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To establish the mechanism of unconventional superconductivity inSr$_2$RUO$_4$, a prerequisite is direct information concerning themomentum-space structure of the energy gaps $\Delta_i(k)$, and in particularwhether the pairing strength is stronger ("dominant") on the quasi-1D ($\alpha$and $\beta$) or on the quasi-2D ($\gamma$) Fermi surfaces. We present scanningtunneling microscopy (STM) measurements of the density-of-states spectra in thesuperconducting state of Sr$_2$RuO$_4$ for $0.1 T_C<T<T_C$, and analyze them,along with published thermodynamic data, using a simple phenomenological model.We show that our observation of a single superconducting gap scale with maximumvalue $2\Delta \approx 5 T_C$ along with a spectral shape indicative of linenodes is consistent, within a weak-coupling model, with magnetically mediatedodd-parity superconductivity generated by dominant, near-nodal Cooper pairingon the $\alpha$ and $\beta$ bands.

Evidence from Tunneling Spectroscopy for a Quasi-One Dimensional Origin of Superconductivity in Sr2RuO4