INTRODUCTION

A number of recent papers (Williams and Garnero, 1996; Revenaugh and Meyer, 1997; Wen and Helmberger, 1998a; 1998b) have shown that the ratio of seismic velocity decrements $d\ln v_s/d \ln v_s$ (where v_s is the shear velocity, v_p is the compressional velocity) is approximately equal to 3 in ultralow velocity zones near the the core-mantle boundary (see Young and Lay (1987) for a review of CMB issues). Changes in both numerator and denominator are negative but the ratio has been found to be on the order of 3, and because this value is so high it is generally argued that these results provide evidence of partial melt in these regions. The rock physics analyses used in these papers are generally based on classical effective medium theories such as those reviewed by Watt et al. (1976). The main problem with such analyses is that the results tend to be quite sensitive to the assumed microstructure of the partial melt system [see Williams and Garnero (1996)] and therefore may not be truly representative of the system being studied. I will give a different derivation here of the velocity decrement ratio that highlights the key assumptions that must be made to arrive at this ratio. This approach shows how general and insensitive to microstructure the ratio really is for partial melt systems, and shows furthermore how to analyze deviations from the assumptions made. The methods presented may also be extended to permit estimates of changes not only of the ratio but also of the two seismic velocities themselves. A procedure for doing so is outlined at the end of the paper.