HANDBOOK OF GEOPHYSICAL EXPLORATION
`
`SEISMIC EXPLORATION
`
`VOLUME 1
`
`BASIC THEORY OF EXPLORATION SEISMOLOGY
`
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`HANDBOOK OF GEOPHYSICAL EXPLORATION
`
`SEISMIC EXPLORATION
`
`Editors: Klaus Helbig and Sven Treitel
`
`PUBLISHED VOLUMES
`
`1984 - Mathematical Aspects of Seismology. 2nd Enlarged Edition
`(M. Båth and A.J. Berkhout)*
`1984 - Seismic Instrumentation (M. Pieuchot) ISBN 0-08-036944-8
`1984 - Seismic Inversion and Deconvolution (a) Classical Methods (E.A. Robinson)*
`1985 - Vertical Seismic Profiling (a) Principles. 2nd Enlarged Edition (B.A. Hardage)*
`1987 - Pattern Recognition & Image Processing (F. Aminzadeh)*
`1987 - Seismic Stratigraphy (B.A. Hardage)*
`1987 - Production Seismology (J.E. White and R.L. Sengbush)*
`1989 - Supercomputers in Seismic Exploration (E. Eisner)*
`1994 - Seismic Coal Exploration (b) In-Seam Seismics (L. Dresen and H. Rüter)*
`1994 - Foundations of Anisotropy for Exploration Seismics (K. Helbig)
`ISBN 0-08-037224-4
`1998 - Physical Properties of Rocks: Fundamentals and Principles of Petrophysics
`(J.H. Schön) ISBN 0-08-041008-1
`1998 - Shallow High-Resolution Reflection Seismics (J. Brouwer and K. Helbig)
`ISBN 0-08-043197-6
`1999 - Seismic Inversion and Deconvolution (b) Dual-Sensor Technology (E.A. Robinson)
`ISBN 0-08-043627-7
`2000 - Vertical Seismic Profiling: Principles. 3d Updated and Revised Edition
`(B.A. Hardage) ISBN 0-08-043518-1
`2001 - Seismic Signatures and Analysis of Reflection Data in Anisotropic Media
`(I. Tsvankin) ISBN 0-08-043649-8
`2001 - Computational Neural Networks for Geophysical Data Processing (M.M. Poulton)
`ISBN 0-08-043986-1
`2001 - Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and
`Porous Media (J.M. Carcione) ISBN 0-08-043929-2
`2002 - Multi-Component VSP Analysis for Applied Seismic Anisotropy (C. MacBeth)
`ISBN 0-08-0424439-2
`2002 - Nuclear Magnetic Resonance. Petrophysical and Logging Applications
`(K.J. Dunn, D.J. Bergman and G.A. LaTorraca) ISBN 0-08-043880-6
`2003 - Seismic Amplitude Inversion in Reflection Tomography (Y. Wang)
`ISBN 0-08-044243-9
`2003 - Seismic Waves and Rays in Elastic Media (M.A. Slawinski)
`ISBN 0-08-043930-6
`2004 - Quantitative Borehole Acoustic Methods (X. Tang and A. Cheng)
`ISBN 0-08-044051-7
`2004 - Seismic While Drilling - Fundamentals of Drill-Bit Seismic for Exploration
`(F. Poletto and F. Miranda) ISBN 0-08-043928-4
`
`* Book out of print.
`
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`
`SEISMIC EXPLORATION
`
`Volume 1
`
`BASIC THEORY OF EXPLORATION SEISMOLOGY
`
`by
`
`John K. Costain and Cahit Çoruh
`Department of Geological Sciences
`Virginia Polytechnic Institute and State University
`Blacksburg, VA, U.S.A.
`
`2004
`
`ELSEVIER
`Amsterdam - Boston - Heidelberg - London - New York - Oxford
`Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo
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`290
`
`CHAPTER 6. TRAVELTIME CURVES AND VELOCITY
`
`6.2.4 The normal moveout correction
`Recording configurations necessarily introduce reflection curvature even from
`a horizontal reflector. The curvature provides the time information required
`to determine the true subsurface velocity (rather the horizontal component of
`the true subsurface velocity). But the curvature must be removed in order
`to provide an accurate image of the subsurface geometry. According to (6.4)
`normal moveout decreases with two-way traveltime to the reflector, decreases as
`the square of the velocity, and increases as the square of the offset distance x.
`Two of these relationships are illustrated in Figure 6.25. The presence of dip
`introduces an additional factor. Several synthetic traces generated using the
`geometry of Figure 6.25b are shown in Figure ??a (no-dip) and b (20° dip).
`First we apply the normal moveout correction to the reflections generated
`from the zero-dip model. This amounts to shifting each point to an earlier time
`by the amount NMO where
`
`NMO =
`
`T-To
`
`/
`v2
`V ° 2v2To
`X2
`2^TO
`
`"
`
`v4
`8v4To
`
`3
`
`v6
`16v6To5
`
`c v8
`128v8Tj
`
`\
`J
`
`°
`
`^
`
`after a binomial expansion and retaining only the first two terms of the ex-
`pansion. A more accurate approach, and that commonly used for the normal
`moveout correction, is obtained by retention of the Xi term. The difference in
`traveltime is shown in Figure 6.17 on page 283. The collection of traces used is
`that shown in Figure 6.26a generated by the program NMOApplication.nb on
`the CD-ROM that accompanies this volume. A minimum-delay wavelet (Mini-
`mumDelayWavelet.txt) was used.
`In Figure 6.26b the normal moveout has been "removed" by the application
`of Equation 6.24 and accomplished by shifting each point in a trace by an
`amount of time given by Equation (6.24). For each value of To (corresponding
`to zero offset) the trace sample at offset X has been shifted to an earlier time
`by the amount NMO defined by Equation (6.24). This has resulted in wavelet
`stretching because the point-by-point application of (6.24) has been applied to
`a wavelet of finite duration causing the earlier parts of the wavelet to be shifted
`upward more than the later parts because the NMO correction is not linear. The
`reader is invited to explore this effect further using different wavelets, offsets, and
`To-times. For zero dip the NMO-corrected traces are now commonly considered
`to be ready for stacking. The result will not be a stack of the original wavelet
`shape, because of wavelet stretching, but generally an acceptable approximation
`to it.
`In Figure 6.27a a 5-trace gather has been generated over a reflector with
`a dip of 20°. Equation (6.24) has again been used to apply the normal move-
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`6.2. REFLECTION TRAVELTIME CURVES
`
`291
`
`Figure 6.26: (a) Synthetic 5-trace gather acquired over zero-dip reflector. Recording
`geometry as in Figure 6.25a. A horizontal reflector is not recorded as a
`horizontal reflector, (b) Same traces after application of the normal move-
`out correction. Note stretching. After application of the NMO correction
`the onset reflection arrival times are correct. The effect of the recording
`geometry has been removed and a horizontal reflector is now recorded as
`a horizontal reflection, but the wavelet shapes now differ markedly. This
`is undesireable because traces in a gather are to be summed together
`in order to increase the signal-to-noise ratio. The optimum summation
`would be one for which the wavelet shape is the same for each trace in the
`gather for any arrival time. Note that the later-arrival wavelets are less
`affected by the stretching caused by application of the NMO correction.
`(NMOApplication.nb ==> NMO2.cdr => NMO2noDip.wmf)
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`292
`
`CHAPTER 6. TRAVELTIME CURVES AND VELOCITY
`
`Figure 6.27: (a) Synthetic 5-trace gather acquired over a reflector dipping 20°. Record-
`ing geometry as in Figure 6.25b. After application of the same Equa-
`tion (6.24) the onset reflection arrival times are not correct. The effect
`of the recording geometry has not been removed and wavelet stretching
`still occurs. (NMOApplication.nb => NMO2.cdr ==> NMOdip.wmf)
`
`In the presence of
`out correction. This time the results are unsatisfactory.
`dip the true rock velocity cannot be used (even if it were known) to flatten
`the reflection to a common offset time (Figure 6.27b). The velocities used to
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`6.3. REFRACTION TRAVELTIME CURVES
`
`293
`
`stack reflection seismic data ("stacking velocities") are commonly obtained by
`examining "constant-velocity panels", which are mini-stacks of a dozen or so
`traces that are inspected visually to see which velocity produces the best look-
`ing (from a geological standpoint) and the most coherent (from a mathematical
`standpoint) result. An example was shown in Figure 6.22 on page 286.
`The reader is referred to Yilmaz [203, p. 668-836], Claerbout [39, p. 160-
`163], and Stolt and Benson [170, This Series, Volume 5] for excellent in-depth
`discussions of the principles of the dip-moveout correction, a related discussion
`of prestack migration, and the theory and practice of seismic migration.
`
`6.3 Refraction traveltime curves
`
`The seismic events of interest in refraction seismology are quite different from
`those of reflection, and are called head waves. The objectives of refraction
`seismology are the same, however: to determine how the velocity changes versus
`depth. Head waves are generated at the top of the boundary between two media,
`rather than being reflected from the boundaries. In order to record such waves,
`greater source-receiver offsets are generally required.
`The general shapes and branches of refraction traveltime curves, and their
`relation between reflection traveltime curves, can be deduced by examining ray-
`paths associated with three general source-receiver offsets:
`
`1. zero offsets
`
`2. critical reflections
`
`3. very long offsets
`
`We first examine refraction traveltime curves qualitatively to place them in
`context with reflection traveltime curves. Then we derive the equations for the
`refraction traveltime curves.
`Assume a multilayer medium for which the velocity of each layer is constant
`within the layer, but the layer velocity increases with depth to the layer. The
`assumption of increasing layer velocity with depth is not required for reflection
`seismology, but is a limitation of refraction seismology, although, in general, the
`velocity does increase with depth in the earth.
`The model is shown in Figure 6.28. Because of the increase in velocity of
`successively deeper layers, refraction events that travel deeper are able to arrive
`ahead of shallower refraction and reflection events that have actually traveled
`shorter paths; hence, refraction arrivals are commonly called head waves. The
`energy source is located at S in Figure 6.28. All of the seismic events to be
`described are P-waves, also called compressional waves, or body waves. The
`earliest events to arrive at any of the receivers on the surface follow a direct
`horizontal path (1) in the upper medium of velocity v\. They define a segment,
`or branch of a traveltime curve whose slope is 1/vi, labeled as such in the figure.
`Representative raypaths for this and other arrivals are shown in Figure 6.28.
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