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- Volume 49, Issue 6, 2001
Geophysical Prospecting - Volume 49, Issue 6, 2001
Volume 49, Issue 6, 2001
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From the Hagedoorn imaging technique to Kirchhoff migration and inversion
Authors Norman Bleistein and Samuel H. GrayThe seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique – a ‘string construction’ or ‘ruler and compass’ method – for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave‐equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle‐dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two.
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The use of instantaneous velocity in uplift investigations
More LessUplift and the accompanying reduction in overburden result in anomalously high velocity in the uplifted rock unit relative to its current depth. The present work utilizes the non‐uniqueness of the parameters of instantaneous velocity versus depth functions as an effective tool for uplift studies. The linear function with its two parameters, V0 and k, is a very simple function and is used as the illustrative vehicle. In the parameter space, i.e. in a plot where one axis represents V0 and the other axis represents k, non‐uniqueness can be represented by contours of equal goodness‐of‐fit values between the observed data and the fitted function. The contour delimiting a region of equivalent solutions in the parameter space is called a ‘solution trough’. Uplift corresponds to a rotation of the solution trough in the parameter space. It is shown that, in terms of relative depth changes, there are five possible configurations (five cases) of uplift in a given area (the mobile location) relative to another area (the reference location). The cases depend on whether the uplifted location had attained a (pre‐uplift) maximum depth of burial that was greater than, similar to, or smaller than the maximum depth of burial at the reference location. Interpretation of the relationships between the solution troughs corresponding to the different locations makes it possible to establish which of the five cases applies to the uplifted location and to estimate the amount of uplift that the unit had undergone at that location. The difficulty in determining the reduction in velocity due to decompaction resulting from uplift is a main source of uncertainty in the estimate of the amount of uplift. This is a common problem with all velocity‐based methods of uplift estimation. To help around this difficulty, the present work proposes a first‐order approximation method for estimating the effect of decompaction on velocity in an uplifted area.
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A new direction for shallow refraction seismology: integrating amplitudes and traveltimes with the refraction convolution section
More LessThe refraction convolution section (RCS) is a new method for imaging shallow seismic refraction data. It is a simple and efficient approach to full‐trace processing which generates a time cross‐section similar to the familiar reflection cross‐section. The RCS advances the interpretation of shallow seismic refraction data through the inclusion of time structure and amplitudes within a single presentation. The RCS is generated by the convolution of forward and reverse shot records. The convolution operation effectively adds the first‐arrival traveltimes of each pair of forward and reverse traces and produces a measure of the depth to the refracting interface in units of time which is equivalent to the time‐depth function of the generalized reciprocal method (GRM). Convolution also multiplies the amplitudes of first‐arrival signals. To a good approximation, this operation compensates for the large effects of geometrical spreading, with the result that the convolved amplitude is essentially proportional to the square of the head coefficient. The signal‐to‐noise (S/N) ratios of the RCS show much less variation than those on the original shot records. The head coefficient is approximately proportional to the ratio of the specific acoustic impedances in the upper layer and in the refractor. The convolved amplitudes or the equivalent shot amplitude products can be useful in resolving ambiguities in the determination of wave speeds. The RCS can also include a separation between each pair of forward and reverse traces in order to accommodate the offset distance in a manner similar to the XY spacing of the GRM. The use of finite XY values improves the resolution of lateral variations in both amplitudes and time‐depths. The use of amplitudes with 3D data effectively improves the spatial resolution of wave speeds by almost an order of magnitude. Amplitudes provide a measure of refractor wave speeds at each detector, whereas the analysis of traveltimes provides a measure over several detectors, commonly a minimum of six. The ratio of amplitudes obtained with different shot azimuths provides a detailed qualitative measure of azimuthal anisotropy and, in turn, of rock fabric. The RCS facilitates the stacking of refraction data in a manner similar to the common‐midpoint methods of reflection seismology. It can significantly improve S/N ratios.Most of the data processing with the RCS, as with the GRM, is carried out in the time domain, rather than in the depth domain. This is a significant advantage because the realities of undetected layers, incomplete sampling of the detected layers and inappropriate sampling in the horizontal rather than the vertical direction result in traveltime data that are neither a complete, an accurate nor a representative portrayal of the wave‐speed stratification. The RCS facilitates the advancement of shallow refraction seismology through the application of current seismic reflection acquisition, processing and interpretation technology.
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Vibroseis deconvolution: a comparison of cross‐correlation and frequency‐domain sweep deconvolution
Authors K.F. Brittle, L.R. Lines and A.K. DeyIdeally, traditional vibroseis processing produces a band‐limited zero‐phase Klauder wavelet through cross‐correlation of the sweep with the recorded signal. An alternative wavelet processing method involves deconvolving the sweep from the recorded vibroseis trace. This deconvolution can be achieved through frequency‐domain division. We compare and contrast the advantages and disadvantages of sweep deconvolution versus cross‐correlation on synthetic and real data.
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Hagedoorn's plus‐minus method: the beauty of simplicity
More LessHagedoorn developed the plus‐minus method with the objective of providing the exploration world with a simple and rapid approximation of Thornburgh's wavefront reconstruction method. Straightforward adding and subtracting produces depths and velocities at all geophones where the refracted waves from a set of reciprocal shots are first arrivals. Even though seismic refraction has not kept up with the revolutionary advance of reflection technology during the past decades, the method still has a lot to offer, especially in shallow engineering, and environmental, groundwater and sea‐bed surveying. Its strong points are the ease of application, the low costs, the effectiveness in the shallow zone, the unique ability to provide detailed velocity information on the deepest refractor and the capability for producing parameters for layer and rock characterization.Because of its simplicity, the plus‐minus method is ideally suited for real‐time processing of refraction data in the field, thus monitoring the data quality and the optimal shot configuration. Today, such field processing is easily performed with a laptop and dedicated software. matlab® is a software package that enables tailor‐made processing, offering a combination of a programming language, visualization tools and a large library of ready‐made functions. This paper presents a plus‐minus program developed in matlab and illustrates its application with a case study in Yemen, where seismic refraction was used in a regional groundwater study. Here, refraction provided not only a detailed section across the recharge area of a coastal plain but also the additional information needed to reduce ambiguity in the interpretation of the vertical electrical soundings made in the area.
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The seismic transmission volume
Authors J.G. Hagedoorn and G. DiephuisParallels are drawn between phenomena observed in optics and typical characteristics in exploration seismology. Considerations are also made in the context of major physical theories throughout the centuries. It is concluded that the one key similarity between optics and seismics is the transmission volume, which has ‘fuzzy’ characteristics. Distribution of energy in this volume determines the achievable resolution and might give an insight into spatial inhomogeneities in the subsurface.
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Common‐reflection‐surface (CRS) stack for common offset
Authors Yonghai Zhang, Steffen Bergler and Peter HubralWe provide a data‐driven macro‐model‐independent stacking technique that migrates 2D prestack multicoverage data into a common‐offset (CO) section. We call this new process the CO common‐reflection‐surface (CRS) stack. It can be viewed as the generalization of the zero‐offset (ZO) CRS stack, by which 2D multicoverage data are stacked into a well‐simulated ZO section. The CO CRS stack formula can be tailored to stack P‐P, S‐S reflections as well as P‐S or S‐P converted reflections. We point out some potential applications of the five kinematic data‐derived attributes obtained by the CO CRS stack for each stack value. These include (i) the determination of the geometrical spreading factor for reflections, which plays an important role in the construction of the true‐amplitude CO section, and (ii) the separation of the diffractions from reflection events. As a by‐product of formulating the CO CRS stack formula, we have also derived a formula to perform a data‐driven prestack time migration.
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3D refraction statics in the wavenumber domain
Authors Luigi Zanzi, Sabrina Bellotti and Eusebio StucchiThe wavenumber iterative modelling (WIM) method was first introduced to estimate the static corrections for 2D land profiles by performing first‐break inversion in the wavenumber domain. The WIM algorithm presents some useful advantages, of robustness, stability and flexibility. Robustness is obtained by intensive exploitation of all the available data and by application of an automatic function for mispick removal. Stability is the result of an iterative procedure that ensures convergence towards a stable and plausible solution even at the end of the profile where the problem is normally ill‐posed. Finally, flexibility is due to the possibility of solving for multilayered structures and of estimating vertical gradients of the velocity.This work extends the WIM method to three dimensions. The extension is feasible because the three‐dimensional (3D) problem can be decomposed into a number of small independent problems, one for any pair of wavenumbers kx, ky. The extension preserves the above‐mentioned advantages. The parameters of the estimated model are affected differently by noise: the analysis of the input/output noise transfer function demonstrates that the high spatial frequencies of the velocity distributions are the components that are most affected by noise; thus, the algorithm includes a gradual damping of the higher wavenumbers of the velocity parameter. Although the WIM 3D algorithm requires a larger amount of RAM compared with other standard approaches, considerable reduction in CPU run time can be achieved as every wavenumber pair can be treated as an independent linear problem.
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Calibrate yourself to your data! A vital first step in seismic interpretation
More LessStratigraphic, reservoir and fluid interpretation demands a thorough understanding of the seismic‐to‐well tie. Data phase, polarity and tuning effects significantly influence this tie and are often poorly understood. By relating seismic character to known subsurface geology, the interpreter should gain better understanding and be able to calibrate himself to his data. This is an important preliminary stage in any seismic interpretation beyond structure.
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J.H. Hagedoorn – inventing the Hapa: A review of a geophysicist's ‘other’ work and how it inspired others
More LessThis paper describes J.G. Hagedoorn's work on ‘ultimate sailing’– the combination of a manned kite and a water kite called a Hapa, constituting a minimal sailing system – and the way others have taken up his challenge to sail while suspended from a kite. Hagedoorn's goal has not been entirely achieved, but ‘near’ and partial solutions have been reached. Kite‐Hapa‐sailing continues to pose a ‘Holy Grail’ type challenge to many kite‐sailors.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 18 (1970 - 2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 28 (1980)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 2 (1954)
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Volume 1 (1953)