## Abstract

This paper is a report of observations of multiple reflections in seismograph work in Argentina, of successful methods of identifying them, and of unsuccessful attempts to eliminate them. The paper begins with generalizations regarding the expectancy of multiples and develops geometrically (using straight-line paths) the relation between multiples and their primary reflections for the cases of multiple reflection between a horizon and the surface and between two horizons, as regards time of reflection, dip and average velocity. The importance of a sharp reflecting contrast at the surface is emphasized, and it is concluded that the base of weathering may be more important in the formation of multiples than the surface of the earth. Early observations of multiple reflections from a volcanic flow and from a shallow basement are described. Other areas showed discordant data on the seismograms and cross sections, which, if due to multiples, could only be caused by multiple reflections from good sedimentary reflectors. In these areas a method for identifying both types of multiple reflections by their low average velocity as obtained by shooting reflection velocity-profiles was developed, the work being facilitated by considerable knowledge of velocity and section from previous refraction shooting. Though this reflection velocity-profile method is considered essential to positive and detailed identification of multiples, two methods of multiple identification using Delta T variations in continuous profiling are described and the results of considerable work with one of them are reported in graphical form, showing not only a separation of multiple from real reflections but also the determination of the true veloity-depth function by means of the real reflections so segregated. Experiments are briefly described in which variations in size or depth of shot and variations in filters were not effective in reducing the ratio of multiple reflections to real reflections. The paper closes with suggestions for identifying multiple reflections by their abnormal curvatures in discontinuous, symmetrical-spread dip shooting, and for using primitive qualitative methods where the topography or subsurface are not suited to the quantitative methods developed here. I. INTRODUCTION AND THEORY OF MULTIPLE REFLECTIONSSince the theory of geometrical optics has provided the solutions for most of the seismic phenomena heretofore observed and is the basis for most of the seismic exploration methods in use today, let us apply this theory to explain the formation of multiple reflections in the transmission of seismic energy. As an example of the application of these principles to determine the characteristics of multiple reflections, let us review the various manifestations of this kind which have been observed in Argentina, and the experiments and theories which have been devised to obtain a better understanding and a better control of this phenomenon. Before trying to find multiple reflections in seismograph work one is led to expect them, and can predict approximately what their properties will be, from the following two general observations:1. Just as the phenomena of refraction, reflection, attenuation, filtration, diffusion, etc. have been observed in seismic waves as in other types of wave energy, so other phenomena common to other types of wave energy should also be found in seismic waves--such as diffraction, transverse waves and multiple reflections (like those obtained with two mirrors properly located with respect to the image), etc.2. A similar problem is well understood in the study made in general seismology on earthquakes, i.e. the refracted waves which are reflected once or more at the surface of the earth (Figs. 1 and 2). If the similarity of this process to the formation of multiple reflections be debatable, the earthquake process at least indicates the ability of the surface of the earth to reflect a large percentage of the seismic energy reaching it from below.The following paragraphs explain the two most common types of multiple reflections that may appear on seismograph records: (1) between a reflecting horizon and the surface of the earth (Fig. 3),FIG. 1. Refracted seismic waves that have been reflected by the surface of the earth.FIG. 2. Reflection of an earthquake wave by the earth's surface. and (2) between two reflecting beds (Fig. 4). Though, in the interest of simplicity only these two cases are described, other more complicated cases can probably occur. CASE 1. MULTIPLE REFLECTIONS BETWEEN A REFLECTING HORIZON AND THE SURFACE OF THE EARTHThis case is easy to solve by the theory of images. In Figure 3, let S be the surface of the earth, R the reflecting horizon 'generating' the multiple reflection, and SP the shot point. Then S' is the image of S with respect to R; SP' and SP' are the image points of SP with respect to the surfaces R and S'. With these elements it is easy to draw the path of the rays which leave SP and arrive at the points A and B which represent the positions of the extreme receptors of a spread symmetric with respect to SP.Since the reflection which seems to come from the imaginary horizon S' is actually reflected twice from R and once from S, the data for the apparent reflection from S' should bear the following relation to the data for a single reflection from R: (1) Approximately double the reflection time (if the dip is not too large), and, (2) approximately double the angle of dip; furthermore, (3) since the ray for the reflection from the imaginary bed S' actually always travels through the formations between S and R, it should have an average velocity equal to that in the interval S-R, regardless of the velocity which exists at the depth corresponding to its reflection time. CASE 2. MULTIPLE REFLECTIONS BETWEEN TWO REFLECTING HORIZONSThis case may also be solved by the theory of images: Let S (Fig. 4) be the surface of the earth and a and b the two reflecting horizonsFIG. 3. Multiple reflections between a reflecting horizon and the surface of the earth. in question. Then (a-b)' is the image of a with respect to b; SP' is the image of SP with respect to (a-b)'; SP' is the image of SP with respect to b; and SP''' is the image of SP' with respect to a.With these points and surfaces it is easy to trace the paths of the rays which reach A and B from SP. The data for a multiple reflection generated between a and b will delineate the imaginary bed (a-b)' having a reflection time equal to that of the deeper actual reflecting bed, plus the difference in the reflection times of the two actual reflecting beds:EquationCompared with the rays reflected from bed b, the seismic rays corresponding to the multiple reflection travel over an additional path entirely between beds a and b, hence the average velocity between b and the imaginary deeper bed (a-b)' is the same as in the interval between a and b.For Case 2 multiple reflections the apparent dip is a complicated function of the dips of its two 'generators,' but, as worked out above, simple relations between the time and the average velocity of the multiple and of its 'generators' may be stated as follows: (3) The time of reflection of a Case 2 multiple reflection is equal to that of the deeper generating bed plus the difference between the reflection times of the two generating beds, and (2) the average velocity in the interval between the deeper generating bed and the multiple is the same as theFIG. 4. Multiple reflections between two reflecting beds. average velocity in the interval between the two generating beds.;The above theoretical relations have been obtained without considering the effects of the surface (weathered layer and topography). These effects modify the conditions for multiple reflections, and in practice can ne