Problems in Exploration Seismology and their Solutions

Abstract

Contents Preface xReferences 505Index 509Downloaded 06/25/14 to 134.153.184.170. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ Preface A number of geophysics texts (including our own) provide problems, but few furnish solutions to the problems. Thus students (and professors) who struggle with the problems but do not work them out for themselves miss many of the benefits of the problems. This work is our attempt to partially remedy this situation. This volume was begun to furnish solutions for the problems in the first edition of Exploration Seismology by Sheriff and Geldart; however, that project was never completed. After the second edition appeared in 1995, we revived and expanded the project to provide solutions not only for the problems in Exploration Seismology but also for additional problems. Our intention is to provide a stand-alone volume independent of Exploration Seismology which can be used with whatever textbooks professors and students are using. To this end many problems provide a brief summary of the basic theory required to solve the problem. These "backgrounds" should be regarded as an aide memoires only since they are not intended to develop the subject rigorously or in detail.Although this volume is independent of Exploration Seismology, we expect that a number of our readers will be using that text, and therefore we have organized and numbered the problems so as to be generally compatible with it; we have also used the same mathematical conventions and symbols (with a few exceptions).Measurements of time, fundamental in exploration seismology, are usually made to the nearest millisecond, but in some of the problems a precision of 10 ms or even less is used, especially when measurements on graphs are involved. Graphical solutions were generally obtained from plots on sheets of graph paper large enough to achieve the required accuracy, but the plots included here are, of necessity, reduced in sizes.A list of references cited is located at the end of the book. Terms which are in effect being defined have been italicized. The authors wish to acknowledge the generous assistance of Michael K. Fenwick in the preparation of this book.We invite readers to advise us of errors and faulty derivations or interpretations and also to send us alternative solutions or interpretations.L. P. Geldart R. E. Sheriffx Downloaded 06/25/14 to 134.153.184.170. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ Problems in Exploration Seismology and their Solutionswhat quantities or factors must be considered in arriving at the correct answer. Thirdly, we must consider the available information from which the answer is to be deduced. Some of the available data may not be relevant. Finally, we must determine how the relations between the various factors can be used to get from the starting point to the final goal, that is, the path that must be followed. We should plan how to obtain the solution. Often a diagram will help to u...

Delineating fracture zones using surface‐tunnel‐surface seismic data, P‐S, and S‐P mode conversions

“…In the second approach, to obtain a more focused and local analysis, the velocities shown in Figure were used to calculate V p / V s and Poisson's ( σ ) ratio for the seven zones in the vicinity of NE‐1. The Poisson's ratio ( σ ) was calculated using the isotropic case formula [ Geldart and Sheriff , ]: …”

“…In the second approach, to obtain a more focused and local analysis, the velocities shown in Figure 11 were used to calculate V p /V s and Poisson's (σ) ratio for the seven zones in the vicinity of NE-1. The Poisson's ratio (σ) was calculated using the isotropic case formula [Geldart and Sheriff, 2004]: 15c and 15d show the variation within the seven different zones based on using the velocities in Figure 11. Red lines and numbers inside blue boxes bounded by the first and third quartiles depict the median value per zone.…”

Determination of Rocks Elastic constants from Compressional and Shear Waves Velocities for Western Niger Delta, Nigeria.

“…The propagation speed of seismic waves through the earth depends on the elastic properties and density of the material. The elastic properties of any medium can be determined from velocity and density (V, ρ) measurements (Sheriff and Geldart, 1995;Sheriff, 1989;Parasnis, 1986;Wang, 2001;Ramana and Rao, 1987). The velocities of the longitudinal and transverse waves, designated V p and V s respectively, are expressed in terms of Lame's constants, µ and λ as: Most of the preceding theory assumes an isotropic medium.…”

“…The relations between the applied forces and the deformations are mostly conveniently expressed in terms of the concepts of stress and strain as stated in Hooke's law. The constant of proportionality is called an elastic constant or modulus (Telford et al, 1985;Sheriff and Geldart, 1995;Omodu and Ebeniro, 2005). Oil exploration activity in the Niger Delta sedimentary basin has resulted in the accumulation of many seismic and well log data.…”

Cavitation induced by shock wave focusing in eye-like experimental configurations

“…(3) The reflection coefficient for pressure w Rp = R p (θ, ρ 1 , α 1 , ρ 2 , α 2 , β 2 ) from the liquid (water)-solid (PMMA) boundary depends on the angle of incidence θ(ã, φ) = arccos[(l 2 −ã(ã − 2)) (2l)] and on the acoustic parameters of each medium. It is calculated using the Zoeppritz equations for reflection/refraction at a liquid/solid interface [31]. (4) As the shock wave propagates in water, it is exponentially attenuated.…”