Vertical arrays provide the most convenient geometry for many underwater passive acoustic applications that require the identification and isolating of propagating normal modes. Unfortunately, practical deployments of vertical arrays face several practical issues, including the need to compensate for vertical array inclination, and incomplete coverage of the water column that makes the use of Sturm-Liouville orthogonality problematic. Here bowhead whale signals collected in the Arctic Ocean are used to demonstrate how the use of non-linear sampling (called “warping”) in the time domain can be used to directly invert for array tilt, as well as yield mode shapes, without resort to the orthogonality relations.