linear methods with an exact alternative form of the anisotropic dispersion relation. The method is demonstrated with an application to data from a walkaway vertical seismic profile (VSP) experiment and then used as a tool to address several questions raised by that experiment. It is shown that given data with realistically achievable accuracy, the prior estimate of A55 cannot be improved by optimizing the fit to qP data. It is shown that a near perfect fit by a transversely isotropic medium with a vertical symmetry axis (TIV) model to qP data collected in a single vertical plane does not rule out azimuthal anisotropy. Finally, it is shown that a variation of the method, combined with an algorithm suggested by Hood and Schoenberg, suggests a practical way to determine from walkaway VSP data, all the parameters of an orthorhombic medium formed by adding vertical fractures to a transversely isotropic medium.