Some inverse problems are characterized by a model consisting of a piecewise continuous function and a set of discrete parameters. For linear problems of this general type, which we call mixed, we show that when the number of data d is greater than the number of parameters p, it is always possible to construct a set of a least d ‐ p equations that are independent of the values of the discrete part of the model. These equations, which we call the annulled data set, can be used to estimate the continuous part of the model. The discrete part of the model can be estimated from a second set of p equations that relate the discrete and continuous parts of the model. The linearization of the nonlinear travel time functional that enter in the hypocenter location problem leads to a mixed inverse problem. The splitting procedure is natural to this problem if the hypocenters are estimated initially by conventional nonlinear least squares by using travel times calculated from some initial estimate of the velocity model. The annulled data are a set of linear combinations of the residuals that are unbiased by that initial location, and as a result, they can be used directly to estimate a perturbation to the velocity model by a Backus‐Gilbert procedure. This makes an iterative algorithm possible that consists of a conventional hypocenter location followed by estimating a perturbation of the velocity model from the annulled data set. The uniqueness of the final velocity model is assessed via the linear resolution analysis of Backus and Gilbert (1968, 1970). We also construct a set of Frechet derivatives that relate perturbations of each hypocenter component to perturbations of the velocity model. These kernels are used to assess the possible error of the hypocenters due to inadequate knowledge of the velocity structure by an application of the generalized prediction approach of Backus (1970a). Good results are obtained when the procedure is applied to a simple synthetic data set.

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Investigations of tectonic and surface processes have shown a clear relationship between climate‐influenced erosion and long‐term exhumation of rocks. Numerical models suggest that most orogens are in a transient state, but observational evidence of a spatial shift in mountain building processes due to tectonic‐climate interaction is missing. New thermochronology data synthesized with geophysical and surface process data elucidate the evolving interplay of erosion and tectonics of the colliding Yakutat microplate with North America. Focused deformation and rock exhumation occurred in the apex of the colliding plate corner from > 4 to 2 Ma and shifted southward after the 2.6 Ma climate change. The present exhumation maximum coincides with the largest modern shortening rates, highest concentration of seismicity, and the greatest erosive potential. We infer that the high sedimentation caused rheological modification and the emergence of the southern St. Elias, intercepting orographic precipitation and shifting focused erosion and exhumation to the south.

We present new estimates of lithospheric shear velocities for the intraplate seismic zones and the Illinois Basin in the U.S. midcontinent by analyzing teleseismic Rayleigh waves. We find that relatively high crustal shear velocities (VS) characterize the southern Illinois Basin, while relatively low crustal velocities characterize the middle and lower crust of the central and northern Illinois Basin. The observed high crustal velocities may correspond to high‐density mafic intrusions emplaced into the crust during the development of the Reelfoot Rift, which may have contributed to the subsidence of the Illinois Basin. The low crustal VS beneath the central and northern basin follow the La Salle deformation belt. We also observe relatively low velocities in the mantle beneath the New Madrid seismic zone where VS decreases by about 7% compared to those outside of the rift. The low VS in the upper mantle also extends beneath the Wabash Valley and Ste. Genevieve seismic zones. Testing expected VS reductions based on plausible thermal heterogeneities for the midcontinent indicates that the 7% velocity reduction would not result from elevated temperatures alone. Instead this scale of anomaly requires a contribution from some combination of increased iron and water content. Both rifting and interaction with a mantle plume could introduce these compositional heterogeneities. Similar orientations for the NE‐SW low‐velocity zone and the Reelfoot Rift suggest a rift origin to the reduced velocities. The low VS upper mantle represents a weak region and the intraplate seismic zones would correspond to concentrated crustal deformation above weak mantle.

P-wave travel-time residuals from USArray helped improve the scale and consistency with which the mantle beneath North America is resolved. Beginning in 2008, we published a series of P-wave velocity models based on a global ray theoretical inversion of USArray and global catalog data. Here, we present the final model update, MITP_2016MAY, which includes the complete set of travel-time residuals from USArray Transportable Array (TA) in the contiguous United States. In this model, the area of high resolution extends to the eastern margin of the continent, allowing us to better estimate the location and extent of slow features in Central Virginia and New England. An increasing number of data from the TA in Alaska also allows us to recover the structure of subducting Pacific plate and Yakutat terrane. In addition to highlighting new features in the final model, we visualize and discuss the improvements to the model due to the addition of USArray data through time. Electronic Supplement: MATLAB MITP_2016MAY model and plotting scripts, figures of checkerboard tests, and animations of model evolution.