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- Volume 52, Issue 4, 2004
Geophysical Prospecting - Volume 52, Issue 4, 2004
Volume 52, Issue 4, 2004
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Determination of the regularization level of truncated singular‐value decomposition inversion: The case of 1D inversion of MT data
More LessABSTRACTThe total mean‐square error (MSE) of the estimated model, defined as the sum of the standard model variance and the bias variance, is used to define the truncation level of the singular‐value decomposition to give a reasonable balance between model resolution and model variance. This balance is determined largely by the data and no further assumptions are necessary except that the bias terms are estimated sufficiently well. This principle has been tested on the 1D magnetotelluric inverse problem with special emphasis on high‐frequency radio magnetotelluric (RMT) data. Simulations clearly demonstrate that the method provides a good balance between resolution and variance. Starting from a homogeneous half‐space, the best solution is sought for a fixed set of singular values. The model variance is estimated from the sum of the inverse eigenvalues squared, up to a certain threshold, and the bias variance is estimated from the model projections on the remaining eigenvectors. By varying the threshold, the minimum of the MSE is found for an increasing number of fixed singular values until the number of active singular values becomes greater than or equal to the estimated number. As a side‐effect, the depth of penetration of a given set of measurements can be estimated very efficiently by simply noting at which depth the final model deviates little from the starting homogeneous half‐space model. A suite of synthetic data is inverted and an example of inversion of one site is shown to illustrate how the truncation is carried out as the non‐linear inversion process proceeds. A field example with a profile across a plume of contaminated groundwater in the Netherlands shows good agreement with the electrical resistivity obtained in a nearby borehole.
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Dispersion and radial depth of investigation of borehole modes
Authors Bikash K. Sinha and Sergey AsvadurovABSTRACTSonic techniques in geophysical prospecting involve elastic wave velocity measurements that are performed by placing acoustic transmitters and receivers in a fluid‐filled borehole. The signals recorded at the receivers are processed to obtain compressional‐ and shear‐wave velocities in the surrounding formation. These velocities are generally used in seismic surveys for the time‐to‐depth conversion and other formation parameters, such as porosity and lithology. Depending upon the type of transmitter used (e.g. monopole or dipole) and as a result of eccentering, it is possible to excite axisymmetric (n= 0), flexural (n= 1) and quadrupole (n= 2) families of modes propagating along the borehole. We present a study of various propagating and leaky modes that includes their dispersion and attenuation characteristics caused by radiation into the surrounding formation. A knowledge of propagation characteristics of borehole modes helps in a proper selection of transmitter bandwidth for suppressing unwanted modes that create problems in the inversion for the compressional‐ and shear‐wave velocities from the dispersive arrivals. It also helps in the design of a transmitter for a preferential excitation of a given mode in order to reduce interference with drill‐collar or drilling noise for sonic measurements‐while‐drilling. Computational results for the axisymmetric family of modes in a fast formation with a shear‐wave velocity of 2032 m/s show the existence of Stoneley, pseudo‐Rayleigh and anharmonic cut‐off modes. In a slow formation with a shear‐wave velocity of 508 m/s, we find the existence of the Stoneley mode and the first leaky compressional mode which cuts in at approximately the same normalized frequency ωa/VS= 2.5 (a is the borehole radius) as that of the fast formation. The corresponding modes among the flexural family include the lowest‐order flexural and anharmonic cut‐off modes. For both the fast and slow formations, the first anharmonic mode cuts in at a normalized frequency ωa/VS= 1.5 approximately. Cut‐off frequencies of anharmonic modes are inversely proportional to the borehole radius in the absence of any tool. The borehole quadrupole mode can also be used for estimating formation shear slownesses. The radial depth of investigation with a quadrupole mode is marginally less than that of a flexural mode because of its higher frequency of excitation.
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Unsupervised separation of seismic waves using the watershed algorithm on time‐scale images
Authors Antoine Roueff, Jocelyn Chanussot, Jerome I. Mars and Minh‐Quy NguyenABSTRACTThis paper illustrates the use of image processing techniques for separating seismic waves. Because of the non‐stationarity of seismic signals, the continuous wavelet transform is more suitable than the conventional Fourier transforms for the representation, and thus the analysis, of seismic processes. It provides a 2D representation, called a scalogram, of a 1D signal where the seismic events are well localized and isolated. Supervised methods based on this time‐scale representation have already been used to separate seismic events, but they require strong interactions with the geophysicist. This paper focuses on the use of the watershed algorithm to segment time‐scale representations of seismic signals, which leads to an automatic estimation of the wavelet representation of each wave separately. The computation of the inverse wavelet transform then leads to the reconstruction of the different waves. This segmentation, tracked over the different traces of the seismic profile, enables an accurate separation of the different wavefields. This method has been successfully validated on several real data sets.
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Optimal use of PP and PS time‐lapse stacks for fluid–pressure discrimination
More LessABSTRACTThe combined use of time‐lapse PP and PS seismic data is analysed for optimal discrimination between pressure and saturation changes. The theory is based on a combination of the well‐known Gassmann model and the geomechanical grain model derived by Hertz and Mindlin. A key parameter in the discrimination process is the opening angle between curves representing constant changes in PP and PS reflectivity plotted against pressure and saturation changes. The optimal discrimination angle in the pressure–saturation space is 90° and this is used to determine optimal offset ranges for both PP and PS data. For typical production scenarios, we find an optimal offset range corresponding to an angle of incidence of 25–30°, for both PP and PS data. For gas we find slightly different results. This means that conventional survey parameters used in marine multicomponent acquisition should be sufficient for the purpose of estimating pressure and fluid saturation changes during production.
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Efficient and accurate computation of seismic traveltimes and amplitudes
Authors S. Buske and U. KästnerABSTRACTWe describe two practicable approaches for an efficient computation of seismic traveltimes and amplitudes. The first approach is based on a combined finite‐difference solution of the eikonal equation and the transport equation (the ‘FD approach’). These equations are formulated as hyperbolic conservation laws; the eikonal equation is solved numerically by a third‐order ENO–Godunov scheme for the traveltimes whereas the transport equation is solved by a first‐order upwind scheme for the amplitudes. The schemes are implemented in 2D using polar coordinates. The results are first‐arrival traveltimes and the corresponding amplitudes. The second approach uses ray tracing (the ‘ray approach’) and employs a wavefront construction (WFC) method to calculate the traveltimes. Geometrical spreading factors are then computed from these traveltimes via the ray propagator without the need for dynamic ray tracing or numerical differentiation. With this procedure it is also possible to obtain multivalued traveltimes and the corresponding geometrical spreading factors.
Both methods are compared using the Marmousi model. The results show that the FD eikonal traveltimes are highly accurate and perfectly match the WFC traveltimes. The resulting FD amplitudes are smooth and consistent with the geometrical spreading factors obtained from the ray approach. Hence, both approaches can be used for fast and reliable computation of seismic first‐arrival traveltimes and amplitudes in complex models. In addition, the capabilities of the ray approach for computing traveltimes and spreading factors of later arrivals are demonstrated with the help of the Shell benchmark model.
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Joint cross‐well and single‐well seismic studies of CO2 injection in an oil reservoir
Authors R. Gritto, T.M. Daley and L.R. MyerABSTRACTA series of time‐lapse seismic cross‐well and single‐well experiments were conducted in a diatomite reservoir to monitor the injection of CO2 into a hydrofracture zone, based on P‐ and S‐wave data. A high‐frequency piezo‐electric P‐wave source and an orbital‐vibrator S‐wave source were used to generate waves that were recorded by hydrophones as well as 3‐component geophones. During the first phase the set of seismic experiments was conducted after the injection of water into the hydrofractured zone. The set of seismic experiments was repeated after a time period of seven months during which CO2 was injected into the hydrofractured zone. The questions to be answered ranged from the detectability of the geological structure in the diatomic reservoir to the detectability of CO2 within the hydrofracture. Furthermore, it was intended to determine which experiment (cross‐well or single‐well) is best suited to resolve these features.
During the pre‐injection experiment, the P‐wave velocities exhibited relatively low values between 1700 and 1900 m/s, which decreased to 1600–1800 m/s during the post‐injection phase (−5%). The analysis of the pre‐injection S‐wave data revealed slow S‐wave velocities between 600 and 800 m/s, while the post‐injection data revealed velocities between 500 and 700 m/s (−6%). These velocity estimates produced high Poisson's ratios between 0.36 and 0.46 for this highly porous (∼50%) material. Differencing post‐ and pre‐injection data revealed an increase in Poisson's ratio of up to 5%. Both velocity and Poisson's ratio estimates indicate the dissolution of CO2 in the liquid phase of the reservoir accompanied by an increase in pore pressure.
The single‐well data supported the findings of the cross‐well experiments. P‐ and S‐wave velocities as well as Poisson's ratios were comparable to the estimates of the cross‐well data.
The cross‐well experiment did not detect the presence of the hydrofracture but appeared to be sensitive to overall changes in the reservoir and possibly the presence of a fault. In contrast, the single‐well reflection data revealed an arrival that could indicate the presence of the hydrofracture between the source and receiver wells, while it did not detect the presence of the fault, possibly due to out‐of‐plane reflections.
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Calibration of cross‐line components for sea‐bed 4C acquisition systems
Authors Claudio Bagaini and Everhard MuyzertABSTRACTFaithful recording of the elastic wavefield at the sea‐bed is required for quantitative applications of 4C seismic. The accuracy of the recorded vectorial wavefield depends on factors that vary from deployment to deployment. This paper focuses on one such factor: the interaction of the acquisition system with the sea‐bed, which is referred to here as coupling. We show, using multi‐azimuth data recorded with a cable‐based sea‐bed acquisition system, whose sensor housing is cylindrically shaped and with the in‐line geophone fixed to the cable, that coupling depends on the propagation direction and wave type (P‐ or S‐waves) of the incident wavefield. We show that coupling is more critical for S‐waves than for P‐waves. Detection of inconsistent coupling using both P‐ and S‐waves is therefore mandatory. A data‐driven processing method to compensate for the frequency‐dependent coupling response of the cross‐line geophone is derived. Its application to field data verifies the effectiveness of the method.
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A simple method of magnetic declination fluctuation correction for long single‐streamer positioning in a seismic survey
Authors Victor Martin, Mark S. Noble and Georges PascalABSTRACTIn single‐streamer acquisition, the use of acoustic transducers to constrain the receiver positions is not possible, thus implying the use of compass birds to gather information on the streamer location. The compasses are, however, sensitive to the declination of the local magnetic field of the earth, and local fluctuations not accounted for can degrade the accuracy of reconstructed positions. In order to correct these small‐scale fluctuations, we propose a simple deterministic method to calculate a spatial correction to apply to the compasses that enhances the positioning accuracy. The local compass declination is calculated after a first reconstruction on the whole survey area. This method was applied with success to navigation data from a 3D survey offshore Japan, and the positioning accuracy was improved to the level of the DGPS accuracy.
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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)