Ray Velocity Research Articles

Ray and energy-flux velocities at a contact of two viscoelastic anisotropic materials

Summary A g*-Hamiltonian method for tracing real rays was developed that can handle cusps and triplication of quasi-shear wave in a general viscoelastic anisotropic medium. We demonstrate that the g*-Hamiltonian method can produce homogeneous ray-velocity vectors (with parallel real and imaginary parts) and the slowness vectors of reflected and transmitted waves at the interface based on the real Snell's law (RSL), which constrains only the continuity of the real parts of the slowness vectors, or the real slowness direction (RSD) method, which ignores the inhomogeneous component of the slowness vector. These methods are based on the characteristic lines with different Hamiltonians. Our research indicates that these methods are limited to pre-critical incidence ranges. Moreover, we derived a complex energy velocity vector (energy flux velocity) expression, which is always homogenous. We found that directions of corresponding energy velocity calculated with complex Snell's law (CSL) at a contact of two viscoelastic anisotropic materials well match the solutions of the RSL and RSD methods for all R/T waves except post-critical incidence, whereas the RSL and RSD methods fail to obtain homogenous ray velocities. The RSL and RSD methods result in discrepancies in the ray quality factor, R/T coefficients, and energy ratios, especially for post-critical incidence. However, the exact critical angle determined by the RSD method approximates the ‘critical’ angle for anelastic/inhomogeneous waves, which was a previous challenge. Our calculations suggest that the energy velocity and energy quality factor obtained with the CSL method can be used for real ray tracing at the interface of viscoelastic anisotropic media, and the complex energy flux velocity vector is always exactly homogeneous. For the post-critical incidence, the RSL and RSD methods fail because the ray quality factor drastically changes from the infinite down to near 2, which contradicts homogeneous ray velocity in elastic anisotropic materials. However, the energy quality factor for the elastic-anisotropic material is all infinite, even for post-critical incidence, which is correct. We also show that the CSL method has the same efficiency as the RSD method.

Machine learning assisted Kriging to capture spatial variability in petrophysical property modelling

Machine learning (ML) models have been widely used for estimating formation geophysical properties. While ML models excel at capturing non-linear correlations among parameters, incorporating the impact of spatial variability into the training and testing process remains challenging. On the other hand, deterministic geostatistical models such as Kriging are capable of capturing spatial variability to a great extent but often rely on the assumption of linearity, making them less suitable for non-linear relations. In this study, a machine learning (Least Squared Support Vector Regression, LSSVR) model is integrated into Kriging interpolation to estimate the sonic compressional wave velocity with high spatial variability over a geological setting. This new methodology consists of two steps: (1) constructing an initial machine learning model using LSSVR and calculating the residuals, and (2) applying Kriging interpolation and gradually modifying the training data using Kriging estimation to optimize the machine learning model. The proposed model effectively captures the non-linear relation between auxiliary and target variables along with the spatial autocorrelation of data. To evaluate the performance of proposed hybrid model, a dataset comprising geophysical downhole logging measurements including density, gamma ray, depth and sonic velocity were extracted from 122 boreholes in a mine site located at the Bowen basin in Queensland, Australia. The data was averaged over a sandstone interval and divided into training and testing sets. Four models, namely linear regression, regression Kriging, LSSVR and the hybrid model were developed and compared with each other based on their R2 and RMSE values. The results demonstrate that the hybrid model outperforms the other models highlighting the effectiveness of employing a hybrid approach in capturing the spatial variability in petrophysical data over geological formations.

Real-time correlators in chaotic quantum many-body systems

We study real-time correlators $\ensuremath{\langle}\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\ensuremath{\rangle}$ of local operators in chaotic quantum many-body systems. These correlators show universal structure at late times, determined by the geometry of the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbit{x},t)$. These trajectories, which involve the operator contracting to a point at both the initial and final time, are qualitatively different from those that dominate the out-of-time-order correlation function. In the absence of conservation laws, local correlations decay exponentially: $\ensuremath{\langle}\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\ensuremath{\rangle}\ensuremath{\sim}exp(\ensuremath{-}{s}_{\text{eq}}\phantom{\rule{0.16em}{0ex}}r(\mathbit{v})\phantom{\rule{0.16em}{0ex}}t)$, where $\mathbit{v}=\mathbit{x}/t$ defines a ray in spacetime, and $r(\mathbit{v})$ is a rate function associated with this ray. We express $r(\mathbit{v})$ in terms of cost functions for various spacetime structures. In $1+1\mathrm{D}$ the operator histories can exhibit a phase transition at a critical value ${v}_{c}$ of the ray velocity, which leads to a singular behavior in $r(\mathbit{v})$. At low velocities, the dominant Feynman histories are ``fat'': The operator grows to a size of order ${t}^{\ensuremath{\alpha}}$ (with $\ensuremath{\alpha}=1/2$ in the simplest case) before contracting to a point again. At high velocities the trajectories are ``thin'': The operator always remains of order-one size. In a Haar-random quantum circuit, this transition maps to a simple binding transition for a pair of random walks, which represent the left and right spatial boundaries of the operator. In higher-dimensional systems, thin trajectories always dominate. We discuss the circumstances in which the butterfly velocity ${v}_{B}$ can be deduced from a time-ordered two-point function, rather than the out-of-time ordered correlator. In the random circuit, correlators may also be computed in the framework of an effective Ising-like statistical mechanics model: we describe this calculation, as well as a special feature of the weights in the case of a $1+1\mathrm{D}$ Haar-random brickwork circuit. The present paper addresses lattice models, but also suggests the possibility of morphological phase transitions for real-time Feynman diagrams in continuum quantum field theories.

Approximate reflection and transmission coefficients at an interface between two contrasting viscoelastic anisotropic half-spaces

SUMMARY We present and compare two new methods to calculate the reflection and transmission coefficients of qP, qSV and qSH waves at a flat interface between two contrasting viscoelastic anisotropic half-spaces. The first method is a new version of the real ray tracing method that extends the traditional real ray tracing method to tackle the triplications of the qSV wave. This new version is valid for computing the reflection and transmission coefficients of the qP and qSV waves for all pre- and post-critical angles of incidence, which cannot be handled by the previous approach. The second method employs the real slowness direction and Snell's law to provide approximate reflection and transmission coefficients for such wave modes. This approximate method has attractive advantages which are not only the avoidance of the searching process inherent in the real ray tracing method but also offers competitive economical solutions to the first method. Many viscoelastic VTI models are utilized to validate the two methods. The numerical results show that (1) the ray angles, ray velocities, ray Q-factors, and the magnitudes of the reflection and transmission coefficients obtained by the two methods closely agree with each other, except in the vicinity of the critical angles and (2) the phase angles of the reflected and transmitted waves exhibit complexities due to the existence of some reverse phenomena between the approximate and the real ray tracing solutions. However, such phase discrepancies do not affect the magnitudes of the reflection and transmission coefficients. Moreover, the energy ratios of the different wave modes satisfy the energy conservation criterion at the interface.

An advanced computational intelligent framework to predict shear sonic velocity with application to mechanical rock classification

Shear sonic wave velocity (Vs) has a wide variety of implications, from reservoir management and development to geomechanical and geophysical studies. In the current study, two approaches were adopted to predict shear sonic wave velocities (Vs) from several petrophysical well logs, including gamma ray (GR), density (RHOB), neutron (NPHI), and compressional sonic wave velocity (Vp). For this purpose, five intelligent models of random forest (RF), extra tree (ET), Gaussian process regression (GPR), and the integration of adaptive neuro fuzzy inference system (ANFIS) with differential evolution (DE) and imperialist competitive algorithm (ICA) optimizers were implemented. In the first approach, the target was estimated based only on Vp, and the second scenario predicted Vs from the integration of Vp, GR, RHOB, and NPHI inputs. In each scenario, 8061 data points belonging to an oilfield located in the southwest of Iran were investigated. The ET model showed a lower average absolute percent relative error (AAPRE) compared to other models for both approaches. Considering the first approach in which the Vp was the only input, the obtained AAPRE values for RF, ET, GPR, ANFIS + DE, and ANFIS + ICA models are 1.54%, 1.34%, 1.54%, 1.56%, and 1.57%, respectively. In the second scenario, the achieved AAPRE values for RF, ET, GPR, ANFIS + DE, and ANFIS + ICA models are 1.25%, 1.03%, 1.16%, 1.63%, and 1.49%, respectively. The Williams plot proved the validity of both one-input and four-inputs ET model. Regarding the ET model constructed based on only one variable,Williams plot interestingly showed that all 8061 data points are valid data. Also, the outcome of the Leverage approach for the ET model designed with four inputs highlighted that there are only 240 “out of leverage” data sets. In addition, only 169 data are suspected. Also, the sensitivity analysis results typified that the Vp has a higher effect on the target parameter (Vs) than other implemented inputs. Overall, the second scenario demonstrated more satisfactory Vs predictions due to the lower obtained errors of its developed models. Finally, the two ET models with the linear regression model, which is of high interest to the industry, were applied to diagnose candidate layers along the formation for hydraulic fracturing. While the linear regression model fails to accurately trace variations of rock properties, the intelligent models successfully detect brittle intervals consistent with field measurements.

Sedimentary noise modeling of lake-level change in the Late Triassic Newark Basin of North America

Two different hypotheses, glacioeustasy and groundwater aquifer eustasy, have been proposed to explain short-term, high-amplitude sea-level oscillations during past greenhouse-dominated intervals. However, the veracity of aquifer eustasy on long-term, high amplitude sea level has never been rigorously tested. We evaluate these competing hypotheses using the objective approach of sedimentary noise modeling for lake-level reconstruction. Statistical tuning and astronomical calibration of paleoclimate and paleoenvironment proxies (depth rank, rock color, gamma ray, and sonic velocity) from the lacustrine Newark Basin enable the construction of a 31.55-Myr long astronomical time scale (ATS) for the Late Triassic that is comparable to the classic Newark ATS previously presented. Using this timescale, sedimentary noise modeling in the lacustrine Newark Basin is carried out through the Late Triassic. Lake level fluctuations reconstructed by sedimentary noise modeling and principal component analysis reveal that million-year scale lake-level variations were linked to astronomical forcing with periods of ~3.3 Myr, ~1.8 Myr, and ~1.2 Myr. Our results demonstrate that astronomical forcing, as a driver of groundwater dynamics, may have had an impact on global sea-level changes during the Late Triassic. This study thus emphasizes the importance of high-resolution, objective reconstruction of sea- and lake-levels for further testing the hypotheses of glacioeustasy and aquifer eustasy under warm conditions. • We reconstruct high-resolution lake-level changes in the Late Triassic. • Long-period astronomical forcing drove lake-level and sea-level variations. • Continental groundwater could have an impact on global sea-level fluctuations. • High-resolution, objective reconstruction of lake- and sea-levels is key to test aquifer eustasy versus glacioeustasy.

Ray velocity derivatives in anisotropic elastic media – Part I: general anisotropy

SUMMARY We present an original, generic and efficient approach for computing the first and second partial derivatives of ray (group) velocities along seismic ray paths in general anisotropic (triclinic) elastic media. As the ray velocities deliver the ray element traveltimes, this set of partial derivatives constructs the so-called kinematic and dynamic sensitivity kernels which are used in different key seismic modelling and inversion methods, such as two-point ray bending methods and seismic tomography. The second derivatives are useful in the solution of the above-mentioned kinematic problems, and they are essential for evaluating the dynamic properties along the rays (amplitudes and phases). The traveltime is delivered through an integral over a given Lagrangian defined at each point along the ray. In our approach, we use an arclength-related Lagrangian representing a reciprocal of the ray velocity magnitude. Although this magnitude cannot be explicitly expressed in terms of the medium properties and the ray direction components, its derivatives can still be formulated analytically using the corresponding arclength-related Hamiltonian that can be explicitly expressed in terms of the medium properties and the slowness vector components; this requires first to obtain (invert for) the slowness vector components, given the ray direction components. Computation of the slowness vector and the ray velocity derivatives is considerably simplified by using an auxiliary scaled-time-related Hamiltonian obtained directly from the Christoffel equation and connected to the arclength-related Hamiltonian by a simple scale factor. This study consists of two parts. In Part I, we consider general anisotropic (triclinic) media, and provide the derivatives (gradients and Hessians) of the ray velocity, with respect to (1) the spatial location and direction vectors and (2) the elastic model parameters. The derivatives are obtained for both quasi-compressional and quasi-shear waves, where other types of media, characterized with higher symmetries, can be considered particular cases. In Part II, we apply the theory of Part I explicitly to polar anisotropic media (transverse isotropy with tilted axis of symmetry, TTI), and obtain the explicit ray velocity derivatives for the coupled qP and qSV waves and for SH waves. The derivatives for polar anisotropy are simplified (as compared to general anisotropy), obviously yielding more effective computations. The ray velocity derivatives are tested by checking consistency between the proposed analytical formulae and the corresponding numerical ones.

Ray velocity derivatives in anisotropic elastic media. Part II—polar anisotropy

SUMMARY Considering general anisotropic (triclinic) media and both, quasi-compressional (qP) and quasi-shear (qS) waves, in Part I of this study, we obtained the ray (group) velocity gradients and Hessians with respect to the ray locations, directions and the elastic model parameters along ray trajectories. Ray velocity derivatives for anisotropic elastic media with higher symmetries were considered particular cases of general anisotropy. In this part, Part II, we follow the computational workflow presented in Part I, formulating the ray velocity derivatives directly for polar anisotropic media (transverse isotropy with tilted axis of symmetry, TTI) for the coupled qP waves (quasi-compressional waves) and qSV waves (quasi-shear waves polarized in the ‘axial’ plane) and for SH waves (shear waves polarized in the ‘normal’ plane). The acoustic approximation for qP waves is considered a special case. In seismology, the medium properties, normally specified at regular 3-D fine gridpoints, are the five material parameters: the axial compressional and shear wave velocities, the three (unitless) Thomsen parameters and two geometric parameters: the polar angles defining the local direction (the tilt) of the medium symmetry axis. All the parameters are assumed spatially (smoothly) varying, so that their spatial gradients and Hessians can be reliably numerically computed. Two case examples are considered; the first represents compacted shale/sand rocks (with positive anellipticity) and the second, unconsolidated sand rocks with strong negative anellipticity (manifesting a qSV triplication). The ray velocity derivatives obtained in this part are first tested by comparing them with the corresponding numerical (finite difference) derivatives. Additionally, only for validation purpose, we show that exactly the same results (ray velocity derivatives) can be obtained if we transform the given polar anisotropic model parameters (five material and two geometric) into the 21 stiffness tensor components of a general anisotropic (triclinic) medium, and apply the theory derived in Part I. Since in many practical wave/ray-based applications in polar anisotropic media only the spatial derivatives of the axial compressional wave velocity are taken into account, we analyse the effect (sensitivity) of the spatial derivatives of the other parameters on the ray velocity and its derivatives (which, in turn, define the corresponding traveltime derivatives along the ray).

Approximations to a generalized real ray-tracing method for heterogeneous anisotropic viscoelastic media

The real ray-tracing approach leads to an effective solution in the real space domain using a homogeneous ray velocity vector. However, it fails to yield solutions for quasi-S-waves, which suffer from triplications of the wavefronts. To address this challenging problem, a new real ray-tracing method and its two approximations are developed to solve the complex ray equation. The numerical results indicate that the new real ray-tracing method is superior to the common real ray-tracing method in the presence of triplications of the quasi-S-waves in the computation of ray velocity, ray attenuation, and ray quality factors, as well as the reflection and transmission coefficients in viscoelastic anisotropic media. Based on the assumptions of the real slowness direction and real polarization vectors, two new approximations of the new real ray-tracing method are developed for directly computing the homogeneous complex ray velocity vectors of three wave modes (qP, qS1, and qS2). These approximations significantly improve computational efficiency by avoiding the iterative process required by the new real ray-tracing method that is inherited from the common real ray-tracing method. The computational accuracies are verified through transversely isotropic and orthorhombic models with different strengths of attenuation and anisotropy. Incorporation of the new approximation into the shortest-path method turned out to be efficient and accurate for seismic ray tracing in heterogeneous viscoelastic and transversely isotropic media with a vertical axis of symmetry, even in the presence of strong attenuation and anisotropy.

Spatiotemporal instability of a shear-imposed viscous flow

We study the linear spatiotemporal instability of a two-dimensional gravity-driven viscous fluid flow where the fluid surface is subjected to an imposed shear stress. The fourth order Orr–Sommerfeld boundary value problem is derived and solved numerically up to moderate values of the Reynolds number. Numerical solution based on AUTO07p identifies four spatial branches, viz., I, II, III, and IV, where the spatial branches I, II, and IV lie in the upper half zone, while the spatial branch III lies in the lower half zone of the complex wavenumber plane. The spatial growth rate −ki corresponding to branch I becomes stronger as long as the imposed shear stress increases and ensures a destabilizing effect. Furthermore, the spatial branch I enters in the lower half zone of the complex wavenumber plane as soon as the temporal growth rate ωi decreases and may collide with other spatial branch lying in the lower half zone of the complex wavenumber plane. Moreover, a study of absolute and convective instabilities is carried out within the frameworks of saddle point technique and collision criterion. The saddle point technique provides only one unstable branch of the unstable wavepacket, while the collision criterion provides two unstable branches of the wavepacket. The unstable range of the wavepacket with ray velocity enhances in the presence of imposed shear stress. It is observed that the shear-imposed fluid flow is convectively unstable. In addition, the simplified second order two-equation model is developed for a shear-imposed flow in terms of the local fluid layer thickness and local flow rate, which in fact renders three spatial branches rather than four. However, the two-equation model recovers the physically relevant spatial branch I very well. Finally, nonlinear spatiotemporal simulation of the two-equation model displays a formation of the regular train of solitary waves downstream at low forcing frequency.

Group velocity of light in biaxial crystals.

Based on the wave vector surface, we have derived the analytical expressions for the group velocity of light traveling in an optically biaxial crystal in an arbitrary direction. Our formulas are in terms of either the wave vector direction or the ray direction. An axis dispersion vector is introduced to specify the rotation of the dielectric frame in monoclinic and triclinic crystals, which is found to be responsible for the asymmetry of the group velocity surfaces of these two crystal systems when compared to their phase and ray velocity surfaces. Our formulas confirm that the group velocity of light in a nondissipative medium equals the ratio between the Poynting vector and the total energy density of the electromagnetic field. The group index of light is found to be decomposable into three parts: the ray index, the group index due to principal refractive index dispersion, and that due to axis dispersion. Numerical calculations are performed for the group velocity of light in ${\rm Sn}_2{\rm P}_2{\rm S}_6$ crystal at 550 nm wavelength. Our results show that the dispersion of the principal refractive indices has a considerable contribution to the group index.

Asymmetry of the group velocity of light in monoclinic crystals.

We have proved that compared to phase velocity and ray velocity surfaces, the group velocity surface of a monoclinic crystal has a reduced symmetry, due to the loss of the two mirror planes that contain the crystallographic b axis. We have derived a formula for calculation of the group velocity of the extraordinary light traveling in a principal plane of a biaxial crystal, which takes into account the rotation of the dielectric frame due to frequency dispersion. The maximum asymmetry of the group velocity of light traveling in the a-c plane is found to be 2.4% at 365 nm in BiB3O6 and 1.4% at 550 nm in Sn2P2S6.

Group velocity of light in uniaxial crystals.

Using the wave vector surface, we have derived the analytical expressions for the group velocities of the extraordinary light and the ordinary light traveling in an optically uniaxial crystal. Our formulas are in terms of either the wavevector direction or the ray direction, and they use only the principal refractive indices and their frequency dispersions. The algebraic equation for the group velocity surface of the crystal is also derived. While the group velocity is in the same direction as the ray velocity, numerical calculation shows that in the visible region the group velocity is slower than the ray velocity, and the difference between them becomes significant at short wavelengths.

Slowness vector versus ray direction in polar anisotropic media

SUMMARY The inverse problem of finding the slowness vector from a known ray direction in general anisotropic elastic media is a challenging task, needed in many wave/ray-based methods, in particular, solving two-point ray bending problems. The conventional resolving equation set for general (triclinic) anisotropy consists of two fifth-degree polynomials and a sixth-degree polynomial, resulting in a single physical solution for quasi-compressional (qP) waves and up to 18 physical solutions for quasi-shear waves (qS). For polar anisotropy (transverse isotropy with a tilted symmetry axis), the resolving equations are formulated for the slowness vectors of the coupled qP and qSV waves (quasi-shear waves polarized in the axial symmetry plane), and independently for the decoupled pure shear waves polarized in the normal (to the axis) isotropic plane (SH). The novelty of our approach is the introduction of the geometric constraint that holds for any wave mode in polar anisotropic media: The three vectors—the slowness, ray velocity and medium symmetry axis—are coplanar. Thus, the slowness vector (to be found) can be presented as a linear combination of two unit-length vectors: the polar axis and the ray velocity directions, with two unknown scalar coefficients. The axial energy propagation is considered as a limit case. The problem is formulated as a set of two polynomial equations describing: (i) the collinearity of the slowness-related Hamiltonian gradient and the ray velocity direction (third-order polynomial equation) and (ii) the vanishing Hamiltonian (fourth-order polynomial equation). Such a system has up to twelve real and complex-conjugate solutions, which appear in pairs of the opposite slowness directions. The common additional constraint, that the angle between the slowness and ray directions does not exceed ${90^{\rm{o}}}$, cuts off one half of the solutions. We rearrange the two bivariate polynomial equations and the above-mentioned constraint as a single univariate polynomial equation of degree six for qP and qSV waves, where the unknown parameter is the phase angle between the slowness vector and the medium symmetry axis. The slowness magnitude is then computed from the quadratic Christoffel equation, with a clear separation of compressional and shear roots. The final set of slowness solutions consists of a unique real solution for qP wave and one or three real solutions for qSV (due to possible triplications). The indication for a qSV triplication is a negative discriminant of the sixth-order polynomial equation, and this discriminant is computed and analysed directly in the ray-angle domain. The roots of the governing univariate sixth-order polynomial are computed as eigenvalues of its companion matrix. The slowness of the SH wave is obtained from a separate equation with a unique analytic solution. We first present the resolving equation using the stiffness components, and then show its equivalent forms with the well-known parametrizations: Thomsen, Alkhalifah and ‘weak-anisotropy’. For the Thomsen and Alkhalifah forms, we also consider the (essentially simplified) acoustic approximation for qP waves governed by the quartic polynomials. The proposed method is coordinate-free and can be applied directly in the global Cartesian frame. Numerical examples demonstrate the advantages of the method.

Effective and efficient approaches for calculating seismic ray velocity and attenuation in viscoelastic anisotropic media

In viscoelastic anisotropic media, the elastic moduli, slowness vector, phase, and ray velocity are all complex-valued quantities in the frequency domain. Solving the complex eikonal equation becomes computationally complex and time-consuming. We have developed two approximate methods to effectively calculate the ray velocity vector, attenuation, and quality factor in viscoelastic transversely isotropic media with a vertical symmetry axis (VTI) and in orthorhombic (ORT) anisotropy. The first method is based on the perturbation theory (PER) under the assumption of a homogeneous complex ray vector, which is obtained by applying the elastic background and viscoelastic perturbations to the real and imaginary components of the modulus tensor, respectively. The perturbations of the slowness vectors of the three wave modes (qP, qSV, and qSH) are determined through the vanishing Hamiltonian function. The second method is derived by applying a real slowness direction (RSD) to the inhomogeneous complex slowness vector and then approximately calculating the complex ray velocity vector with the condition of the homogeneous complex vector. The numerical results verify that the two approaches can produce accurate ray velocity vector, attenuation, and quality factors of the qP-wave in viscoelastic VTI and ORT media. The RSD method can yield high accuracies of ray velocity for the qSV- and qSH-wave in viscoelastic VTI models even at triplication of the qSV wavefronts, as well as qS1 and qS2 in a weak ORT medium ([Formula: see text] > 20), except for near the cusp of the qS1 wavefronts (errors approximately 6%) where the PER has more than 10% error.

Solar wind temperature–velocity relationship over the last five solar cycles and Forbush decreases associated with different types of interplanetary disturbance

ABSTRACT The behaviour of the solar wind (SW) proton temperature and velocity and their relationship during Forbush decreases (FDs) associated with various types of solar source – coronal mass ejections (CMEs) and coronal holes (CHs) – have been studied. Analysis of cosmic ray variations, SW temperature, velocity, density, plasma beta, and magnetic field (from 1965–2019) is carried out using three databases: the OMNI database, Variations of Cosmic Rays database (IZMIRAN) and Forbush Effects & Interplanetary Disturbances database (IZMIRAN). Comparison of the observed SW temperature (T) and velocity (V) for the undisturbed SW allows us to derive a formula for the expected SW temperature (Texp, the temperature given by a T–V formula, if V is the observed SW speed). The results reveal a power-law T–V dependence with a steeper slope for low speeds (V < 425 km s−1, exponent = 3.29 ± 0.02) and flatter slope for high speeds (V > 425 km s−1, exponent = 2.25 ± 0.02). A study of changes in the T–V dependence over the last five solar cycles finds that this dependence varies with solar activity. The calculated temperature index KT = T/Texp can be used as an indicator of interplanetary and solar sources of FDs. It usually has abnormally large values in interaction regions of different-speed SW streams and abnormally low values inside magnetic clouds (MCs). The results obtained help us to identify the different kinds of interplanetary disturbance: interplanetary CMEs, sheaths, MCs, corotating interaction regions, high-speed streams from CHs, and mixed events.

Seismic complex ray tracing in 2D/3D viscoelastic anisotropic media by a modified shortest-path method

In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.

Deformation of the emission line profile of optically dense spherical plasma caused by rotation of substance

The transfer of resonance radiation in optically dense spherical plasma, rotating around the axis of symmetry, is studied numerically. Frequency shifts in the red and blue wings of the spectrum, frequency broadening of the emission line profile and the absorption line profile, caused by the rotational broadening effect (RBE), are investigated for calcium plasma at the resonant transition with the wavelength of 397 nm. The RBE of absorption and emission lines is explained by broadening of the elementary ion absorption profiles which demonstrate the Doppler dependence on frequency. Location of the frequency of absorption maximum in broadband radiation transmitted through the plasma, as well as location of the frequencies of intensity maximum of the unreabsorbed emission line and intensity minimum of the reabsorbed emission line, unambiguously determine ray velocity of ions in the plasma. The RBE effect of the emission line leads to an increase in probability of photon escape from the medium. This circumstance is indirect evidence for the fact that Holstein’s effective deexcitation time for rotating plasma should decrease. Full width at half maximum (FWHM) of the emission spectrum for rotating plasma increases linearly with the growth of optical thickness of the medium. Measurement of the FWHM value can be a diagnostic method for determining concentration of ions in the plasma.

Application of specific energy for lithology identification

The previous applications of specific energy to drilling operations have focused mainly on drilling optimization and identification of inefficient drilling conditions. Recent advances in specific energy extend its applications to overpressure detection and pore pressure prediction. In this paper, an attempt is made to further extend the application of specific energy to real-time identification of subsurface lithology. The concept is based on the principle that the total energy required to break and remove a unit volume of rock is a function of lithology. The proposed methodology is tested using a recently drilled exploratory gas well in the tertiary deltaic system of the Niger Delta basin. In general, an excellent agreement is observed in trend between the traditional lithology identifiers (gamma ray and sonic velocity ratio) and the total energy consumed in breaking and removing the penetrated rocks. Unlike the logging while drilling (LWD) technique commonly employed in the industry (including the application of near bit sensors placed few feet behind the bit), the proposed methodology can provide a reliable means of picking formation tops and identifying subsurface lithology at the bit with no extra cost since drilling parameters are routinely recorded at the wellsite during the drilling of a well. The proposed methodology will assist the drilling engineers and geologists in determining the casing setting depths and coring points without having to drill too deep into the formation of interest.

A machine learning approach to predict drilling rate using petrophysical and mud logging data

Predicting the drilling rate of penetration (ROP) is one approach to optimizing drilling performance. However, as ROP behavior is unique to specific geological conditions its application is not straightforward. Moreover, ROP is typically affected by various operational factors (e.g. bit type, weight-on-bit, rotation rate, etc.) as well as the geological characteristics of the rocks being penetrated. This makes ROP prediction an intricate and multi-faceted problem. Here we compare data mining methods with several machine learning algorithms to evaluate their accuracy and effectiveness in predicting ROP. The algorithms considered are: artificial neural networks (ANN) applying a multi-layer perceptron (MLP); ANN applying a radial basis function (RBF); support vector regression (SVR), and an hybrid MLP trained using a particle swarm optimization algorithm (MLP-PSO). Data preparation prior to executing the algorithms involves applying a Savitzky–Golay (SG) smoothing filter to remove noise from petrophysical well-logs and drilling data from the mud-logs. A genetic algorithm is applied to tune the machine learning algorithms by identifying and ranking the most influential input variables on ROP. This tuning routine identified and selected eight input variables which have the greatest impact on ROP. These are: weight on bit, bit rotational speed, pump flow rate, pump pressure, pore pressure, gamma ray, density log and sonic wave velocity. Results showed that the machine learning algorithms evaluated all predicted ROP accurately. Their performance was improved when applied to filtered data rather than raw well-log data. The MLP-PSO model as a hybrid ANN demonstrated superior accuracy and effectiveness compared to the other ROP-prediction algorithms evaluated, but its performance is rivalled by the SVR model.