In this article, we propose a new inversion scheme to calculate the melt volume fractions from observed seismic anomalies in a low-velocity layer (LVL) located atop the mantle transition zone. Our method identifies the trade-offs in the seismic signature caused by temperature, solid composition, melt volume fraction, and dihedral angle at the solid-melt interface. Using the information derived from the amplitude of P-to-S conversions beneath the western US, we show that the multiple permissible solutions for melt volume fractions are correlated to each other. Any possible solution can be directly transformed into alternative solutions whilst leaving the model output unchanged. Hence, the additional solutions can be rapidly derived given an initial solution. The calculation of multiple solutions reveals the universal properties of the whole range of solutions. A regional-averaged melt volume fraction of at least 0.5% occurs in every solution, even though a unique interpretation does not exist.