Slip Theory Research Articles

Dynamic Tangential Contact Stiffness and Damping Model of the Solid–Liquid Interface

In order to establish the tangential contact stiffness and damping model of the solid–liquid interface by tangential exciting vibration force under mixed lubrication, the finite difference method was firstly used to solve the average flow equation considering the effect of roughness on the lubrication effect, and the bearing capacity, shear force, and friction coefficient of the oil film were obtained, and thereby the dynamic tangential contact stiffness and damping of the oil film under tangential harmonic excitation were calculated. Then, according to the relationship between the normal deformation and the load of the solid contact microconvex body in the elastic/elastic–plastic/plastic deformation stage, integrating the tangential stick–slip theory, considering the effect of fluid lubrication on the solid contact friction coefficient, and tangential dynamic excitation, the tangential contact stiffness and damping of the microconvex body in three deformation stages were calculated. Furthermore, the dynamic tangential contact stiffness and damping of the solid–liquid interface were obtained by summing the solid surface contact part and the solid–liquid contact part in parallel according to the assumption of microconvex Gaussian distribution. Finally, through simulation analysis and experiments, the variation of the tangential dynamic contact stiffness and damping of the solid–liquid interface with normal load, tangential exciting frequency, and displacement amplitude was revealed and verified.

Optimizing the Clearance Fit of a Progressive Cavity Pump for the Thermal Recovery of Petroleum Using Fluid-Structure Thermal Coupling.

It is important to incorporate the effects of fluid–structure thermal coupling and the boundary conditions when calculating the thermal dynamics and response of progressive cavity pumps. This study develops a fluid–structure thermal coupling model of the progressive cavity pump to improve the accuracy of its measured field of deformation and the temperature field of the stator. A function for the macroscopic motion of a rigid body is written in a typical fluid domain, and the user-defined function (UDF) in FLUENT is used to load the boundary of the rotor to realize its planetary motion. Local remeshing is used to update the moving grid, and the viscoelastic hysteretic heat of the stator is treated as the internal source of heat. One-way decoupling is used based on tire slip theory, and heat flux on the surface of the stator is calculated by the ANSYS Parametric Design Language (APDL). The sequential fluid–structure thermal coupling of the progressive cavity pump is calculated by using the ANSYS workbench. A scheme for optimizing the fit clearance of the stator and rotor is given to improve the volumetric efficiency of the progressive cavity pump and prevent the stator from being stuck owing to a large deformation, and the calculations are verified by experiments on volumetric efficiency. The average deviation in the calculated volumetric efficiency was less than 5% compared with the experimental values. The proposed scheme provides a theoretical basis for the optimal design of the progressive cavity pump for the thermal production of petroleum.

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

The propagation of microseismicity in subsurface media is complex. We developed an anisotropic petrophysical model based on an empirical formula, linear slip theory and the bond transform method considering real underground conditions. Using Biot's equations, the seismic response to a general dislocation source in fracture-induced anisotropic two-phased media was solved using a staggered grid high-order finite-difference algorithm. To understand the relationship between the microseismic wave and fracture parameters, we then designed several different models to calculate the wavefield snapshots and analyse the effect of the fracture volume ratio and orientation. The modelling results indicate that the shear faulting source generates three types of waves in two-phase media. Fractures can render homogeneous media anisotropic, and anisotropy becomes more noticeable with an increase in the fracture volume ratio. This decreases the velocity of the fast longitudinal and transverse waves in the vertical direction and increases the velocity of the slow longitudinal wave in a certain range. The fracture orientation mainly influences the moment tensor and then affects the wavefronts. These simulations lay the foundation for further studies on microseismic wave propagation in fracture-induced anisotropic media.

Study on formation mechanism of serrated chip of Ti-6Al-4V titanium alloy based on shear slip theory

Titanium alloy is a typical hard-to-machine metal and a lot of serrated chips are often formed in the cutting process. The appearance of serrated chips will not only cause the fluctuation of cutting force, resulting in the decline of cutting accuracy, but also lead to the rapid wear of tools. In this study, the formation mechanism of serrated chip of Ti-6Al-4V titanium alloy was investigated by a two-dimensional cutting simulation model of Ti-6Al-4V titanium alloy, which was established by using the Johnson–Cook constitutive model and Johnson–Cook fracture model. It is found that shear slip occurs with the decrease of the shear band and the overall stress during the formation of serrated chips. The peak temperature is reached at the end of the shear band. Meanwhile, the “dead zone” of temperature and stress is formed near the edge of the tool, which has an obvious periodic alternating trend in the cutting process, resulting in the macro curl and micro serration of chips.Graphical abstractThe stress and temperature of the “dead zone” have an alternating trend with that of the shear band.

Double minimum creep processing and mechanism for γʹ strengthened cobalt-based superalloy

The double minimum creep, characterized by two creep rate minima, in Co-based superalloy is investigated using a phase-field model coupled with a crystal plasticity model. The constitutive modeling, based on the dislocation slip theory considering dislocation interaction, is applied to simulate microstructural evolution and deformation behavior. Rafting process commences at the beginning of creep until the global minimum of creep rate is reached, demonstrating a strengthening effect from N-type rafts under compressive creep. The high shear strain rate of (111)[01¯1] slip system in the intersections of horizontal and vertical γ channels leads to a slight increase of creep rate after the first local minimum. The evolution of stress field shows that the softening effect is the combined effect of the increase of resolved shear stress and the decrease of hardening stress in the intersections. Further, these changes in stress are primarily caused by the dislocation annihilation and the inhomogeneous plastic deformation. This study indicates that the intermediate local softening stage during creep may be eliminated if the initial inter-distance between γʹ precipitates is decreased.

Wavefield simulation of fractured porous media and propagation characteristics analysis

ABSTRACTMost fractured reservoirs are two‐phase media, that is, mixture of solid matrix and void. It contains rock skeleton and fractures or pores filled with oil, gas and water. These fractures are the channels of oil and gas storage and migration. In two‐phase media, the interaction between the fluid and solid phases will further complicate the seismic wave propagation. Natural fractures are typically irregular in shape, thereby causing difficulties in the exploration of fractured reservoirs. Therefore, the key to the prediction of fractures is to study the equation of motion of seismic waves and energy distribution of seismic waves at the fracture interface. To derive the propagation law for complex irregular shape fractures in two‐phase media, we combined the stiffness matrix of the media with linear slip theory and derived a numerical simulation scheme. The simulation scheme considers the fractures in the two‐phase media to be in any direction. In addition, seismic wave energy distribution at the fracture interface was obtained. The linear slip boundary condition was introduced into the conventional Zoeppritz equation, and a modified Zoeppritz equation was proposed for two‐phase fractured media. The reflection and transmission due to the fracture interface were considered in the new equation, thereby making the equation more flexible. Using the new numerical simulation scheme, we analysed the elastic waves produced by the linear slip fracture interface in two‐phase media and provided the long‐term stability results of the new scheme. Moreover, we provided the relationship between the reflection and transmission coefficients of the linear slip fracture interface and the incident angle and compliance in two‐phase media using the new Zoeppritz equation. The results show that the reflection wave of two‐phase fractured media can be divided into wave impedance and fracture parts to accurately describe the properties of underground rocks.

Electroosmosis of the Second Kind on Flat Charged Surfaces - a Direct Numerical Simulation Study

While the electroosmosis of the first kind (equilibrium) is accepted widely, the electroosmosis of the second kind (nonequilibrium) is still controversial. In this work, the theory of electroosmosis slip, of either the first kind or of the second kind at electrolyte membrane system is revisited via our direct numerical simulation. The obtained results show that above a certain voltage threshold, the basic conduction state becomes electroconvectively unstable. This instability provides a mechanism for explaining the over-limiting conductance in concentration polarization at a permselective membrane. The most important work in our study is to examine the famous electroosmosis of the second kind formula suggested by Rubinstein and Zaltzman in 1999. Although their formula has been presented for a long time, there has been no work to validate its accuracy experimentally or numerically due to the difficulty in pinpointing exactly the extended space charge layer in their formula. By using direct numerical simulation, we could solve this problem and inspect the application range of their formula. This also helps to strongly confirm the relationship between the electroosmosis of the second kind and the instability in concentration polarization at electrodialysis membranes.

Fatigue life assessment of nickel-based single crystals considering equivalent initial flaw size model and anisotropy

This paper presents a novel modeling framework for predicting fatigue life performance with varying film cooling holes (FCHs). Within this framework, in-situ crack propagation tests of nickel-based single-crystal plate specimens with two different drilling FCHs were carried out at room temperature. Based on the equivalent initial flaw size (EIFS) concept, a novel EIFS value proposed by modified Kitagawa-Takahashi diagram method for plastic correction of anisotropic Hill criterion, and the initial fatigue quality of these two types of FCHs was quantitatively evaluated and verified using surface integrity detection. Subsequently, the EIFS value with 95% confidence and 95% reliability (EIFS95/95) was obtained, which considered the data dispersion. The anisotropic equivalent stress-intensity factor ΔKeq calculated by the crystal slip theory is used to describe the mixed fracture mode under the action of KI, KII, and KIII. In addition, a novel fatigue-crack growth function with EIFS95/95 is proposed, which can effectively describe the actual crack growth behavior. Finally, combined with the EIFS and fatigue crack rate, considering the values of two stress intensity factor thresholds for testing different survival rates, a robust fatigue-life prediction results within the range of twice error bands were in significant agreement with the experimental results.

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

AbstractA computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.

Quasi-Analytical Solution of Optimum and Maximum Depth of Transverse V-Groove for Drag Reduction at Different Reynolds Numbers

Reducing the skin-friction drag of a vehicle is an important way to reduce carbon emissions. Previous studies have investigated the drag reduction mechanisms of transverse grooves. However, it is more practical to investigate which groove geometry is optimal at different inflow conditions for engineering. The purpose of this paper is to establish the physical model describing the relationship between the dimensionless depth (H+=Huτ/υ) of the transverse groove, the dimensionless inflow velocity (U∞+=U∞/uτ), and the drag reduction rate (η) to quasi-analytically solve the optimal and maximum transverse groove depth according to the Reynolds numbers. Firstly, we use the LES with the dynamic subgrid model to investigate the drag reduction characteristics of transverse V-grooves with different depths (h = 0.05~0.9 mm) at different Reynolds numbers (1.09×104~5.44×105) and find that H+ and U∞+ affect the magnitude of slip velocity (Us+), thus driving the variation of the viscous drag reduction rate (ην) and the increased rate of pressure drag (ηp). Moreover, the relationship between Us+, ην, and ηp is established based on the slip theory and the law of pressure distribution. Finally, the quasi-analytical solutions for the optimal and maximum depths are solved by adjusting Us+ to balance the cost (ηp) and benefit (ην). This solution is in good agreement with the present numerical simulations and previous experimental results.

Effect of Size on the Stability of Narrow Foundation Pits

The traditional design method for narrow foundation pits ignores size effects. Engineering practice shows that this is too conservative and causes large‐scale waste. In this study, with the help of ABAQUS finite element software, retaining‐structure models in semi‐infinite and infinite elastic space are used to simulate the mechanical performances of pile‐supported structures under different combinations of excavation depth, retaining pile‐embedded depth, and excavation width. Furthermore, based on antioverturning stability theory and circular slip theory, the intrinsic relationship among these variables and their effects on the stability of excavation is analysed. Finally, based on the restraint effect of retaining structures on the soil below the pit bottom under actual working conditions, critical width is determined and used to classify foundation pits. Moreover, the applicability of existing codes is discussed. These results can improve the design and construction of narrow excavations, benefitting the construction industry and society in general.

A Porous Media Leakage Model of Contact Mechanical Seals Considering Surface Wettability

The fluid leakage channel found in contact mechanical seals belongs to the microchannel category. Thus, upon further inspection, the influence of surface wettability and other factors neglected in previous studies becomes obvious. The porous leakage model of contact mechanical seals considering the surface wettability presented in this paper was based on the Cassie model and slip theory. The variations of the microchannel slip length and the velocity under various wettability conditions were studied and the relationship between the slip length and the apparent contact angle was established. Moreover, using porous media theory, the theoretical model of the leakage rate in contact mechanical seals considers the surface wettability depending on various parameters. The observed parameters included the surface contact angle, sealing medium pressure, viscosity coefficient, fractal dimension, and maximum pore diameter. The simulation results obtained using the proposed model have shown that the leakage rate increases with the increase of the apparent contact angle. Particularly when the contact pressure is small, the influence of the surface wettability is more significant. Furthermore, the leakage rate results obtained via the proposed model were compared to those of existing models. The comparison confirmed that the proposed model is applicable and that the necessity of considering wettability significantly affects the leakage rate calculation accuracy. The proposed model lays a foundation for further improving the calculation accuracy, making it easier for both the researchers and practitioners to suppress the leakage in contact mechanical seals.

Interfacial interaction induced synergistic lubricating performance of MoS2 and SiO2 composite nanofluid

SiO 2 was employed as an auxiliary lubricant for MoS 2 nanofluid to gain superior lubricating effect. Tribological properties and cold rolling lubrication performance of pure SiO 2 nanofluid, pure MoS 2 nanofluid and the MoS 2 +SiO 2 composite nanofluid were investigated to reveal the synergistic lubrication of MoS 2 nanosheets and SiO 2 nanoparticles. The results of tribological tests indicated that the composite nanofluid with κ (mass ratio of MoS 2 and SiO 2 ) ≥1 showed more excellent tribological properties than pure MoS 2 nanofluid depended on a low shear composite lubricating film formed on steel surface. The formation mechanism of the composite lubricating film was investigated through both experimental characterization and molecular dynamics simulation. During cold rolling process, SiO 2 nanoparticles which did not readily adsorb to steel surface firstly absorbed on the surface of MoS 2 . And then adsorb on the steel surface together with MoS 2 in virtue of the adsorption between MoS 2 and steel surface. A pressurized interlayer slip theory was creatively provided to explain the synergistic lubrication mechanism of the low shear composite lubricating film. The SiO 2 adsorbed on MoS 2 nanosheets changed the contact type between MoS 2 nanosheets from surface contact to point contact. Thus, the normal pressure on the surface of MoS 2 nanosheets was increased. According to the results of molecular dynamics simulation, the increase of normal pressure promoted the interlayer slip and reduced the friction coefficient between MoS 2 nanosheets. The relationship between lubrication mechanism and the mass ratio of MoS 2 and SiO 2 was also investigated to provide a systemic understanding of the synergistic lubrication performance. • SiO 2 could be used as an auxiliary lubricant for MoS 2 nanofluid. • The formation mechanism of the composite lubricating film was investigated. • A pressurized interlayer slip mechanism was creatively provided. • Sustainable lubrication mechanism of the composite nanofluid was studied.

Effect of Fluids on the Elastic Properties of 3D-Printed Anisotropic Rock Models

Laboratory physical models play an important role in understanding rock properties and wave propagation, both theoretically and at the field scale. In some cases, 3D-printing technology can be adopted to construct complex rock models faster, more inexpensively, and with more specific features than previous model-building techniques. In this study, we use 3D-printed rock models to assist in understanding the effects of various fluids (air, water, engine oil, crude oil, and glycerol) on the models’ elastic properties. We first used a 3D-printed, 1-in. cube-shaped layered model. This model was created with a 6% primary porosity and a bulk density of 0.98 g/cc with VTI anisotropy. We next employed a similar cube but with horizontal inclusions embedded in the layered background, which contributed to its total 24% porosity (including primary porosity). For air to liquid saturation, P-velocities increased for all liquids in both models, with the highest increase being with glycerol (57%) and an approximately 45% increase for other fluids in the inclusion model. For the inclusion model (dry and saturated), we observed a greater difference between two orthogonally polarized S-wave velocities (Vs1 and Vs2) than between two P-wave velocities (VP0 and VP90). We attribute this to the S2-wave (polarized normal to both the layering and the plane of horizontal inclusions), which appears more sensitive to horizontal inclusions than the P-wave. For the inclusion model, Thomsen’s P-wave anisotropic parameter (ɛ) decreased from 26% for the air case to 4% for the water-saturated cube and to 1% for glycerol saturation. The small difference between the bulk modulus of the frame and the pore fluid significantly reduces the velocity anisotropy of the medium, making it almost isotropic. We compared our experimental results with theory and found that predictions using Schoenberg’s linear slip theory combined with Gassmann’s anisotropic equation were closer to actual measurements than Hudson’s isotropic calculations. This work provides insights into the usefulness of 3D-printed models to understand elastic rock properties and wave propagation under various fluid saturations.

Separation of split S-waves in two nonorthogonal sets of vertical fractures

The phenomenon of S-wave splitting indicates the development of fractures in the shallow crust. Therefore, methods based on S-wave splitting have been established to predict the development of one set of parallel fractures. However, for rocks containing two nonorthogonal sets of vertical fractures, the mechanism of S-wave splitting is more complex, and the available methods cannot be applied. To resolve this inadequacy, we have developed a two-way rotation method to separate split S-waves with the aim of restoring the split S-wave polarizations and predicting the fracture azimuths. First, we calculate the stiffness matrix of fractured media based on the linear slip theory and derive the phase velocities and polarizations of split S-waves induced by fractures using the Christoffel equation. Second, we clarify the S-wave splitting mechanism in this media by using velocity analysis and deconstruct the S-wave polarizations on the horizontal components. Third, we deduce a two-way rotation matrix obtained by the S-wave splitting modes to separate the split S-waves. To solve for the angle parameters related to the fracture azimuths in the two-way rotation matrix, we superpose the subspace polarizations in two dimensions to determine the polarization azimuths of the split S-waves. Numerical model tests demonstrate that our method is stable under noisy conditions. Finally, we apply our method to real near offset and walkaround vertical seismic profiling data, and the predicted fracture results are verified by imaging logs and prior knowledge.

Calculation Model for Stick-Slip Deformation in Weak Horizontal Structural Surface Formation after Water Inflow.

In the process of reservoir exploration, the weak horizontal structural surface easily slips and cracks, and casing shearing often occurs during the formation process, which significantly affects the economic viability and effective development of an oilfield. Additionally, repeated damage at the same casing position indicates the possibility of numerous cracks in the weak structural surface. In this study, we propose the geomechanical stick–slip theory to verify the above phenomenon. The stress calculation method for the weak horizontal structural surface in the upper part of the reservoir is devised under the influence of inter-regional pore pressure differences. Based on the process of accumulation–release–reaccumulation–rerelease in the formation and deformation processes, we construct the calculation model of shear stress release and slips on the cracked surface. While considering the influence of water inflow on the cracked surface, the pressure exerted on the formation stick–slip is analyzed. Then, the model was verified by the data of block X in the Daqing oilfield. The results demonstrate that under wet conditions, the maximum static and dynamic frictional stresses on the cracked surface decrease significantly, and this makes the cracked surface more prone to a greater slip degree. After the weak horizontal structural surface cracks and slips occur for the first time, the pressure difference between regions required for formation of the next slip decreases significantly. With the continuous formation of slips, the slip range gradually expands with an increase in inter-regional pressure variance. The research work in this study provides a theoretical basis for the prevention and control of casing damage in oil development zones.

Full waveform inversion in fractured media based on velocity–stress wave equations in the time domain

SUMMARY In the process of seismic wave propagation, the presence of fractures will cause a seismic wave response associated with fracture compliance. Full waveform inversion (FWI) is an effective way to quantitatively obtain fracture compliance values, which can simulate seismic wave propagation in a fractured medium and compute the gradient expression of the fracture compliance parameters. To obtain the fracture compliance parameters quantitatively, a new technique based on FWI needs to be proposed. Based on linear slip theory, a new finite-difference scheme using a rotated grid has been developed to simulate the propagation of seismic waves in fractured media. The corresponding adjoint equation for FWI and the gradient of fracture parameter expression are presented. The crosstalk between normal compliance and tangential compliance is analysed in a homogeneous background medium. Numerical simulations in double-layer media show that the new gradient equation is effective.

Effect of Hydrophobic Silica Nanochannel Structure on the Running Speed of a Colloidal Damper

A colloidal damper (CD) can dissipate a significant amount of vibrations and impact energy owing to the interface power that is generated when it is used. It is of great practical significance to study the influence of the nanochannel structure of hydrophobic silica gel in the CD damping medium on the running speed of the CD. The fractal theory was applied to observe the characteristics of the micropore structure of the hydrophobic silica gel by scanning electron microscopy (SEM), the primary particles were selected to carry out fractal analysis, and the two-dimensional fractal dimension of the pore area and the tortuous fractal dimension of the hydrophobic silica gel pore structure were calculated. The fractal percolation model of water in hydrophobic silica nanochannels based on the slip theory could thus be obtained. This model revealed the relationship between the micropore structure parameters of the silica gel and the running speed of the CD. The CD running speed increases with the addition of grafted molecules and the reduction in pore size of the silica gel particles. Continuous loading velocity testing of the CD loaded with hydrophobic silica gels with different pore structures was conducted. By comparing the experimental results with the calculation results of the fractal percolation model, it was determined that the fractal percolation model can better characterize the change trend of the CD running velocity for the first loading, but the fractal dimension was changed from the second loading, caused by the small amount of water retained in the nanochannel, leading to the failure of fractal characterization.

Energy efficiency prediction model and energy characteristics of subsea disc pump based on velocity slip and similarity theory

The variable-speed energy efficiency prediction model (EEPM) of subsea disc pump is the key to achieve double gradient in deepwater drilling, and it has also been the difficulty of pressure control matching and energy conservation. In this paper, the radial slip vortices are fully considered, and average slip method of circumferential velocity, relative velocity and absolute velocity at impeller outlet is proposed. Based on hydraulic energy loss and mechanical energy loss, the calculation method of theoretical head and similar parabola in similarity theory is improved, and EEPM is established. In addition, a new multifunctional test system and data processing model are designed to reduce the error. The experimental results show that the accuracy of EEPM is increased by about 4% when deviating from the rated speed by more than 20%, and the accuracy is about 99% within 20%. From the simulation, the flow passage is mainly a mixed-type movement, such as S-type double vortex and O-type single vortex. The turbulence kinetic energy near the volute tongue is the largest. The study improves the energy efficiency of drilling pressure regulation, and also provides a new perspective to the energy efficiency optimization and energy conservation of similar centrifugal pump and vortex pump.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle that leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuthally dependent, introduce a Gaussian function to describe the fractures’ azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over the azimuth. We investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the [Formula: see text] plane than in the [Formula: see text] plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can degenerate into the VFTI medium.