ENERGIE DES VIBRATIONS ET FILTRAGE NON LINEAIRE*

A filtered seismic trace often appears as an almost sinusoidal curve. The reflected energy arrivals are superimposed and interfere with the continuous oscillations of the trace, and are therefore often difficult to distinguish. This is the chief difficulty in picking reflections. The situation is similar to that met with in gravimetry when a strong regional anomaly conceals small local anomalies. However, a regional anomaly is regular and broad, and owing to these two characteristics it can be removed. In reflection seismology batches of energy may also be concealed by oscillations of a continuous character. The main difference lies in the fact that the background of continuous seismic vibrations is not static, as is the case in gravimetry, but variable with time. However, a fairly constant physical quantity corresponds to these vibrations, which are composed partly of noise, partly of undesired secondary reflections. This quantity is the energy of motion of the surface layer of the ground. It is this troublesome energy that we intend to remove, in order to keep only the useful, actually reflected, energy.

These remarks clearly demonstrate the importance of an investigation of the energy contained in the surface layer of the ground. After showing that, in the simplest case, the density of this energy can be expressed almost exactly by the formula

u^′2−uu′′

in which u′ is the velocity of a ground particle, we show how the non‐linear filtering defined by this formula can be realized, and we provide a few examples.