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The Wolfe Creek Meteorite Crater is an impact structure 880 m in diameter, located in the Tanami Desert near Halls Creek, Western Australia, The crater formed < 300000 years ago, and is the second largest crater from which fragments of the impacting meteorite (a medium octahedrite) have been recovered. We present the results of new ground-based geophysical (magnetics and gravity) surveys conducted over the structure in July-August 2003. The results highlight the simple structure of the crater under the infilling sediments, and forward modelling is consistent with the true crater floor being 120 m beneath the present surface. The variations in the dip of the foliations around the crater rim confirm that the meteorite approached from the east-northeast, as is also deduced from the ejecta distribution. Crater scaling arguments suggest a projectile diameter of > 12.0 m, a crater formation time of 3.34 s, and an energy of impact of similar to 0.235 Mt of TNT. We also use the distribution of shocked quartz in the target rock (Devonian sandstones) to reconstruct the shock loading conditions of the impact. The estimated maximum pressures at the crater rim were between 5.59 and 5.81 GPa. We also use a Simplified Arbitrary Langrangian-Eulerian hydrocode (SALE 2) to simulate the propagation of shock waves through a material described by a Tillotson equation of state. Using the deformational and PT constraints of the Wolfe Creek crater, we estimate the maximum pressures, and the shock-wave attenuation, of this medium-sized impact.