Ray Parameter Research Articles

Ultra-low velocity zone heterogeneities at the core\u2013mantle boundary from diffracted PKKPab waves

Diffracted waves around Earth’s core could provide important information of the lowermost mantle that other seismic waves may not. We examined PKKPab diffraction waves from 52 earthquakes occurring at the western Pacific region and recorded by USArray to probe the velocity structure along the core–mantle boundary (CMB). These diffracted waves emerge at distances up to 10° past the theoretical cutoff epicentral distance and show comparable amplitudes. We measured the ray parameters of PKKPab diffraction waves by Radon transform analysis that is suitable for large-aperture arrays. These ray parameters show a wide range of values from 4.250 to 4.840 s/deg, suggesting strong lateral heterogeneities in sampling regions at the base of the mantle. We further estimated the P-wave velocity variations by converting these ray parameters and found the CMB regions beneath the northwestern edge of African Anomaly (Ritsma et al. in Science 286:1925–1928, 1999) and southern Sumatra Islands exhibit velocity reductions up to 8.5% relative to PREM. We suggest that these low velocity regions are Ultra-low velocity zones, which may be related to partial melt or iron-enriched solids.Graphical abstract.

Heat kernel estimates on Julia sets

We give heat kernel estimates on Julia sets J(fc) for quadratic polynomials fc(z)= z2 + c for c in the main cardioid or the ±1k-bulbs where k ≥2. First we use external ray parametrization to construct a regular, strongly local and conservative Dirichlet form on Julia set. Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric. Finally, we give heat kernel estimates under the resistance metric.

Geographic variations in lowermost mantle structure from the ray parameters and decay constants of core‐diffracted waves

AbstractWe introduce an array‐based approach for constraining seismic velocity structure in the lowermost mantle by measuring the frequency dependence of the ray parameter p and decay constant γ for core‐diffracted waves (Pdiff and SHdiff). The approach uses an iterative multichannel cross‐correlation algorithm that solves for relative arrival times and amplitudes of core‐diffracted waveforms from multiple peaks in normalized correlograms from pairs of coazimuthal stations. The approach is applied to 60 mb ≥ 5.8 earthquakes for Pdiff and 36 for SHdiff during 2001–2002, with nearly 50,000 unique profile station pairs with epicentral‐distance differences of Δd ≥ 10° and azimuth differences of Δφ ≤ 10°, sampling a significant portion of the lowermost mantle. Cap‐averaging the resulting ray parameter estimates produces geographic variations that are largely consistent with the distribution of lowermost mantle large low‐velocity provinces and seismically fast slab‐accumulation regions seen in seismic tomography models, whose locations also strongly influence the geographic distribution of heat flow out of the core. Geographic variations in station‐pair diffracted‐wave decay constants differ from those of the ray parameters, suggesting that variations in the decay of core‐diffracted waves are more linked to lowermost mantle seismic velocity gradients than absolute values of seismic velocity. The ray parameters and decay constants of core‐diffracted waves are strongly frequency‐dependent, and these frequency variations also vary significantly with geographic location. Combining lateral and vertical seismic‐velocity variations with mineral‐physics data on elasticity and conductivity of lowermost mantle species can provide constraints on D″ composition and CMB heat flux.

Plane wave refraction on convex and concave angles in geometric acoustics approximation

An exact analytical solution to the eikonal equation for a plane wave refracted on a boundary comprising both convex and concave obtuse angles has been built. Under the convex angle summit the solution has a line of discontinuity in the ray vector field and in the first derivatives of the first arrival times, and under the concave angle it has a cone of waves diffracted on this angle. This cone corresponds to the Keller diffraction cone in the geometric diffraction theory. The relation between the eikonal equation and the resultant Hamilton–Jacoby equation for arrival times of downward waves and the ray parameter conservation equation is investigated. Solutions to these equations coincide for pre-critical incidence angles and differ for super-critical angles. It is shown that the arrival times of maximum amplitude waves, which are of the greatest practical interest, coincide with the times calculated from the ray parameter field for the ray parameter conservation equation. The numerical algorithm proposed for calculation of these times can be used for arbitrary speed models.

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

The aim of the paper is to study weak gravitational lensing of quantum (perturbed) and classical lukewarm black holes (QLBHs and CLBHs respectively) in the presence of cosmological parameter Λ. We apply a numerical method to evaluate the deflection angle of bending light rays, image locations θ of sample source and corresponding magnifications μ. There are no obtained real values for Einstein ring locations for CLBHs but we calculate them for QLBHs. As an experimental test of our calculations, we choose mass M of 60 types of the most massive observed galactic black holes acting as a gravitational lens and study quantum matter field effects on the angle of bending light rays in the presence of cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause absolute values of the quantum deflection angle to be reduced with respect to the classical ones. The sign of the quantum deflection angle is changed with respect to the classical values in the presence of the cosmological constant. This means dominance of the anti-gravity counterpart of the cosmological horizon on the angle of bending light rays with respect to absorbing effects of 60 local types of the most massive observed black holes. Variations of the image positions and magnifications are negligible when increasing dimensionless cosmological constant . The deflection angle takes positive (negative) values for CLBHs (QLBHs) and they decrease very fast (slowly) by increasing the closest distance x0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes with .

Tight rock wettability and its relationship to other petrophysical properties: A Montney case study

Understanding and modelling the wettability of tight rocks is essential for designing fracturing and treatment fluids. In this paper, we measure and analyze spontaneous imbibition of water and oil into five twin core plugs drilled from the cores of a well drilled in the Montney Formation, an unconventional oil and gas play in the Western Canadian Sedimentary Basin. We characterize the samples by measuring the mineralogy using XRD (x-ray diffraction), total organic carbon content, porosity, and permeability. Interestingly, the equilibrated water uptake of the five samples is similar, while, their oil uptake increases by increasing the core porosity and permeability. We define two wetta-bility indices for the oil phase based on the slope and equilibrium values of water and oil imbibition curves. Both indices increase by increasing porosity and permeability, with the slope affinity index showing a stronger correlation. This observation suggests that part of the pore network has a stronger affinity to oil than to water. We also observe that the two indices decrease by increasing neutron porosity and gamma ray parameters measured by wireline logging tools. The samples with higher gamma ray and neutron porosity are expected to have greater clay content, and thus less effective porosity and permeability.

Estimation of Lateral Variations of the Mohorovičić Discontinuity Using 2D Modeling of Receiver Functions

We used 2D finite‐difference modeling and azimuthally binned receiver functions (RFs) to explore whether abrupt offsets in Moho depth can be detected by one or a few closely spaced P ‐wave RFs. Our results show that 2D synthetic RFs generated in the immediate vicinity above a Moho depth change can provide important clues to the abruptness of the offset. In particular, diffraction of the waves impinging onto the Moho offset may generate a split P S arrival, causing systematic variation of peak‐to‐peak P ‐ P S delay times with increasing ray parameter, depending on the location relative to the Moho offset and the incidence direction of the RFs. We outline an approach using a slant‐stack method to constrain the location of a relatively abrupt depth change of Moho (![Graphic][1] ) using separate RF stacks incident from opposite directions. For a station located on the western border of the Caspian Sea in Azerbaijan (LKR), our 2D models with an ∼8 km transition from a shallower Moho to the east and deeper Moho to the west generate synthetic RFs with features in general agreement with observations. These models, which include step‐ and ramp‐like offsets of Moho, are in general agreement with estimates of crustal thickness from seismic data. Thus, our results suggest that characteristics in one or a few azimuthally binned radial P ‐wave RFs can be used in concert with a slant‐stack analysis to pinpoint a relatively abrupt change in underlying Moho depth. Online Material: Discussion and figures of a verification study of receiver functions (RFs) computed by different methods, crustal phases generated in our 2D model using animations of the simulated wave propagations, as well as estimated crustal structures, and RFs for Moho offset models, including realistic levels of noise. [1]: /embed/inline-graphic-1.gif

Shallow gas cloud illumination analysis by the focal beam method

This research will address the illumination issue of seismic data below a shallow gas cloud, also known as shallow gas accumulation. In general, poor and distorted seismic data underneath gas zones depend on four major factors; namely the velocity of the gas zones, the depth of the target reflector, the location of the source and the receiver during seismic acquisition, and the frequency of the seismic signals. These factors will be scrutinized in detail by using the focal beam method. The focal beam method incorporates the double focusing concept in order to obtain two important attributes for illumination analysis: (i) Resolution function beam, (ii) amplitude versus ray parameter (AVP) imprint, which is obtained by transforming the modelled data into the radon domain. Both illumination attributes are then applied to a gas-affected field in the Malaysia Basin. The results show well-defined illumination beneath the shallow anomalies and provide a better representation of the subsurface. © 2016 Sinopec Geophysical Research Institute.

Receiver Function and Geometric Tomography along the Monterey Microplate to Test Slab Delamination or Lithospheric Drip Models of the Isabella Anomaly, California

Abstract Two hypotheses were tested for the origin of the Isabella tomographic anomaly, which has been interpreted as either a lithospheric drip (Jones et al. , 1994; Ducea and Saleeby, 1998) or a remnant of the Farallon plate, possibly attached to the Monterey microplate (Wang et al. , 2013). P ‐wave receiver functions and travel‐time residuals based on teleseismic events recorded by 41 stations were used to construct simple geometric tomography models of the Isabella anomaly and to test whether the Monterey microplate, or a similar fragment of the Farallon slab, can be connected with the location of the anomaly. The travel‐time residual pattern was modeled with a slab geometry composed of a high‐velocity rectangular block, and a lithospheric drip was modeled as a dipping cylindrical anomaly. Both gave statistically similar fits, but the cylindrical block appears less well constrained than the rectangular block. The top surface of the best‐fit rectangular block was located at 50 km below the Great Valley and dips 65° northeast toward the Sierra Nevada, with 100 km thickness. West of the Isabella anomaly, receiver‐function P ‐to‐ S converted phases from the top and bottom surfaces of the oceanic crust of the Monterey microplate were modeled as late‐arriving negative–positive dipole signals. Such dipoles are observed at times that place their origin at 10 km below the Moho at the Coast Ranges. These converted phases from the oceanic crust could also be traced from the Coast Ranges to the Great Valley, where the top surface of the slab model is located. The combined result of the receiver functions and a geometric tomography model is consistent with the fossil slab hypothesis, which initiated as a flat subduction system that later went through a delamination process. Online Material: Figures of receiver functions, sorted by back azimuth and ray parameter at 31 stations.

Crustal shear-wave velocity structure of northeastern Tibet revealed by ambient seismic noise and receiver functions

The Tibetan plateau is formed by the persistent convergence between the Indian and Eurasian plates. The northeastern Tibetan plateau is undergoing young deformation that has been noticed for a long time. We conduct a passive-source seismic profile with 22 stations in NE Tibet in order to investigate the crustal shear-wave velocity structure and its relationship with tectonic processes. In this paper we obtain the Rayleigh-wave phase velocity dispersion data among all station pairs within the period bandwidth of 5–20s from the method of ambient noise cross-correlations. Phase velocity variations correlate well with surface geological boundaries and tectonic features, for instance, low phase velocity beneath the Songpan–Ganzi block and the Guide basin. We also compute P-wave receiver functions based on the selected teleseismic events with similar ray parameters, and perform the joint inversion of surface wave dispersion data and receiver functions to obtain the 2-D crustal shear-wave velocity structure along the profile. The inversion results show that low shear-wave velocities beneath the Songpan–Ganzi block are widespread in the middle-to-lower crust. In together with high crustal Vp/Vs ratios and high temperature suggested by the P-wave velocities obtained from the active-source seismic study, we suggest that the low velocity zone beneath the Songpan–Ganzi block is probably attributed to partial melting. Across the North Kunlun fault, there is no crustal LVZ found beneath the Kunlun block. This structural difference may have already existed before the collision of the two blocks, or due to limit of the northward extension for the crustal LVZ across the North Kunlun fault.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Iterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections.

Efficient pseudo-Gauss-Newton full-waveform inversion in the τ-p domain

Full-waveform inversion (FWI) seeks to estimate subsurface elastic properties by iterative minimization of the difference between synthetic and observed data. Its industrial application suffers from several well-defined obstacles, including high computational cost, slow convergence rate, and the phenomenon of cycle skipping. We have developed an efficient [Formula: see text] domain waveform inversion aimed at reducing the computational burden of FWI with a phase-encoding technique. The gradient is constructed in the [Formula: see text] domain using linear phase-encoding, and a slant update strategy further reduces the computational burden. Poorly scaled and blurred gradient updates can be enhanced using exact or approximate versions of the inverse Hessian, which leads to a faster convergence rate. We developed a new chirp phase-encoding strategy for diagonal Hessian construction. Preconditioning the gradient using the diagonal phase-encoded approximate Hessian forms what we refer to as a pseudo-Gauss-Newton (PGN) step. To test the effectiveness of the [Formula: see text]-domain FWI, the strategies were enacted on a modified Marmousi model. We compared the computational cost of the PGN method with traditional methods, and we evaluated the quality of the inversion results. The PGN method can get a better inversion result with the same computational cost. We have also analyzed the effects of different ray parameter settings and the influence of source spacing, and we compared different preconditioning methods for [Formula: see text]-domain FWI.

Global scale observations of scattered energy near the inner-core boundary: Seismic constraints on the base of the outer-core

We have collected a global dataset of several thousands of high quality records of PKPdf, PKPbc, PKPbc-diff and PKPab phase arrivals in the distance range [149–178°]. Within this collection, we have identified an energy packet that arrives 5–20s after the PKPbc (or PKPbc-diff) and represents a phase that is not predicted by 1D reference seismic models. We use array analysis techniques to enhance the signal of these scattered phases and show that they originate along the great-circle path in a consistent range of arrival times and narrow range of ray parameters. We therefore refer to this scattered energy the “M” phase. Using the cross-correlation technique to detect and measure the scattered energy arrival times, we compiled a dataset of 1116 records of this M phase. There are no obvious variations with source or station location, nor with the depth of the source. After exploration of possible location for this M phase, we show that its origin is most likely in the vicinity of the inner-core boundary. A tentative model is found that predicts an M-like phase, and produces good fits to its travel times as well as those of the main core phases. In this model, the P velocity profile with depth exhibits an increased gradient from about 400km to 50km above the ICB (i.e. slightly faster velocities than in AK135 or PREM), and a ∼50km thick lower velocity layer right above the ICB.

Inverting interpolated receiver functions with surface wave dispersion and gravity: Application to the western U.S. and adjacent Canada and Mexico

AbstractWe use P wave receiver functions from the western U.S. and adjacent regions to construct a receiver function wavefield interpolation scheme that helps to equalize the lateral sampling of the receiver functions and the surface wave dispersion and to greatly simplify the receiver functions. Spatial interpolation and smoothing suppress poorly sampled and difficult to interpret back azimuthal variations and allow the extraction of the first‐order features in the receiver function wavefield, including observations from several ray parameter ranges. We combine the interpolated receiver functions with Rayleigh wave dispersion estimates and surface gravity observations to estimate the 3‐D shear wave speed beneath the region. Speed variations in the 3‐D model correlate strongly with expected geologic variations and illuminate broad‐scale features of the western U.S. crust and upper mantle. The model is smooth, self‐consistent, and demonstrates the compatibility of the interpolated receiver functions and dispersion observations.

The characteristic wave decomposition and imaging in VTI media

The characteristic wave decomposition (CWD) method is presented, which takes full advantages of the local linear characteristics of the original seismic data. The CWD is performed by double beam forming for a compressed seismic wavefield in the characteristic ray parameter domain. Based on the beam-formed wavefield in characteristic domain, a beam-based characteristic wave imaging method (CWI) is put forward. Due to the flexibility and efficiency to output angle gathers for velocity model building, the CWI is a useful alternative to Kirchhoff and wave-equation migrations. It alters the application of Kirchhoff migration which smears the seismic data in imaging domain along quasi-ellipsoid trajectories and it has the capacity for steep dip reflector imaging with turning waves. In this paper, the CWI method is applied to prestack depth migration in transverse isotropic with a vertical symmetry (VTI) media. Compared with the conventional Kirchhoff migration methods, the proposed CWI method has a theoretical speedup of 1–2 orders. Besides, it can handle low signal-to-noise-ratio (SNR) data and target oriented imaging conveniently, and angle gathers can be produced naturally by CWI. Consequently, the CWI is an efficient technique for large scale seismic imaging and angle gather outputting. The direct mapping scheme from data space to model space establishes the relation between the characteristic data and the subsurface reflector, which can be used for the subsequent tomography conveniently. Some benchmark tests demonstrate the effectiveness of this method.

A new atmospheric GNSS method for improving the absolute positioning accuracy

A new method for positioning a signal receiver of the global navigation satellite system is proposed within the ray theory and under the assumption that the atmosphere is spherically stratified and the dependence of the speed of the radio signal sent by each navigation satellite on the distance from the center of the Earth is known. A new basic system of equations is presented. For the minimum number of four navigation satellites, it consists of eight equations in eight unknowns, four of which are accessory ray parameters. The correctness of the new basic system is proved, and an algorithm for its solution is described. The purpose of the new method is a significant improvement in the accuracy of the absolute positioning of the signal receiver of the global navigation satellite system through the proper account of irregularities of the ionosphere and troposphere.

Multichannel filtering and reconstruction of ultrasonic guided wave fields using time intercept-slowness transform.

Multichannel ultrasonic axial-transmission data are multimodal by nature. As guided waves are commonly used in nondestructive material testing, wave field filtering becomes important because the analysis is usually limited to a few lower-order modes and requires their extraction. An application of the Radon transform to enhance signal-to-noise ratio and separate wave fields in ultrasonic records is presented. The method considers guided wave fields as superpositions of plane waves defined by ray parameters (p) and time intercepts (τ) and stacks the amplitudes along linear trajectories, mapping time-offset (t - x) data to a τ - p or Radon panel. The transform is implemented using a least-squares strategy with Cauchy-norm regularization that serves to enhance the focusing power. The method was verified using simulated data and applied to an uneven spatially sampled bovine-bone-plate data set. The results demonstrate the Radon panels show isolated amplitude clusters and the Cauchy-norm constraint provides a more focused Radon image than the damped least-squares regularization. Wave field separation can be achieved by selectively windowing the τ - p signals and inverse transformation, which is illustrated by the successful extraction of the A0 mode in bone plate. In addition, the method effectively attenuates noise, enhances the coherency of the guided wave modes, and reconstructs the missing records. The proposed transform presents a powerful signal-enhancement tool to process guided waves for further analysis and inversion.

3-D structure of the Rio Grande Rift from 1-D constrained joint inversion of receiver functions and surface wave dispersion

The Southern terminus of the Rio Grande Rift region has been poorly defined in the geologic record, with few seismic studies that provide information on the deeper Rift structure. In consequence, important questions related to tectonic and lithospheric activity of the Rio Grande Rift remain unresolved. To address some of these geological questions, we collect and analyze seismic data from 147 EarthScope Transportable Array (USArray) and other seismic stations in the region, to develop a 3-D crust and upper mantle velocity model. We apply a constrained optimization approach for joint inversion of surface wave and receiver functions using seismic S wave velocities as a model parameter. In particular, we compute receiver functions stacks based on ray parameter, and invert them jointly with collected surface wave group velocity dispersion observations. The inversions estimate 1-D seismic S-wave velocity profiles to 300 km depth, which are then interpolated to a 3-D velocity model using a Bayesian kriging scheme. Our 3-D models show a thin lower velocity crust anomaly along the southeastern Rio Grande Rift, a persistent low velocity anomaly underneath the Colorado Plateau and Basin and Range province, and another one at depth beneath the Jemez lineament, and the southern RGR.

Seismic Illumination Analysis in Poor Oil & Gas Field Data by Using Focal Beam Method

The area underneath shallow gas cloud is an area where the image of subsurface data is generally poor. This distorted image underneath gas zones usually contains precious information of hydrocarbon accumulation. Previously, we analyse the factors contribute to poor subsurface seismic image underneath the gas cloud model and use focal beam technique to understand subsurface illumination information. Encourage by model-based success, we shift our focus to data-based application by applying the focal beam technique into a real field data. The results from this field were analyse in term of resolution function and amplitude versus ray parameter (AVP) imprint for different reflector depth, followed by acquisition analysis on the surface level. For this purpose, a velocity data of a field located in Malay Basin was built before applying the focal beam calculation. We will demonstrate that by using focal beam analysis for this field, we will able to obtain good imaging particularly for target reflector at 2000ms, 4000ms and 6000ms depth, provided the full 3D acquisition geometry was used during focal beam application.

Global synthetic seismograms using a 2-D finite-difference method

Two-dimensional (2-D) finite-difference (FD) synthetics, which fill the gap between fast 1-D analytic synthetics and time-consuming full 3-D synthetics in our ability to model seismograms, have been used in many studies. We address several issues involving 2-D FD methods in generating global synthetic seismograms. These include: (1) interfacing point source excitation for earthquakes with 2-D FD methods; (2) out-of-plane spreading corrections and (3) reducing the spherical Earth to the flattened models. The first issue is tackled using two methods, a ‘transparent source box’ approach and a moment tensor excitation approach, where each has its own advantages. Moreover, our ‘source box’ excitation does not have the late-time drift problem that occurred in previous studies. The out-of-plane geometric spreading correction is accounted for by estimating the ray parameter and applying a post-simulation filter to 2-D synthetics. Finally, parameters of the Earth-flattening transformation are discussed and validated. The effectiveness of this method is demonstrated by comparing our synthetics with frequency–wavenumber summation, normal-mode and 3-D spectral-element synthetics.