Dipping Interface Research Articles

P-SHconversions in a flat-layered medium with anisotropy of arbitrary orientation

SUMMARY P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV-and SH-polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used ‘receiver function’ technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct (P) and converted (Ps) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.

Finite‐difference modeling of sonic wavefields with a dipping interface

Formation bedding can cause complex wave propagation in a borehole and introduce velocity bias in sonic logs. Because of the lack of symmetry, little is known about sonic wavefields propagating through a dipping bed. In this paper, we investigate effects on the sonic dipole and monopole wavefields across a dipping interface using a 3-D finite‐difference method. For dipole wavefields propagating from a soft to a hard formation across a dipping interface, the transmission is reduced greatly when compared with a horizontal interface. The different transmissions of SV‐ and SH‐waves through the dipping interface result in significant azimuthal amplitude variation and generate large cross‐coupled components. This apparent anisotropy should be taken into account when estimating formation shear anisotropy in a dipping formation. For monopole wavefields, the azimuthal averaging caused by a dipping interface reduces the reflection across an interface. This may affect fracture evaluation using the Stoneley reflection coefficient in a dipping formation.

A 2-D Velocity Model of the Vrancea Region In Romania: Prediction of Teleseismic Waveforms

SUMMARY In previous studies, anomalies in arrival time and amplitudes of depth phases pP and sP recorded at teleseismic distances and produced by large intermediate-depth events of the Vrancea region were pointed out (Perrot et al. 1994). The modelling of major recent events has shown that the presence of a dipping interface and thick low-velocity sediment layer in the upper crust above the hypocentral area can explain such anomalies. Simulating broad-band records of the 1990 May 31 earthquake, it is shown that the 2-D crustal velocity model derived by Perrot et al. (1994) can also be used to explain observed waveforms in an extended azimuthal range from 105 to 243 and is valid for earthquakes having different hypocentral locations in the deep Vrancea seismic zone. Using records in the azimuthal range where a classical spherical model produces a good fit to the observed waveforms, the source is best modelled by two point sources at 90 and 93 km depth releasing the same amount of seismic moment, and separated by 1.5 s in time. Synthetics calculated for this source time history and the 2-D velocity model above the source give a much improved fit of the observed waveforms over what could be achieved with a 1-D spherical model, The results suggest that teleseismic waveforms could be reasonably well predicted for any event in the region with the 2-D velocity model, which accounts for the main structural features in the upper crust of the Vrancea region.

Intermediate‐depth earthquakes in central Mexico: Implications for plate waves

Regional seismograms of intermediate‐depth earthquakes (50≤H≤80 km) that occur below the Central Mexican Plateau show a phase which, at epicentral distances of 150 to 450 km, arrives about 15 to 20 sec after the P wave and 5 to 12 sec before the S wave. This phase was previously interpreted as a seismic wave refracted from a dipping interface below the source, thus apparently providing direct evidence of the structural location of the subducted Cocos plate below México. The phase was called the plate wave. Recent intermediate‐depth events have given rise to better quality data recorded by some newly‐installed broadband seismographs. An analysis of these and previous data strongly suggests that the phase is an S‐to‐P converted phase at the free surface and, therefore, provides no information regarding the subducted plate.

PARABOLIC AND HYPERBOLIC PARAXIAL TWO‐POINT TRAVELTIMES IN 3D MEDIA1

AbstractThe 4 × 4 T‐propagator matrix of a 3D central ray determines, among other important seismic quantities, second‐order (parabolic or hyperbolic) two‐point traveltime approximations of certain paraxial rays in the vicinity of the known central ray through a 3D medium consisting of inhomogeneous isotropic velocity layers. These rays result from perturbing the start and endpoints of the central ray on smoothly curved anterior and posterior surfaces. The perturbation of each ray endpoint is described only by a two‐component vector. Here, we provide parabolic and hyperbolic paraxial two‐point traveltime approximations using the T‐propagator to feature a number of useful 3D seismic models, putting particular emphasis on expressing the traveltimes for paraxial primary reflected rays in terms of hyperbolic approximations. These are of use in solving several forward and inverse seismic problems. Our results simplify those in which the perturbation of the ray endpoints upon a curved interface is described by a three‐component vector. In order to emphasize the importance of the hyperbolic expression, we show that the hyperbolic paraxial‐ray traveltime (in terms of four independent variables) is exact for the case of a primary ray reflected from a planar dipping interface below a homogeneous velocity medium.

APERTURE COMPENSATION TOMOGRAPHY1

AbstractConventional velocity analysis can handle a horizontally stratified medium well. There is no indication, though, that it will be as successful when applied to a more complicated geological structure. In fact, a small angle of incidence may transform to a wide‐angle reflection event for a dipping interface. In this case, conventional velocity analysis may lead to large errors and thus cannot be applied. Seismic tomography is attractive as it is virtually free from any restrictions imposed on the velocity distribution in the model space or on the setup of a seismic experiment. It is important, however, to recall that seismic tomography yields results of inferior quality compared to medical tomography. This paper investigates the reason for this and how to suppress a significant blurring of seismic tomograms. Unlike medical tomography, one cannot provide full angular coverage of the model space in a typical seismic experiment: the sources and the receivers cannot surround an unknown object inside the earth to provide a complete spectrum of view angles. Incomplete angular coverage may lead to the occurrence of large inaccuracies in the computed tomograms especially when the initial model is poorly chosen. We demonstrate a method of suppressing the adverse effects related to an incomplete angular recording. This is ‘compensation tomography’ which can be used efficiently in the case of a limited angular aperture. Numerical experiments illustrate the theory.

Crustal structure of the southeastern Grenville Province, northern New York State and eastern Ontario

The Grenville province exposes an oblique cross section through mid‐lower crustal lithologies that were pervasively deformed and subjected to regional thermal overprinting during the Grenvillian orogeny (1.1 Ga). The southeastern Grenville province is divided into two subterranes by the Carthage‐Colton mylonite zone, a 110‐km‐long lineament characterized by intense ductile shear and igneous intrusion, which separates the amphibolite facies metasediments of the Central Metasedimentary Belt to the west from the granulite facies metaplutonics of the Central Granulite Terrane to the east. The recognition of distinct lithotectonic domains separated by zones of intense ductile shear in the Grenville province raises questions concerning the deep structure of these subterranes and, in particular, the means by which the mid‐lower crustal rocks exposed in the Grenville province were emplaced. Seismic refraction/wide‐angle reflection data were acquired to investigate the deep structural interrelationships within the southeastern Grenville province. A travel time inversion for velocity and interface depth was applied to the seismic data, together with constraints from amplitude modeling to produce a seismic velocity model of the crust in the southeastern Grenville province. In the Central Metasedimentary Belt the upper crust is characterized by velocities in the range 6.3–6.4 km/s and a Poisson's ratio of 0.26 ± 0.01 which are attributed to quartzofeldspathic rocks. Farther east in the Central Granulite Terrane, upper crustal velocities of 6.55 km/s and a Poisson's ratio of 0.28 ± 0.01 are associated with the Marcy Anorthosite. The seismic homogeneity of the upper crust in the region of the Carthage‐Colton mylonite zone suggests that this boundary is a shallow feature, limited to the upper 2–3 km of the crust. The deep crustal structure of the southeastern Grenville province is characterized by two discrete and laterally discontinuous seismic interfaces. In the Central Metasedimentary Belt the top of the lower crust is delineated by an eastward dipping interface at 24–28 km depth. In the Central Granulite Terrane, prominent en echelon reflections, referred to as the Tahawus complex, form a gently arched dome at 17–22 km depth. Interpretation of the Tahawus complex as a zone of layered mafic cumulates is supported by its high velocity (7.1 km/s) and Poisson's ratio (0.27 ± 0.02). The lower crust is characterized by a velocity of 7.0–7.2 km/s and an anomalously high Poisson's ratio of 0.30 ± 0.02, which are representative of pyroxene‐garnet granulites. In contrast, velocities of 6.8–7.0 km/s are modeled beneath the Central Granulite Terrane and appear to signify a lateral change in composition. The Moho lies at 44–45 km depth and is characterized by pronounced en echelon reflection segments, suggesting compositional interlayering around the crust‐mantle boundary. The velocity of the upper mantle is 8.0–8.2 km/s. An anomalous upper mantle layer with a reversed velocity of 8.6 km/s dips eastward from 50 to 60 km depth beneath the southeastern Grenville province. Our results indicate that remnants of magmatic intrusions that mobilized and thickened the crust during the Grenvillian orogeny are preserved in the mid‐lower crust as a layered cumulate body (Tahawus complex) and in the upper mantle as an eclogitic lens, possibly delaminated from the overthickened crust during uplift of the southeastern Grenville province.

CONVERSION POINTS AND TRAVELTIMES OF CONVERTED WAVES IN PARALLEL DIPPING LAYERS1

AbstractFor converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio vp/vs. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration.The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two‐term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates.

Generalized f-k (frequency‐wavenumber) migration in arbitrarily varying media

Migration requires one‐way wave continuation. In the spatial domain, one‐way wave equations are derived based on various approximations to an assumed dispersion relation. In the frequency‐wavenumber domain, the well known f-k method and the phase‐shift method are strictly valid only within homogeneous models and layered models, respectively. In this paper, a frequency‐wavenumber domain method is presented for one‐way wave continuation in arbitrarily varying media. In the method, the downward continuation is accomplished, not with plane waves individually as in the f-k or the phase‐shift method, but with the whole spectrum of plane waves simultaneously in order to account for the coupling among the plane waves due to lateral inhomogeneity. The method is based on a matrix integral equation. The method has the following merits: (1) The method is a generalization of the f-k and the phase‐shift methods, valid in arbitrarily varying models. (2) The method has physical interpretations in terms of upgoing and downgoing plane waves, and as such the method has well defined steps leading from full‐wave continuation (two‐way wave) to one‐way wave continuation for migration. (3) The method is rigorous; the only approximations in the method—other than the one‐way wave approximation necessary for migration—are the discretization of a continuous system (which is necessary in computer methods) and imperfections associated with the limited spatial aperture of the data; as such, the method can achieve high solution accuracy. (4) The method can be fast, since computations are mainly matrix‐vector multiplications, which are easily vectorizable. In particular, compared to spatial domain methods, I contend that the method is (1) more rigorous in one‐way wave theory, (2) more accurate in migration of high‐dip events, and (3) faster for smooth models. I applied the method to a few examples of zero‐offset data migration, including imaging a point diffractor below a dipping interface, migration with sharp lateral variations in velocity, and migration with smooth lateral variations in velocity.

CHARACTERISTICS OF LOVE WAVE GENERATED AROUND A DIPPING BASEMENT

Source mechanism and characteristics of the horizontally propagating waves generated around a dipping basement due to the incident SH wave are investigated. A new analitical method which combines boundary elements, finite elements and energy transmitting boundary is proposed. Two layered media, the upper layer of which has semi-infinite boundary in one side and a dipping interface in the other side, is used in the analysis. It is found that the incident SH wave is mostly transformed into Love wave whose period is close to Airy phase at the horizontal part of the surface layer in the case that both the ratio of wave impedance and the inclination of basement are small; all reflected SH wave is predominant in the other case.

Seismic imaging of the Puritan Batholith, Wisconsin, using split array cross‐correlator processing

A seismic data set was collected in northern Wisconsin in the summers of 1980–1981. The study area overlies a less heterogeneous portion of the Precambrian Puritan batholith, a body which has been intruded, and otherwise deformed since its emplacement. High‐velocity bedrock lies beneath a thin glacial till layer. Other than a shallow penetration first arrival, there was no evidence of refractors or reflectors in the upper few kilometers. The data contain an abundance of energy, and our goal was to determine the source of that energy. A processing technique, based on the split array cross correlator (Jacobsen, 1957; Doll, 1983), was developed for locating diffractors with a sparse data set. The technique is similar to those used in underwater acoustics and radio astronomy for locating point sources. It assumes an acoustic medium with known velocity structure, in which inhomogeneities may be treated as point diffractors. The output is the windowed cross correlation of two stacks of delayed traces. The delays are determined by ray tracing for each source‐to‐grid point and grid point‐to‐receiver path. The cross correlations are calculated over a two‐dimensional array of grid points. The method is useful when data are sparse and conventional linear methods fail to image subsurface structure. Our images show reflections and diffractions from a dipping interface at about 6–8 km depth, as well as other features associated with the Puritan batholith.

Constraints on the subduction geometry beneath western Washington from broadband teleseismic waveform modeling

Abstract Source-equalized P -wave receiver functions from an array of broadband portable instruments located about 50 km from the coast (near 46.8°N, 123.4°W) in western Washington are interpreted to determine the subduction geometry of the Juan de Fuca plate beneath the Pacific Northwest. Waveforms from more than 50 teleseismic events were available from the temporary array. These data display large variations in both amplitude and timing of large secondary arrivals interpreted to be P - to S -converted phases from both the bottom of the subducting oceanic crust and the overlying continental crust-mantle boundary. This behavior is consistent with that expected for plane P waves interacting with a dipping interface at depth. Our model suggests that the Juan de Fuca plate is dipping 20° ± 3° in the direction 110° ± 20°. The continental Moho is at about 31 km depth. Only a thin wedge of upper mantle material exists between the overlying crust and the subducting slab. This wedge may be responsible for anomalous arrivals in the observed receiver functions. The model determined in this study is consistent with large-scale deformation in the Juan de Fuca plate that has been recently proposed based on analysis of seismicity data in the Puget Sound region. The southeasterly dip direction at our site is consistent with its location on the southern flank of an arch in the slab in the vicinity of Puget Sound caused by the change in strike of the subduction zone between latitudes 47° and 48° north.

Estimation of hypocentral parameters of local earthquakes when crustal layers have constantP-velocities and dipping interfaces

The paper describes an algorithm for estimating the hypocentral coordinates and origin time of local earthquakes when the wave speed model to be employed is a layered one with dipping interfaces. A constrained least-squared error problem has been solved using the penalty function approach, in conjunction with the sequential unconstrained optimization technique of Fiacco and McCormick. Joint confidence intervals for the computed parameters are estimated using the approach of Bard for nonlinear problems. These results show that when a hypocentre lies outside the array of recording stations and head waves from a dipping interface are involved, then its inclination must be taken into account for dip angles exceeding 5°.

Fine Structure of a Postfailure Wadati‐Benioff Zone

The hypocentral distribution of locally recorded aftershocks of the great (Ms=8.1) Michoacan, Mexico, earthquake of September 19, 1985, defines a narrow Wadati‐Benioff zone structure, roughly 10 km thick, dipping 14° at N23°E. This is in good agreement with the source geometry obtained by waveform modeling of the 1985 Michoacan mainshock and the large 1979 Petatlán earthquake in the adjoining region. We inverted for the crustal velocity structure in the epicentral region by applying the Levenberg‐Marquardt non‐linear least squares algorithm to our local aftershock data. The velocity model consists of a layer with linearly increasing velocity in depth overlying a dipping, constant velocity halfspace. Our hypocentral location program uses a velocity model of the same form together with ray tracing. The earthquake hypocentral resolution obtained with this program is significantly better than that from conventional approaches (HYPO) and looks very promising for use in velocity structures with an important dipping interface like subduction zones.

Three‐dimensional terrain corrections for mise‐à‐la‐masse and magnetometric resistivity surveys

Three‐dimensional modeling of topographic effects in mise‐à‐la‐masse and magnetometric resistivity surveys is accomplished using the surface integral equation method. The technique provides a means for (1) analyzing these effects on earth models of homogeneous conductivity; and (2) removing terrain effects from field data. A new method combining current source images with surface charge is developed to treat the electric field boundary conditions at the air‐earth interface. The method uses an image of each subsurface current source positioned above the surface, so as to induce a surface charge distribution which approximately cancels the charge distribution induced by the subsurface current source. The resulting residual surface charge distribution varies spatially more gradually than either of the original charge distributions, and hence may be represented accurately on a coarsely segmented model surface with simple basis functions. The topographic surface is modeled by a finite number of facets, each with constant slope and surface charge density. Charge values are obtained with an iterative solution technique. Surface electric fields are calculated from the surface charge distribution, current sources, and images. The magnetic field is found by evaluating a surface integral involving surface slopes and electric fields. The numerical solution is verified by comparisons with dipole‐dipole resistivity results from a two‐dimensional finite‐element model of a valley, and with analytic solutions for the magnetic fields over a dipping interface. Methods for terrain correcting mise‐à‐la‐masse and magnetometric resistivity data are demonstrated with examples using actual field measurements. The results of this study show that (1) rugged topography can significantly distort measurements in mise‐à‐la‐masse and magnetometric resistivity surveys; and (2) the described modeling technique provides an effective means of calculating terrain corrections for both the mise‐à‐la‐masse and magnetometric resistivity methods over complex three‐dimensional topography.

Three-Dimensional Terrain Corrections for mise-á-la-masse and Magnetometric Resistivity Surveys

Three dimensional modeling of topographic effects in mise-a-la-masse and magnetometric resistivity surveys is accomplished using the surface integral equation method. The technique provides a means for (1) analyzing these effects on earth models of homogeneous conductivity; and (2) removing terrain effects from field data. A new method combining current source images with surface charge is developed to treat the electric field boundary conditions at the air-earth interface. The method uses an image of each subsurface current source positioned above the surface, so as to induce a surface charge distribution which approximately cancels the charge distribution induced by the subsurface current source. The resulting residual surface charge distribution varies spatially more gradually than either of the original charge distributions, and hence may be represented accurately on a coarsely segmented model surface with simple basis functions. The topographic surface is modeled by a finite number of facets, each with constant slope and surface charge density. Charge values are obtained with an iterative solution technique. Surface electric fields are calculated from the surface charge distribution, current sources, and images. The magnetic field is found 'by evaluating a surface integral involving surface slopes and electric fields. The numerical solution is verified by comparisons with dipole dipole resistivity results from a two-dimensional finite-element model of a valley, and with analytic solutions for the magnetic fields over a dipping interface. Methods for terrain correcting mise-a-la-masse and magnetometric resistivity data are demonstrated with examples using actual field measurements. The results of this study show that (1) rugged topography can significantly distort measurements in mise-a-la-masse and magnetometric resistivity surveys; and (2) the described modeling technique provides an effective means of calculating terrain corrections for both the mise-á-la-masse and magnetometric resistivity methods over complex three-dimensional topography.

Structural corrections for slowness and azimuth of seismic signals arriving at Gauribidanur array

AbstractSlowness and azimuth anomalies directly measured from the data recorded at seismic arrays have been used for observing deviations from spherical symmetric earth. Interpretation of such observations for reliable refinement of earth models requires correction for the effect of irregularities in the crust and upper mantle structure beneath the recording sites because it introduces large systematic errors in slowness and ray direction. Observations of large systematic errors in slowness and azimuth for teleseismic events approaching Gauribidanur (GBA) seismic array from the east were compensated by introducing a number of dipping Moho beneath recording sites. It was found that a dipping interface having a dip of 6° and a strike of N13°E explains observations of ray direction anomalies in a satisfactory manner. This can deviate seismic rays up to 11.5 per cent in slowness and 6.5° in azimuth. The quantum of errors seems quite significant as far as refinement of earth models is concerned. A correction table has been prepared which would be useful in the analysis of slowness and azimuth of earthquakes recorded at GBA from the eastern direction. We have applied these structural corrections successfully to the observed slowness and azimuth of earthquakes from this direction. This is illustrated in the form of array diagrams.

Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces

A quadratic approximation for the square of the traveltime from a source region to a receiver region is given for a three‐dimensional (3-D) medium consisting of inhomogeneous layers with curved interfaces. The square of the traveltime, being a function of source and receiver coordinates, is developed in a Taylor series around a reference source and receiver point. The relationships of the traveltime parameters to the ray parameters and the wavefront curvature matrices are shown. Using midpoint, half‐offset coordinates gives a simplified traveltime function compared to using source‐receiver coordinates only in the case that the reference source point and the reference receiver point coincide (zero‐offset approximation). For a medium consisting of homogeneous layers with plane dipping interfaces, the traveltime approximation is further simplified. The derived traveltime approximation is shown to be exact for a reflection from a plane dipping interface in a homogeneous medium. Explicit expressions for the traveltime parameters in terms of the layer parameters are derived for a horizontally layered medium. The traveltime errors of two different approximations are compared for a given layered model in a numerical example.

Direct evidence of a subducted plate under southern Mexico

The hypothesis1 of subduction of oceanic plates under active continental margins has become a fundamental idea in plate tectonics. Yet the evidence for the existence of oceanic plates beneath continental borders is still largely circumstantial. In seismology, the presence of a new layer or structural unit is taken as confirmed only after seismic phases corresponding to reflections or refractions from that layer have been identified on seismograms. I report here the presence of a mantle phase, interpreted as a seismic wave refracted from a dipping interface on records of aftershocks from the intermediate earthquake of 24 October 1980 in the Mixtec Highlands of south-central Mexico which may be direct evidence on the structural position of the subducted plate under the Mexican active continental margin.

An estimate of the conductivity structure for the Vancouver Island region from geomagnetic results

The depth to the highly conductive layer of the mantle below the Vancouver Island region is estimated using the results from a scaled laboratory analogue model, a two-dimensional numerical model and field observations. At the centre of the island the responses of numerical models with depths to the mantle of 40 and 80 km bracket the field results. The subduction regime in the Vancouver Island region suggests a dipping interface for the conducting layer. The numerical model based on this type of tectonic structure has a conducting layer within the mantle that varies in depth from 40 km at the continental margin, increasing under the island to 80 km at the shallow channel and decreasing again to 40 km near the mainland coast. The response of this model is compatible with the field observations.