Because very few soil point observations were available within the area, we calibrated the regression model by sampling the soil map on a grid.
We have computed the b-value at each node of the 0.1° × 0.1° grid by sampling the closest 100 earthquakes, determining Mc, and then computing the b-value for earthquakes with magnitudes above Mc, using a maximum likelihood procedure (Aki, 1965).
In these methods, the whole angular domain is divided into some predefined grids and a measurement matrix is constructed by sampling these grids.
Under these calculation conditions, our simulations examined seismic wave propagation at frequencies below f = 4.375 Hz (wavelength λ = 0.8 km) by sampling 8 grid points per minimum S-wavelength (e.g., Takemura et al. 2015).
However, it is worth noticing that this idea can be straightforwardly extended to any dictionary obtained by sampling a continuous function over a grid.
The original technique took advantage of 2-dimensional image processing tools for gradient calculation and edge detection by sampling time courses from a Cartesian grid of ROIs projected onto a patch on a flattened cortical surface (e.g., Nelson et al. 2010).
The accuracy of the simulation is dependent on the number of discrete points that the surface is sampled at, defined by the grid size n, which corresponds to the FFT indices k x and k y. Figure 5 shows the global error, or the difference between the final converged wavelength, and the analytical result, for different grid sizes.
Once applied to the grid, the samples were stained with 2% uranyl formate by floating the grid sample face down on a pool of stain.
Fig. 2 National total carbon stock estimation using systematic grid sampling showing a the relationship between the sampling grid dimensions and number of 1-ha field plots, b the percent difference between total field plot estimated and total model national carbon stocks by grid size and c same as in b but with the number of plots required by the grid sampling on the x-axis (log scale).
The sample was fixed by flooding the grid with a solution of 4% paraformaldehyde containing 0.05% ruthenium red.
