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, $ u_{rm max}$, we find shifts from $delta u$=-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 $delta u( u_{rm max})/ u_{rm max}$, ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962 K, 2.20).
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