It is widely acknowledged that many geotechnical properties are correlated over space and/or time. Consequently, cross-correlated random fields play a pivotal role in geotechnical reliability analysis for properly modeling both the auto- and cross-correlation structures of correlated geotechnical properties. Existing methods for simulating cross-correlated random fields typically require precise knowledge of random field parameters as input. However, in a typical site investigation program, engineering constraints such as limited time, budget, and space often lead to sparse, non-co-located, and irregularly distributed measurements of geotechnical properties. Estimating reliable random field parameters, particularly the auto-correlation and cross-correlation structures of a two-dimensional (2D) cross-correlated random field, from such data is a notorious challenge. To address this issue, this study introduces a 2D cross-correlated random field generator that is able to directly simulate 2D multivariate cross-correlated geotechnical random field samples (RFSs) from sparsely measured and non-co-located data points. This generator leverages the method developed by Guan and Wang (2023), which employs a joint sparse representation to simultaneously exploit auto- and cross-correlation structures of various spatial/temporal quantities directly from sparse measurements. The effectiveness of the proposed generator is demonstrated using real geotechnical properties data. The results demonstrate that RFSs generated using this method from sparse measurements accurately capture the spatial auto- and cross-correlation structures of different geotechnical properties.