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We investigated the velocity measurements of leaky surface acoustic waves (LSAW) by line-focus-beam (LFB) acoustic microscopy of thin specimens for which the waves reflected from the back surface of the specimen (back reflection) must be included in the measurement model. The influence of back reflection resulted in a serious problem in measurement accuracy of the apparent changes of measured velocities. Using several samples of thin synthetic silica glasses, the determination of LSAW velocity affected by the reflected waves and the relationship between the specimen thickness and the apparent velocity change with a periodic frequency interval in the frequency dependence of measured LSAW velocities are discussed in detail. Three useful methods for eliminating that influence are proposed and demonstrated: first, separating the radio frequency (RF) pulsed wave signal from the specimen surface and the pulses reflected from the back surface by reducing the RF pulse width; second, scattering acoustic waves from the roughened back surface; and third, taking the moving average of measured frequency characteristics of LSAW velocities. It is shown that, among these methods, the moving average method is the most useful and effective as a general means to eliminate the influence and to determine intrinsic velocity values because this method needs no specimen process and no system change, and the same conventional V(z) curve measurement and analysis can be employed.