Structure of the crust and upper mantle beneath the Great Valley and Allegheny Plateau of eastern Pennsylvania 1. Comparison of linear inversion methods for sparse wide‐angle reflection data

We use τ(p) data extracted from a small number of wide-angle recordings of quarry blasts to construct averaged, one-dimensional velocity models of the crust beneath portions of the Great Valley, Newark Basin, Valley and Ridge, and Allegheny Plateau of the central Appalachians of Pennsylvania. Using the linear form of the equations for τ(p) in terms of slowness-depth structure, we compare inversion results for the extremal, Backus-Gilbert, and generalized least squares methods. Although the uncertainties are large, the models do show a well-constrained increase in midcrustal velocities and crustal thickness beneath the Allegheny Plateau. Inversion of precritical reflections from the Moho suggests bounds of 7.1–7.6 km/s on P wave velocity and 3.9–4.2 km/s on S wave velocity near the base of the crust. P wave velocity models for the Great Valley show a crustal thickness between 40 and 45 km, with an average velocity between 6.4 and 6.6 km/s. Models for the Allegheny Plateau show a larger crustal thickness (47–52 km) and a much higher average velocity (6.8–6.9 km/s). Estimates of average shear wave velocities for the Great Valley range from 3.6 to 3.8 km/s, with crustal thickness estimates between 37 and 44 km. For the relatively small number of singular values retained, standard errors in depth for models derived by generalized least squares range from ±1 to 2 km for the P wave slowness models and from ±2 to 4 km for the S wave models; extremal depth bounds in general are 2 to 3 times as wide. Corresponding uncertainties in interval velocity, estimated from resolving kernels in slowness, range from 0.15 to 0.45 km/s for P wave models and from 0.15 to 0.40 km/s for S wave models. T2–X2 inversion of PmP data gives similar estimates for total crustal thickness and average velocity after correction for refraction effects. T2–X2 inversion of PmP data for a fourth profile suggests the possibility of a slight thickening of the crust (47–48 km) directly beneath the axis of the Great Valley gravity low. Estimates of average VP/VS for the crust based on average velocities for models derived by generalized least squares inversion range from 1.73 to 1.77. Estimates based on travel time ratios for events interpreted as P wave and S wave reflections from the Moho lie between 1.75 and 1.79. For a crust in which the effects of velocity anisotropy can be neglected, these estimates correspond to crustal averages between 0.25 and 0.27 for Poisson's ratio. The one-dimensional velocity models derived here provide estimates of the long-wavelength component of velocity structure. Besides demonstrating the maximum resolving power inherent in a limited τ(p) data set, these averaged models can be used for migrating reflection data and as starting models for determining two-dimensional velocity structure.