  We analyse the effect on adiabatic stellar oscillation frequencies of
replacing the near-surface layers in 1D stellar structure models with averaged
3D stellar surface convection simulations. The main difference is an expansion
of the atmosphere by 3D convection, expected to explain a major part of the
asteroseismic surface effect; a systematic overestimation of p-mode frequencies
due to inadequate surface physics.
  We employ pairs of 1D stellar envelope models and 3D simulations from a
previous calibration of the mixing-length parameter, alpha. That calibration
constitutes the hitherto most consistent matching of 1D models to 3D
simulations, ensuring that their differences are not spurious, but entirely due
to the 3D nature of convection. The resulting frequency shift is identified as
the structural part of the surface effect. The important, typically
non-adiabatic, modal components of the surface effect are not included in the
present analysis, but relegated to future papers.
  Evaluating the structural surface effect at the frequency of maximum mode
amplitude, $\nu_{\rm max}$, we find shifts from $\delta\nu$=-0.8 microHz for
giants at $\log g$=2.2 to -35 microHz for a ($T_{\rm eff}=6901$ K, $\log
g$=4.29) dwarf. The fractional effect $\delta\nu(\nu_{\rm max})/\nu_{\rm max}$,
ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962
K, 2.20).
