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The range of the source can be estimated using the concept of waveguide invariant that describes the interference pattern of sound fields in water. Previous works have been shown that the interference pattern suffers from temporal and spatial variations in uncertain environment. This could cause the performance degradation of the processor. Theoretical analyses are presented for water-depth mismatch and sound-speed profile (SSP) mismatch. The theoretical results are then demonstrated by examples using both simulations and ocean acoustic data. The results suggest that the water-depth mismatch just shifts the peak around the correct one and the sound-speed mismatch can be neglected for the very low frequency even without constant water sound speed. But its robustness to SSP mismatch does not exist for higher frequency. For sediment-type mismatch, although a large modelled mistake is introduced, the results are acceptable. This implies that the effect of sediment-type mismatch is minor compared to that of mismatches in water column. On the whole, the processor is robust to environmental mismatch and can be applied to lower frequency with minimal environmental information.