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Short acoustical signals like those caused by explosions will in a waveguide split into mode arrivals. If the distance is long enough, they can at the receiver be resolved in time with appropriate narrowband filters. They can simultaneously be resolved in vertical angle (incidence-) with an endfire array and a beamformer. Combined in a beam-time diagram the arrivals will line up along a straight line. The slope of this line is invariant with frequency, mode indexes, source and receiver depths. It can conveniently be linked to the so-called waveguide invariant β. An alternative approach to β is to compute it from the bathymetric profile. This is valid for range variable waveguides under adiabatic conditions, constant water sound speed over a harder bottom, and small grazing angles. Together these two approaches to β can be combined in a formula, where direct range determination is the end product. The applicability of the method is demonstrated on data from an experiment at sea. An 820-m array with 10 hydrophones was deployed at the bottom in 320-m water depth. For two endfire runs in opposite directions, small explosive charges out to 115 km were used as sound sources. Typical range estimation errors were 5-10%.