A color representation of two-dimensional discontinuous seismic structures

Abstract

We present a computational procedure to represent with colors two-dimensional piecewise continuous functions. Seismic wave velocities are used as examples. Vertically and laterally heterogeneous layers are separated by structural discontinuities. Vertical lines divide each layer into trapezoidal cells; the non-parallel sides are the interfaces. A bivariate function is parametrized by assigning a value to each trapezoid vertex. The value at any point inside a trapezoid is obtained by linear interpolations applied along the non parallel sides up to the vertical line passing through the point and, then, along this line. Based in this already reported interpolation scheme, the procedure searches at each layer for points associated with a specific value range of the seismic parameter being represented; the resulting contiguous points define on area which is filled with a unique color from a palette. This procedure gives an accurate representation of a smooth, bivariate function with finite step discontinuities along layer interfaces, and does not introduce spurious features in the interpolation/smoothing numerical process.