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- Volume 56, Issue 3, 2008
Geophysical Prospecting - Volume 56, Issue 3, 2008
Volume 56, Issue 3, 2008
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Seismic reflection coefficients of faults at low frequencies: a model study
Authors Joost Van Der Neut, Mrinal K. Sen and Kees WapenaarABSTRACTWe use linear slip theory to evaluate seismic reflections at non‐welded interfaces, such as faults or fractures, sandwiched between general anisotropic media and show that at low frequencies the real parts of the reflection coefficients can be approximated by the responses of equivalent welded interfaces, whereas the imaginary parts can be related directly to the interface compliances. The imaginary parts of low frequency seismic reflection coefficients at fault zones can be used to estimate the interface compliances, which can be related to fault properties upon using a fault model. At normal incidence the expressions uncouple and the complex‐valued P‐wave reflection coefficient can be related linearly to the normal compliance. As the normal compliance is highly sensitive to the infill of the interface, it can be used for gas/fluid identification in the fault plane. Alternatively, the tangential compliance of a fault can be estimated from the complex‐valued S‐wave reflection coefficient. The tangential compliance can provide information on the crack density in a fault zone. Coupling compliances can be identified and quantified by the observation of PS conversion at normal incidence, with a comparable linear relationship.
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Finite‐difference modelling of S‐wave splitting in anisotropic media
Authors Reeshidev Bansal and Mrinal K. SenABSTRACTWe have implemented a 3D finite‐difference scheme to simulate wave propagation in arbitrary anisotropic media. The anisotropic media up to orthorhombic symmetry were modelled using a standard staggered grid scheme and beyond (monoclinic and triclinic) using a rotated staggered grid scheme. The rationale of not using rotated staggered grid for all types of anisotropic media is that the rotated staggered grid schemes are more expensive than standard staggered grid schemes. For a 1D azimuthally anistropic medium, we show a comparison between the seismic data generated by our finite‐difference code and by the reflectivity algorithm; they are in excellent agreement.
We conducted a study on zero‐offset shear‐wave splitting using the finite‐difference modelling algorithm using the rotated staggered grid scheme. Our S‐wave splitting study is mainly focused on fractured media. On the scale of seismic wavelenghts, small aligned fractures behave as an equivalent anisotropic medium. We computed the equivalent elastic properties of the fractures and the background in which the fractures were embedded, using low‐frequency equivalent media theories. Wave propagation was simulated for both rotationally invariant and corrugated fractures embedded in an isotropic background for one, or more than one, set of fluid‐filled and dry fractures. S‐wave splitting was studied for dipping fractures, two vertical non‐orthogonal fractures and corrugated fractures. Our modelling results confirm that S‐wave splitting can reveal the fracture infill in the case of dipping fractures. S‐wave splitting has the potential to reveal the angle between the two vertical fractures. We also notice that in the case of vertical corrugated fractures, S‐wave splitting is sensitive to the fracture infill.
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Sediment shear properties from seafloor compliance measurements: Faroes‐Shetland basin case study
Authors Wayne C. Crawford and Satish C. SinghABSTRACTShear properties provide important information about the lithology, fluid content and stability of sediments but are difficult to measure using conventional seismics in the marine environment. Seafloor compliance measurements are sensitive to subsurface shear properties but have only been used in the Pacific Ocean and on shallow coastal shelves, where the source wave energy is known to be strong. We show here that seafloor compliance measurements can provide useful information about shear properties of marine sediments in less energetic settings and under high noise conditions caused by strong seafloor currents. We measured compliance at three sites in the Faroes‐Shetland sedimentary basin north of the Atlantic ocean. The sites have 1000 times higher noise levels than quiet seafloor sites and the source wave power is highly variable, but the data still reveal significant differences in sediment properties between two sites down to 2 kilometres beneath the seafloor. The first site, at the northern end of the basin, has an average shear velocity of 400 m/s in the upper 0.6 kilometres beneath the seafloor, increasing to approximately 2100 m/s at 2 kilometres beneath the seafloor. The second site, further south and to the west of the basin axis, has an average shear velocity of 150 m/s in the upper 0.6 kilometres beneath the seafloor, increasing to 1400 m/s at 2 kilometres beneath the seafloor. The sediments are probably unconsolidated in the upper 0.6 kilometres beneath the seafloor at both sites, with a mean grain size of 1 μm at the southern site and 20 μm at the northern site. The southern site has higher porosity at all depths and a higher risk of borehole collapse during drilling.
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Receiver function method in reflection seismology
Authors Pascal Edme and Satish C. SinghABSTRACTThe receiver function method was originally developed to analyse earthquake data recorded by multicomponent (3C) sensors and consists in deconvolving the horizontal component by the vertical component. The deconvolution process removes travel path effects from the source to the base of the target as well as the earthquake source signature. In addition, it provides the possibility of separating the emergent P and PS waves based on adaptive subtraction between recorded components if plane waves of constant ray parameters are considered. The resulting receiver function signal is the local PS wave's impulse response generated at impedance contrasts below the 3C receiver.We propose to adapt this technique to the wide‐angle multi‐component reflection acquisition geometry. We focus on the simplest case of land data reflection acquisition. Our adapted version of the receiver function approach consists in a multi‐step procedure that first removes the P wavefield recorded on the horizontal component and next removes the source signature. The separation step is performed in the τ−p domain while the source designature can be achieved in either the τ−p or the t−x domain. Our technique does not require any a priori knowledge of the subsurface. The resulting receiver function is a pure PS‐wave reflectivity response, which can be used for amplitude versus slowness or offset analysis. Stack of the receiver function leads to a high‐quality S wave image.
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Non‐double‐couple mechanism of moderate earthquakes near Zakynthos, Greece, April 2006; explanation in terms of complexity
Authors J. Zahradnik, E. Sokos, G.‐A. Tselentis and N. MartakisABSTRACTDeviation of earthquakes from the double‐couple mechanism is an important, but delicate tool to study their source processes. For assessing the double‐couple percentage, the paper suggests to complement the standard least‐square moment‐tensor retrieval with a hierarchic spatio‐temporal grid search, progressively closer to the true source position and time. It enables identification of the double‐couple percentage convergence, while its limit is the resulting double‐couple percentage value, or range. The so‐called double‐couple percentage (DC%) versus correlation plots are introduced and difficulties of the double‐couple percentage assessment are discussed. It is proved that even close to the true source position, where the strike‐dip‐rake angles are already stable (within a few degrees), the double‐couple percentage may still vary by dozens of per cent. Moreover, even at the optimum spatial position, the double‐couple percentage estimate is extremely sensitive (0 to 100%) to small variations of the subevent origin time. This behaviour is explained in terms of the source complexity, implying a time‐dependent moment tensor. Therefore, the double‐couple percentage of complex events depends on the studied frequency band and, in general, also on the station azimuth. This explains broad variations of the double‐couple percentage reports among seismic agencies. Three earthquakes of mutually close epicentres were investigated (Zakynthos, Western Greece, April 2006, magnitudes ∼5.5) and a strong non‐double‐couple component of one of them was identified (double‐couple percentage of about 20%). Two equivalent models of this earthquake were found: a single‐event non‐ double‐couple model, and a double‐event model consisting of two double‐couple sources with highly different mechanisms.
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Improved Monte Carlo inversion of surface wave data
Authors Laura Valentina Socco and Daniele BoieroABSTRACTInversion of surface wave data suffers from solution non‐uniqueness and is hence strongly biased by the initial model. The Monte Carlo approach can handle this non‐uniqueness by evidencing the local minima but it is inefficient for high dimensionality problems and makes use of subjective criteria, such as misfit thresholds, to interpret the results. If a smart sampling of the model parameter space, which exploits scale properties of the modal curves, is introduced the method becomes more efficient and with respect to traditional global search methods it avoids the subjective use of control parameters that are barely related to the physical problem. The results are interpreted drawing inference by means of a statistical test that selects an ensemble of feasible shear wave velocity models according to data quality and model parameterization. Tests on synthetic data demonstrate that the application of scale properties concentrates the sampling of model parameter space in high probability density zones and makes it poorly sensitive to the initial boundary of the model parameters. Tests on synthetic and field data, where boreholes are available, prove that the statistical test selects final results that are consistent with the true model and which are sensitive to data quality. The implemented strategies make the Monte Carlo inversion efficient for practical applications and able to effectively retrieve subsoil models even in complex and challenging situations such as velocity inversions.
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Cross‐correlation of random fields: mathematical approach and applications
ABSTRACTRandom field cross‐correlation is a new promising technique for seismic exploration, as it bypasses shortcomings of usual active methods. Seismic noise can be considered as a reproducible, stationary in time, natural source. In the present paper we show why and how cross‐correlation of noise records can be used for geophysical imaging. We discuss the theoretical conditions required to observe the emergence of the Green's functions between two receivers from the cross‐correlation of noise records. We present examples of seismic imaging using reconstructed surface waves from regional to local scales. We also show an application using body waves extracted from records of a small‐scale network. We then introduce a new way to achieve surface wave seismic experiments using cross‐correlation of unsynchronized sources. At a laboratory scale, we demonstrate that body wave extraction may also be used to image buried scatterers. These works show the feasibility of passive imaging from noise cross‐correlation at different scales.
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Global‐scale seismic interferometry: theory and numerical examples
Authors Elmer Ruigrok, Deyan Draganov and Kees WapenaarABSTRACTProgress in the imaging of the mantle and core is partially limited by the sparse distribution of natural sources; the earthquake hypocenters are mainly along the active lithospheric plate boundaries. This problem can be approached with seismic interferometry. In recent years, there has been considerable progress in the development of seismic interferometric techniques. The term seismic interferometry refers to the principle of generating new seismic responses by cross‐correlating seismic observations at different receiver locations. The application of interferometric techniques on a global scale could create sources at locations where no earthquakes occur. In this way, yet unknown responses would become available for the application of travel‐time tomography and surface‐wave dispersion studies. The retrieval of a dense‐enough sampling of source gathers would largely benefit the application of reflection imaging.
We derive new elastodynamic representation integrals for global‐scale seismic interferometry. The relations are different from other seismic interferometry relations for transient sources, in the sense that they are suited for a rotating closed system like the Earth. We use a correlation of an observed response with a response to which free‐surface multiple elimination has been applied to account for the closed system. Despite the fact that the rotation of the Earth breaks source‐receiver reciprocity, the seismic interferometry relations are shown to be valid. The Coriolis force is included without the need to evaluate an extra term.
We synthesize global‐scale earthquake responses and use them to illustrate the acoustic versions of the new interferometric relations. When the sampling of real source locations is dense enough, then both the responses with and without free‐surface multiples are retrieved. When we do not take into account the responses from the sources in the direct neighborhood of the seismic interferometry‐constructed source location, the response with free‐surface multiples can still be retrieved. Even when only responses from sources at a certain range of epicentral distances are available, some events in the Green's function between two receiver locations can still be retrieved. The retrieved responses are not perfect, but the artefacts can largely be ascribed to numerical errors. The reconstruction of internal events – the response as if there was a source and a receiver on (major) contrasts within the model – could possibly be of use for imaging.
With modelling it is possible to discover in which region of the correlation panel stationary phases occur that contribute to the retrieval of events. This knowledge opens up a new way of filtering out undesired events and of discovering whether specific events could be retrieved with a given source‐receiver configuration.
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Seismic and electromagnetic controlled‐source interferometry in dissipative media
Authors Kees Wapenaar, Evert Slob and Roel SniederABSTRACTSeismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry‐by‐deconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlled‐source electromagnetic (CSEM) data. Interferometry‐by‐deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.
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Consistency of the spatial autocorrelation method with seismic interferometry and its consequence
Authors Toshiaki Yokoi and Sos MargaryanABSTRACTWe have cross‐checked the conventional theory of the spatial autocorrelation method and the consequence of seismic interferometry: the retrieval of the elastodynamic Green's function. Their mutual consistency is almost complete. The basic formulas of the conventional spatial autocorrelation theory can be derived by an alternative approach based on the retrieval of the elastodynamic Green's function. The only discrepancy is found with the average of the complex coherence function over azimuth in a wavefield dependent on azimuth. It is hypothesized, in discussion, that this discrepancy is due to the way of representing the wavefield in the background theory of seismic interferometry that can produce only wavefields moderately dependent on azimuth and that the mentioned consequence of seismic interferometry can also only make sense in a wavefield moderately dependent on azimuth.
Our field experiment with a wavefield dependent on azimuth showed that the consequence of seismic interferometry in the logical framework of the conventional spatial autocorrelation theory is appropriate under such degrees of approximation as the measure proposed in this study, i.e., the deviation of the total dispersion curves is between about 10 and 16 per cent at the maximum from those averaged over azimuth.
The acceptance of the retrieval of Green's function gives a proper physical meaning to the complex coherence function: the real part of the elastodynamic Green's function normalized by its zero‐offset version. This makes it possible to take a deterministic approach rather than the statistical one on which the conventional spatial autocorrelation method is based and gives fruitful new aspects and perspectives. For example, the formula for the multi‐mode case is given and the possibility of exploration of two or three dimensional velocity structures is suggested.
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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 31 (1983)
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Volume 30 (1982)
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Volume 23 (1975)
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Volume 20 (1972)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 15 (1967)
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Volume 6 (1958)
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Volume 4 (1956)
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Volume 1 (1953)