  The analysis of continuously spatially varying processes usually considers
two sources of variation, namely, the large-scale variation collected by the
trend of the process, and the small-scale variation. Parametric trend models on
latitude and longitude are easy to fit and to interpret. However, the use of
simple parametric models for characterizing spatially varying processes may
lead to misspecification problems if the model is not appropriate. Recently,
Meil\'an-Vila et al. (2019) proposed a goodness-of-fit test based on an
L2-distance for assessing a parametric trend model with correlated errors,
under random design, comparing a parametric and a nonparametric trend
estimators. The present work aims to provide a detailed computational analysis
of the behavior of this approach using different bootstrap algorithms for
calibration, under a fixed-design geostatistical framework. Asymptotic results
for the test are provided and an extensive simulation study, considering
complexities that usually arise in geostatistics, is carried out to illustrate
the performance of the proposal.
