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About 10,000 papers for “multiple reflections”

Multiple Reflections

The Physics Video Demonstration Database (Cornell University)

This activity on multiple reflections is produced by the International Society for Optical Engineering, the Optical Society of America, and the Association of Universities for Research in Astronomy. Two plane rectangular mirrors, that meet on one edge, produce various reflection patterns. Students learn the relationship between the number of images produced and the orientation of the two mirrors. The site lists all necessary tools and materials and includes numerous helpful photographs and diagrams.

Cited by 0

Multiple reflections

T. P. Ellsworth · Geophysics · 1948

Abstract This is the lead paper of a symposium on the subject of multiple reflections. Possible types of multiple reflections are considered and compared with unusual reflections observed on records taken in the Northern Sacramento Valley of California. Geological and geophysical data are presented to demonstrate that a shallow basalt flow is producing identifiable multiple reflections. Consideration is given to the possible frequency of occurrence of multiple reflections in seismic surveys generally and limitations they may place upon seismic interpretations.

Cited by 6

Discussion; multiple reflections

C. H. Dresbach · Geophysics · 1948

Abstract In various places along the east side of the San Joaquin Valley, roughly thirty miles north of Bakersfield, reflected events have been observed that plotted below the known top of the basement. Sufficient well and velocity data are available to locate them quite closely. From what is known of the character of the basement material, it appears unlikely that the rather smoothly plotting, fairly continuous events could originate from within the basement. The conclusion is therefore forced that they must represent multiple events of some sort.

Cited by 1

Discussion of multiple reflections

Oliver C. Lester · Geophysics · 1948

Abstract A field experiment designed for the purpose of recording and identifying sound reflections from the surface of the earth is described. Shot and recording points at varying depths in adjacent deep holes were used. This experiment was performed at several locations in the Mid-Continent and Gulf Coast areas. No evidence of reflections from the ground-air contact was observed.

Cited by 0

2-D multiple reflections

Don Riley, Jon F. Claerbout · Geophysics · 1976

Abstract Starting with a 1-D subsurface model, a method is developed for modeling and inverting the class of multiple reflections involving the near-perfect reflector at the free surface. A solution to the practical problem of estimating the source waveform is discussed, and application of the 1-D algorithm to field data illustrates the successful elimination of seafloor and peg-leg multiples. Extending the analysis to waves in two dimensions, we make the approximation that the subsurface behaves as an acoustic medium. Based on several numerical and theoretical considerations, the scalar wave equation is split into two separate partial differential equations: one governing propagation of upcoming waves and a second describing downgoing waves. The result is a pair of propagation equations which are coupled where reflectors exist. Finite difference approximations to the initial boundary value problem are developed to integrate numerically the surface reflection seismogram. Use of the 2-D algorithm for modeling free-surface multiple reflections is illustrated by several reflector models. The 2-D inverse problem of simultaneously migrating primary reflections and inverting diffracted multiples consists of reversing the forward calculation with the data as boundary conditions. Causal directions of propagation are related to downward continuation of surface data. Reflector mapping principles are used to develop a general reflection coefficient estimator. The inverse algorithm is illustrated using the results of the 2-D forward calculation as the boundary conditions.

Cited by 70

Remarks on multiple reflections

B. Gutenberg, Chit Yaw Fu · Geophysics · 1948

Abstract One cannot help being impressed by the wonderful arrays of seismograms depicted in Mr. Ellsworth's paper and in the prepared discussions. The regularity of the time intervals of successive impulses and the alternating sequence of the change of phase are readily adapted to a mechanism of multiple reflections. If the latter is accepted, the following questions seem to merit some consideration: (a) the energy concentration, (b) the positions of the reflecting surfaces, (c) the sharpness of the source-impulse, and (d) the velocity contrast of the adjacent media.

Cited by 4

Notes on multiple reflections

Dean Walling · Geophysics · 1948

Abstract Since the inception of the reflection seismograph, apparent reflections have been observed from time to time, which for one reason or another, do not meet the requirements of normal reflections from interfaces in the sedimentary section. Various theories have served to explain and allow the proper interpretation of a large percentage of these spurious energies. Among these is the multiple-reflection theory which has proven to be applicable in many cases.

Cited by 0

Imaging of multiple reflections

A. J. Berkhout, D. J. Verschuur · Geophysics · 2006

Abstract Current multiple-removal algorithms in seismic processing use either differential moveout or predictability. If the differential moveout between primaries and multiples is small, prediction is the only option available. In the last decade, multidimensional prediction-error filtering by weighted convolution, such as surface-related multiple elimination (SRME), have proved to be very successful in practice. So far, multiples have been considered as noise and have been discarded after the removal process. In this paper, we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability. In the near future, one may expect that the so-called weighted-crosscorrelation (WCC) concept may offer an attractive alternative in approaching the multiple problem. WCC creates an option to avoid the adaptive subtraction process as applied in prediction-error algorithms. Moreover, it allows the transformation of multiples into primaries. The latter means that seismic imaging with primaries and multiples (nonlinear process) can be implemented by a sequence of linear processes, including the transformation of multiples into primaries and the imaging of primaries.

Cited by 117

Reflections on Multiple Modernities

Dominic Sachsenmaier, Jens Riedel, Shmuel N. Eisenstadt · 2002

This volume explores a rapidly emerging paradigm in the social sciences, which assumes culturally specific forms of modernity. Modernization is thus no longer equated with homogenization. Leading scholars from history, sociology, area studies, and economics discuss the concept’s implications. The first part covers a range of theoretical questions arising from the new approach. Issues such as the common features of all modernities and their interrelation with regional particularities, the reasons for antinomies of modernity, and the preconditions for a peaceful coexistence of cultures are raised. The second and third parts deal with Europe and China as two specific encounters with modernity, the tensions between universalism and cultural identities, both in past and present. The fourth part analyzes how Multiple Modernities translates into formal and informal institutions of “diverse capitalisms”. Authors include well-known specialists Mark Juergensmeyer, Hartmut Kaelble, Bruce Mazlish and Frederic Wakeman.

Cited by 88

Multiple Reflections of a Superball

Wolfram Demonstrations Project · 2007

This Demonstration shows the path of a multiply reflected superball in a horizontal channel (ignoring gravity). At each reflection, the energy and the angular momentum of the ball are conserved, but due to friction, translational and rotational energy can be converted into each other. The initial position of the ball is the red point and the final position is the blue pointThe graphic is scaled so

Cited by 0Open access

Multiple reflections of seismic energy

Raul F. Hansen, Curtis H. Johnson · Geophysics · 1948

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

Cited by 15