1. A method of obtaining a representation of characteristics of the earth comprising; receiving and recording geophysical seismic signals which are measurements of pressure at a plurality of receivers, monitoring the response of the earth to a seismic source at a plurality of receivers, processing the signals wherein the method further includes; determining gradients of the signal measured pressure values, evaluating sums or integrals of functions of weighted signal values over a one or multidimensional domain, wherein the domain is split into a plurality of simplices and the signal values are interpolated across the simplices using the gradients of the signal measured pressure values to give non-linear approximations of the functions within simplices, and using the evaluated sums or integrals to obtain a representation of characteristics of the earth.