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Virtually all practical algorithms for aberration correction in medical ultrasound have thus far modeled the aberrating tissues with a thin time-delay screen. While this assumption is probably reasonable for small image regions (isoplanatic patches), practical application is still difficult. In many cases, an inability to estimate the screen parameters with sufficient accuracy in the presence of aberration and speckle targets has led to disappointing performance. A new aberration correction approach is proposed, inspired by the geophysical imaging concept of time migration. This technique is motivated by considering complete, bistatic, pulse-echo data acquired from layered media, where sound speed is a function of depth only. Reflection travel times as a function of source-receiver offset in such a model are approximately hyperbolic, just as they would be if the sound speed in the medium were constant and equal to the rms speed of the layers. Seismic imaging practice has shown this approximation to be robust in the presence of minor lateral speed variations. By focusing each point in the image using a constant sound-speed assumption, but allowing this assumed speed to change from point to point, a well-focused image may be obtained. A focusing criterion is all that is needed to determine the optimum focusing speed at each image point, without a priori knowledge of the medium properties. FDTD simulations provide synthetic data acquired from a 64-element array. A simple skull model was interposed between the array and targets in one simulation; in another, a speckle-producing region with embedded cysts was imaged through a Gaussian-shaped, high-speed anomaly. In both cases, images formed using different assumed sound speeds show different parts of the image in good focus. Application of the proposed focusing criterion produces a composite image showing improvement over any single image formed assuming a constant speed of sound.