Pp-wave Research Articles

Curvelet-based registration of multi-component seismic waves

Abstract Registration of the travel time of PP waves and PS waves on the same coordinate is critical for joint interpretation in multi-component seismic exploration. In this paper, we propose a new curvelet-based registration method to improve the precision of registration, especially for the data with heavy random noises. By making registration in curvelet multiscale spaces from coarser to finer scale, the proposed method is not sensitive to initial values of velocity ratio of PP waves and PS waves. Applications of the new method to real seismic dataset from Shengli Oilfield, China show good registered results in terms of both qualitative and quantitative analysis, in comparison with a traditional registration method and a wavelet-based method.

OPEN STRING IN THE PRESENCE OF THE pp-WAVE, LINEAR DILATON, AND KALB--RAMOND BACKGROUNDS

Open strings on a D$p$-brane in the pp-wave spacetime, accompanied by a linear dilaton background, will be studied. Various properties of this system such as solvability of equations of motion and quantization will be investigated.

The regularity of geodesics in impulsive pp-waves

We consider the geodesic equation in impulsive pp-wave space-times in Rosen form, where the metric is of Lipschitz regularity. We prove that the geodesics (in the sense of Caratheodory) are actually continuously differentiable, thereby rigorously justifying the $C^1$-matching procedure which has been used in the literature to explicitly derive the geodesics in space-times of this form.

Pure radiation metric with stable closed timelike curves

Here we present an example of an axially symmetric spacetime, representing pure radiation, and admitting circular closed timelike curves (CTCs) on the \(z= \hbox {constant plane}\). The spacetime is regular everywhere, having no curvature singularities and is locally isometric to (non-vacuum) pp wave spacetimes. The stability of the CTCs under linear perturbations is studied and they are found to be stable from a calculation of the Lyapunov exponent for the deviation vector. We also demonstrate that the spacetime also admits non-circular CTCs which do not lie in this plane. A modification of the metric is also studied and we find that a region of this spacetime behaves like a time-machine where CTCs appear after a certain instant of time.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset (AVO) analysis and inversion in exploration geophysics. However, the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically. To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers, we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient, which establishes the direct relationship between PP-wave reflection coefficient and P-wave velocities, S-wave velocities and densities across the interface. (A PP wave is a reflected compressional wave from an incident compressional wave (P-wave).) This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle. Model tests demonstrate that, compared with the reflection coefficients of the linearized approximations, the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle. Furthermore, we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver, to implement the direct inversion for the six parameters including P-wave velocities, S-wave velocities, and densities in the upper and lower layers across the interface. This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way. Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface, and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

Lithospheric cooling trends and deviations in oceanic PP‐P and SS‐S differential traveltimes

The thermal and compositional structure of oceanic lithosphere, which exerts an important control on plate behavior, is still debated. Our set of 60,000 PP‐P and SS‐S traveltime differences with oceanic PP and SS bounce points provides a good constraint on both compressional‐ and shear‐wave velocity. By calculating traveltimes for thermal models that are converted to seismic structures with a thermodynamic approach, we test whether lithospheric cooling can explain PP‐P and SS‐S traveltime variations with plate age. The PP‐P and SS‐S traveltimes have substantial scatter but, on average, decrease by 0.2 and 0.7 s/Myr½, respectively, when the PP and SS waves reflect off progressively older oceanic crust. Both a half‐space and a plate cooling model with a mid‐ocean ridge basalt‐source mantle potential temperature (1315° ± 50°C) explain the average values of the PP‐P and SS‐S anomalies and their decrease with plate age. Residual PP‐P and SS‐S anomalies relative to a cooling model reveal large‐scale patterns. Along a few paths (e.g., Tonga–Fiji to western North America), seismic heterogeneity in the deep mantle is responsible for a significant fraction of the PP‐P and SS‐S traveltime variation. Most anomalies probably correspond to broad temperature variations in the upper mantle, such as a very slow central–northern Pacific (which may require a 100°C excess temperature) and high‐ and low‐velocity anomalies along the ridges that correlate with deep and shallow bathymetry, respectively.

Invariant classification of vacuum pp-waves

We solve the equivalence problem for vacuum pp-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete invariant classification of the vacuum pp-waves. In particular, we derive the invariant characterization of the G2 and G3 sub-classes in terms of these invariants. It is known [J. M. Collins, “The Karlhede classification of type N vacuum spacetimes,” Class. Quantum Grav. 8, 1859–1869 (1991)10.1088/0264-9381/8/10/011] that the invariant classification of vacuum pp-waves requires at most the fourth order covariant derivative of the curvature tensor, but no specific examples requiring the fourth order were known. Using our comprehensive classification, we prove that the q ⩽ 4 bound is sharp and explicitly describe all such maximal order solutions.

Vacuum plane waves: Cartan invariants and physical interpretation

As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.

Interpreting spacetimes of any dimension using geodesic deviation

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corresponding deformations caused by a generic higher-dimensional gravitational waves observed in such physical subspace, need not be tracefree.

Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes, the symmetry group of the Stäckel-Killing tensors is the well-known Newton-Hooke group.

Noncommutative Killing vectors

Within the context of a deformed theory of gravity, we consider a solution to the noncommutative Killing equations associated to a noncommutative pp-wave space-time.Received 27 June 2011DOI:https://doi.org/10.1103/PhysRevD.84.064002© 2011 American Physical Society

Application of 3D vertical seismic profile multi‐component data to tight gas sands‡

ABSTRACTDue to the complicated geophysical character of tight gas sands in the Sulige gasfield of China, conventional surface seismic has faced great challenges in reservoir delineation. In order to improve this situation, a large‐scale 3D‐3C vertical seismic profiling (VSP) survey (more than 15 000 shots) was conducted simultaneously with 3D‐3C surface seismic data acquisition in this area in 2005. This paper presents a case study on the delineation of tight gas sands by use of multi‐component 3D VSP technology. Two imaging volumes (PP compressional wave; PSv converted wave) were generated with 3D‐3C VSP data processing. By comparison, the dominant frequencies of the 3D VSP images were 10–15 Hz higher than that of surface seismic images. Delineation of the tight gas sands is achieved by using the multi‐component information in the VSP data leading to reduce uncertainties in data interpretation. We performed a routine data interpretation on these images and developed a new attribute titled ‘Centroid Frequency Ratio of PSv and PP Waves’ for indication of the tight gas sands. The results demonstrated that the new attribute was sensitive to this type of reservoir. By combining geologic, drilling and log data, a comprehensive evaluation based on the 3D VSP data was conducted and a new well location for drilling was proposed. The major results in this paper tell us that successful application of 3D‐3C VSP technologies are only accomplished through a synthesis of many disciplines. We need detailed analysis to evaluate each step in planning, acquisition, processing and interpretation to achieve our objectives. High resolution, successful processing of multi‐component information, combination of PP and PSv volumes to extract useful attributes, receiver depth information and offset/ azimuth‐dependent anisotropy in the 3D VSP data are the major accomplishments derived from our attention to detail in the above steps.

Some spacetimes with higher rank Killing–Stäckel tensors

By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson–Schouten–Nijenhuis algebra. We discuss the extension to the quantum regime.

Note on I-brane near horizon PP-wave background

We find out a PP-wave spacetime with constant Neveu–Schwarz (NS) three form flux by taking a Penrose limit on the ( 1 + 1 ) -dimensional intersection of two orthogonal stacks of fivebranes in type IIB string theory. We further find out an intersecting (D1–D5)-brane solution in this background and analyze its supersymmetry properties by solving the dilatino and gravitino variations explicitly.

Wave separation for the great Sumatra-Andaman earthquake with regional seismic array

We analyzed the seismic waveforms from the December 26, 2004 Sumatra-Andaman earthquake recorded at broadband seismic stations in western Europe. Previous studies involving of the beam-forming technique and high frequency analysis suggest that the earthquake ruptured with a duration of around 500 s. This very long duration makes P wave overlap with later arrivals such as PP wave, which follows P in about 200 s. Since P waves are crucial for modeling earthquake processes, we propose an iterative method to separate P and PP waveforms. The separated P waveform confirms a second large energy release around 300 s after the initial rupture. The iterative signal separation technique is particularly useful for mixed signals that are not independent and the number of recording stations far exceeds number of mixed signal sources.

Converted-wave elastic impedance and fluid identification factor in fractured reserviors

Identification and prediction of fracture and its developmental zone is meaningful to reservoir exploration and development. According to solid mechanics ,fracture strata is anisotropic media . Previous formulation for S-wave elastic impedance neglects seismic anisotropic. In order to incorporate anisotropic , we use an approximation of converted PS-wave reflection coefficients to deduce converted wave elastic impedance in weakly anisotropic media for the first time. Through numerical simulation, the effect of Thomsen parameter, incident angle and azimuthal angle on the formulation are described in detail. At the same time, we analyze the precision of new approximation formulation and compare the hydrocarbon detection effect of PP wave and converted wave elastic impedance. The future work is to select the newest nonlinear inversion algorithm and realize elastic impedance inversion in anisotropic media.On the basis of sensitive fluid identification factor in isotropic media,we construct the new fluid identification factor in weakly anisotropic media, which is composed of PP wave and converted wave elastic impedance. The advantage of new fluid identification factor is to allow investigating AVO anomalies with the effect of anisotropic parameters .Then ,we can analyze the difference of fluid identification factor with azimuthal angle and anisotropic parameters in 3D space .Adding Thomsen parameter to the 25 formation models gived by Castagna and Smith, we analyze the identification effect. Numerical simulation results show that the new fluid factor can identify the gas sand and brine sand effectively.

Killing tensors in pp-wave spacetimes

The formal solution of the second-order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.

Relationship Between Urinary Salt Excretion and Pulse Pressure and Central Aortic Hemodynamics Independent of Steady State Pressure in the General Population

Although central pulse pressure (PPc) is strongly related to central mean arterial pressure (MAPc), PPc predicts cardiovascular outcomes beyond MAPc. Whether modifiable risk factors for hypertension contribute to PPc and its determinants, independent of MAPc, is uncertain. In 635 randomly recruited participants, we assessed the independent relationship between 24-hour urinary sodium (Na(+)) or potassium (K(+)) excretion and brachial artery PP (in office or 24-hour; n = 487), PPc, the forward (P1) and augmented (Paug) pressure wave components of PPc, central augmentation index, and determinants of central pressure waves, including aortic pulse wave velocity, effective reflecting distance, and reflective wave transit time. Central dynamics were determined using applanation tonometry of the carotid, femoral, and radial arteries. With adjustments for potential confounders, urinary Na(+)/K(+) was independently associated with in-office, central, and 24-hour PP, as well as Paug, P1, and central augmentation index (P<0.05 to P<0.005). With further adjustments for MAPc (or diastolic BP), urinary Na(+)/K(+) was independently associated with PPc, 24-hour PP, Paug, P1, and central augmentation index (P<0.05 to P = 0.005) but not with in-office PP, pulse wave velocity, effective reflecting distance, or reflective wave transit time. In conclusion, in a population of African ancestry, urinary salt excretion is independently related to central and 24-hour PP independent of MAPc or diastolic BP, effects that are attributed to increases in both P1 and Paug but not to pulse wave velocity. Hence, modifying salt intake could influence cardiovascular risk through effects on 24-hour and central PPs, as well as P1 and Paug, independent of steady-state pressure (MAP or diastolic BP) or pulse wave velocity.

Local vertical seismic profiling (VSP) elastic reverse-time migration and migration resolution: Salt-flank imaging with transmitted P-to-S waves

To avoid the defocusing effects of propagating waves through salt and overburden with an inaccurate overburden velocity model, we introduce a vertical seismic profiling (VSP) local elastic reverse-time-migration (RTM) method for salt-flank imaging by transmitted P-to-S waves. This method back-projects the transmitted PS waves using a local velocity model around the well until they are in phase with the back-projected PP waves at the salt boundaries. The merits of this method are that it does not require the complex overburden and salt-body velocities and it automatically accounts for source-side statics. In addition, the method accounts for kinematic and dynamic effects, including anisotropy, absorption, and all other unknown rock effects outside of this lo-cal subsalt velocity model. Numerical tests on an elastic salt model and offset 2D VSP data in the Gulf of Mexico, using a finite-difference time-domain staggered-grid RTM scheme, partly demonstrate the effectiveness of this method over interferometry PS-PP transmission migration and local acoustic RTM. Our method separates elastic wavefields to vector P- and S-wave velocity components at the trial image point and achieves better resolution than local acoustic RTM and interferometric transmission migration. The analytical formulas of migration resolution for local acoustic and elastic RTM show that the migration illumination is limited by data frequency and receiver aperture, and the spatial resolution is lower than standard poststack and prestack migration. This new method can image salt flanks as well as subsalt reflectors.

Determination of synthetic pharmaceuticals in phytotherapeutics by capillary zone electrophoresis with contactless conductivity detection (CZE-C 4D)

In this work, a method for simultaneous determination of amfepramone, fenproporex, sibutramine and fluoxetine was developed by capillary zone electrophoresis with capacitively coupled contactless conductivity detection (C 4D) using a homemade capillary electrophoretic system. The optimized conditions for the separation of the pharmaceuticals by CZE were as follows: 50 mmol L − 1 phosphate buffer (pH 5.0) in 50/50 (v/v) mixture of water/acetonitrile as the working electrolyte, 15 kV separation voltage, 25 °C separation temperature, hydrodynamic injection by gravity using 20 cm injection height and 60 s injection time. The detection by C 4D was carried out by using a homemade detector, which employs a sinusoidal wave generator operating at 600 kHz frequency and 2 V pp wave amplitude. The optimized and validated CZE-C 4D method was applied for the determination of the studied pharmaceuticals as adulterants in phytotherapeutic formulations commercialized in Brazil for slimming purposes.