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- Volume 43, Issue 7, 1995
Geophysical Prospecting - Volume 43, Issue 7, 1995
Volume 43, Issue 7, 1995
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Point‐to‐curve ray tracing in complicated geological models1
Authors Andrzej Hanyga and Jan PajchelAbstractBoundary‐value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one‐parameter family of BVPs and makes it easy to obtain all the solutions of a BVP.
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Monitoring subsurface changes over time with cross‐well electromagnetic tomographyt1
Authors David L. Alumbaugh and H.F. MorrisonAbstractA fast imaging technique is developed to deduce the spatial conductivity distribution in the earth from low‐frequency (> 1 MHz) cross‐well electromagnetic measurements. A sinusoidally oscillating, vertically orientated, magnetic dipole employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3D vector problem to a more manageable 2D scalar form. Additional efficiency is obtained by using the Born series approximation which is derived from nonlinear integral equations that account for the scattered magnetic fields generated by inhomogeneities embedded in a layered earth. Stabilization of the inversion problem is accomplished through the use of bounding constraints and a regularization method which results in a smooth model that fits the data to the desired noise level.
The applicability of cross‐well electromagnetics for imaging and monitoring changes caused by subsurface processes has been tested by simulating plumes of conductive fluid with 2D models. The images that result from inverting these synthetic data indicate that the vertical resolution of the method is better than the horizontal, increasing the noise decreases the image resolution, and incorporating a priori knowledge in the form of positivity constraints improves the results. Although higher operating frequencies are usually associated with better resolution, frequencies as low as 100 Hz can produce acceptable images in simulated oilfield environments.
The imaging scheme has been applied to data collected during a salt‐water injection experiment at the Richmond Field Station test site in Richmond, California. Both the data and the resulting images clearly reveal the presence of the plume and indicate that it is migrating towards the north‐northwest rather than spreading symmetrically about the injection well. Applying the imaging code to synthetic data generated by a 3D sheet model verifies the interpretation of these results.
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Downward continuation of (Vs)L profile in 1P (time‐domain) with linear excitation using point electrodes. A short notet1
Authors A. Apparao, R. Sivarama Sastry and V. Subrahmanya SarmaAbstractIt is seen that the apparent chargeability (Ma)L anomaly over a 2D graphite body splits into two distinct (Vs)L anomalies which closely follow the apparent resistivity profile. This suggests that the electric field amplitude is distorted due to a superficial inhomogeneity creating a (Vs)L anomaly, which bears no relation to the polarized body. The target depth obtained by continuation of such a profile is therefore, not acceptable.
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One‐dimensional non‐linear inversion of magnetotelluric data: the importance of data errorrs1
Authors R. Belay and T.M. RasmussenInversion of noisy magnetotelluric data over a horizontally stratified earth has no unique solution. Instead, the resistivities and thicknesses of the layers can only be specified to lie within certain bounds at a particular confidence level. The significance of having correctly estimated data errors when calculating the parameters and parameter bounds is discussed. Emphasis is put on the very corrunon problem of not being able to obtain models which can be considered acceptable with a reasonable certainty from a statistical point of view. A method is presented to obtain a pragmatic data error description by adjustment of wrongly estimated data errors while keeping the suppression of 1D data features at a minimum. A comparison is made between calculation of the parameter bounds based on approximating the confidence surface by hyperellipsoids and a calculation based on a full non‐linear most‐squares analysis. In general it is found that the approximation works very well when the confidence limit is small. However, significant deviations are found in some cases.
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Fourier finite‐difference migration for steeply dipping reflectors with complex overburden1
More LessAbstractThe improvement in accuracy and efficiency of wave‐equation migration techniques is an ongoing topic of research. The main problem is the correct imaging of steeply dipping reflectors in media with strong lateral velocity variations. We propose an improved migration method which is based on cascading phase‐shift and finite‐difference operators for downward continuation. Due to these cascaded operators we call this method‘Fourier finite‐difference migration’(FFD migration).
In our approach we try to generalize and improve the split‐step Fourier migration method for strong lateral velocity variations using an additional finite‐difference correction term. Like most of the current migration methods in use today, our method is based on the one‐way wave equation. It is solved by first applying the square‐root operator but using a constant velocity at each depth step which has to be the minimum velocity. In a second step, the approximate difference between the correct square‐root operator and this constant‐velocity squareroot operator (the error made in the first step) is implemented as an implicit FD migration scheme, part of which is the split‐step Fourier correction term.
Some practical aspects of the new FFD method are discussed. Its performance is compared with that of split‐step and standard FD migration schemes. First applications to synthetic and real data sets are presented. They show that the superiority of FFD migration becomes evident by migrating steeply dipping reflectors with complex overburden having strong lateral velocity variations. If velocity is laterally constant, FFD migration has the accuracy of the phase‐shift method. The maximum migration angle is velocity adaptive, in contrast to conventional FD migration schemes. It varies laterally depending on the local level of velocity variation. FFD migration is more efficient than higher‐order implicit FD schemes. These schemes use two cascaded downward‐continuation steps in order to attain comparable migration performance.
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The stable‐beam seismic modelling method1
Authors Xiutian Wang and Dave WalthamAbstractThe stable‐beam method for forward modelling of seismic data is introduced. The method is applicable to geometries which may be approximated by a series of single‐valued (in depth) interfaces separating constant‐velocity layers. For models of this restricted type, the results are of similar accuracy to those from waveequation‐based methods whilst the run times are similar to, or better than, those for simple ray‐tracing approaches. The basis of the method is to approximate interfaces by a series of straight‐line segments. This allows very rapid and stable ray tracing through the model. Pseudodiffractions are then added from all of the interface discontinuities formed between adjacent segments. These pseudodiffractions have the effect of correcting for the phase, amplitude and wavefront continuity errors introduced by the interface approximation. Comparison of the stable‐beam results to analytical, Kirchhoff, finite‐difference and physical model results confirm the accuracy ofthe technique.
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Accurate and efficient shot‐gather dip moveout processing in the log‐stretch domain1
Authors B. Zhou, I.M. Mason and S.A. GreenhalghAbstractAn accurate analytical expression for shot‐gather dip‐moveout (DMO) in the timespace log‐stretch domain has until now not been published. We present a simpler, alternative derivation of the exact DMO relationships of Black et al. which correctly take account of the repositioning of the midpoint. A new computationally efficient frequency‐wavenumber (F‐K) DMO operator for shot profiles is then derived, based on these DMO relationships in the time‐space log‐stretch domain. The newly derived DMO operator is, unlike most other log‐stretch DMO operators) accurate for the full range of reflector dips. Along with other schemes which are performed in the log‐stretch domain, it offers considerable time savings over conventional DMO processing. We have compared numerically the impulse response of the new operator with those of a number of other shot‐gather DMO operators, and found it to be superior and well match to the theoretical elliptical DMO response.
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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 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 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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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 18 (1970)
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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 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)