The amplitude and slowness anomalies for P waves have been measured, at 0.8 Hz, within the nine subarrays located on the A, B, C rings at LASA. These measurements are made possible by the use of a high-resolution wave-number analysis program. It is found that these anomalies exhibit remarkably large fluctuations between the various relatively closely spaced subarrays. A model is proposed to explain these variations in which the crust and upper mantle structure under LASA is characterized as a random, or Chernov-type, medium. A statistical analysis of the amplitude, phase, and slowness fluctuations is made which, along with some theoretical results due to Chernov, are used to determine the properties of the random medium. It is found that the correlation distance of the random medium is 12 km and that the standard deviation of the index of refraction is 1.9 per cent. These random inhomogeneities are determined to exist in the crust and upper mantle of the Earth down to a depth of about 136 km.