Considering fractures with heterogeneous aperture distributions, we explore the reliability of constant-aperture estimates derived from ground penetrating radar (GPR) reflection data. We generate geostatistical fracture aperture realizations that are characterized by the same mean-aperture and variance, but different Hurst exponents and cut-off lengths. For each of the 16 classes of heterogeneity considered, we generate 1000 fracture realizations from which we compute GPR reflection data using our recent effective-dipole forward model. We then use each (noise-contaminated) data set individually to invert for a single ‘apparent’ aperture, that is, we assume that the fracture aperture is homogeneous. We find that the inferred ‘apparent’ apertures are only reliable when fracture heterogeneity is non-fractal (the Hurst exponent is close to 1) and the scale of the dominant aperture heterogeneities is larger than the first Fresnel zone. These results are a direct consequence of the nonlinear character of the thin-bed reflection coefficients. As fracture heterogeneity is ubiquitous and often fractal, our results suggest that robust field-based inference of fracture aperture can only be achieved by accounting for the nonlinear response of fracture heterogeneity on GPR data.