Receiver-function (RF) is a crustal imaging technique that entails deconvolving the radial or transverse component with the vertical component seismogram. Analysis of the variations of RFs along backazimuth and slowness is the key in determining the geometry and anisotropic properties of the crustal layers. Nonetheless, pseudorandom nuisance effects, influenced by the unknown earthquake source signature and seismic noise, are produced by the deconvolution process and obstruct precise comparisons of RFs across different backazimuths. Various methods such as weighted stacking, sparsity-induced transform and supervised denoising neural-network have been developed to reduce the nuisance effects. However, the common assumption of the nuisance effects as random Gaussian proves inadequate. Supervised denoising neural-network struggles to generalize effectively in intricate tectonic environments like subduction zones. In this study, we take an unsupervised approach where a network-based representation of a group of RFs with similar raypaths, enables disentanglement of the coherent crustal effects from the RF-specific nuisance effects. The representation learning task is performed using symmetric autoencoders (SymAE). SymAE effectively generates virtual RFs that capture coherent crustal effects and mitigate nuisance effects. Applied to synthetic RFs with real data-derived nuisances, our method exceeds bin-wise and phase-weighted stacking in quality and accuracy. Using real Cascadia Subduction Zone data, it enhances RFs and aids in interpreting a dual-layer subducting slab. We also provided sanity checks to verify the accuracy of the network-derived virtual RFs. One major advantage of our method is its ability to utilize all available earthquakes, irrespective of their signal quality, thereby enhancing reproducibility and enabling automation in RF analysis.