Offset Approximation Research Articles

Seismic fluid identification method based on the joint PP‐ and SH–SH‐wave stochastic inversion

AbstractPre‐stack seismic inversion is an effective method for elastic parameter inversion using seismic data, which facilitates seismic fluid identification. However, pure PP‐wave inversion has issues of strong multi‐solution and limited prediction accuracy. Therefore, we propose a seismic fluid identification approach based on the joint PP‐ and SH–SH‐wave stochastic inversion. First, the linearized SH–SH‐wave amplitude variation with offset approximation parameterized by shear modulus and density is derived. Numerical simulations demonstrate that the SH–SH‐wave amplitude variation with offset approximation has a good accuracy. Reflection coefficient contribution analysis indicates that the new formulation has better parameter sensitivity to shear modulus and density than the PP wave amplitude variation with offset approximation derived by Russell, which helps one to improve the inversion of shear modulus and density. On this basis, we construct a joint inversion equation of PP and SH–SH waves for a Russell fluid indicator, a shear modulus and density and present a novel joint stochastic inversion method based on the ensemble smoother with multiple data assimilation. Stanford VI‐E model tests reveal that the Russell fluid indicator factor, shear modulus and density obtained from the joint PP‐ and SH–SH‐wave inversion have higher identification accuracy and smaller relative errors than those from pure PP‐wave inversion. Furthermore, field data tests indicate that this method has practical applicability in seismic fluid identification.

$ G^2/C^1 $ Hermite interpolation of offset curves of parametric regular curves

<abstract><p>In this paper we presented a method of $ G^2 $ Hermite interpolation of offset curves of regular plane curves based on approximating the normal vector fields. We showed that our approximant is also $ C^1 $ Hermite interpolation of the offset curve. Our method is capable of achieving circular precision. Another advantage of our method is that if the input curve is a polynomial curve, then our method also yields a polynomial curve. Our approximation method was applied to numerical examples and its numerical results were compared to previous offset approximation methods. It was observed that our method is almost optimal with respect to the number of control points of the approximation curves for the same tolerance.</p></abstract>

STTM-SFR: Spatial–Temporal Tensor Modeling With Saliency Filter Regularization for Infrared Small Target Detection

Detecting small Infrared (IR) targets against the low-altitude complex background is always a challenge for Infrared search and tracking (IRST) system due to limited small target characteristics, the moving background caused by camera motion, and extremely cluttered backgrounds. The existing methods usually cause high false alarm or do not work against the chaotic low-altitude complex background. In this paper, a novel spatial-temporal tensor model with saliency filter regularization (STTM-SFR) is developed to detect small IR targets. Firstly, the small target detection task is transformed into a sparse and low-rank tensor optimization problem by using the spatial-temporal prior knowledge of background and target. The construction of the holistic spatial-temporal tensor model (STTM) can retain the complete spatial-temporal information of the original IR image sequence. Then, the saliency filter regularization term limited between background and foreground aims to promote target saliency learning. That is to say, the saliency filter regularization term can avoid the offset approximation of the low-rank tensor, so as to recover a clean target image from the original IR tensor. Finally, an effective alternating direction method of multipliers (ADMM) algorithm framework is designed to solve the proposed STTM-SFR model. The effectiveness and robustness of STTM-SFR model are verified in six real IR scenes. Experimental results show that our method outperforms other baseline methods. Moreover, the proposed STTM-SFR method is more robust than the existing state-of-the-art STTMs against low-altitude moving backgrounds.

Offset Approximation of Rational Trigonometric Bezier ´ Curves

Offset curves are one of the crucial curves, but the presence of square root function in the representation is main hindrance towards their applications in CAD/CAM. The presented technique is based on offset approximation using rational trigonometric Bezier curves. The idea is ´ to construct a new control polygon parallel to original one. The two end points of the offset control polygon have been taken as exact offset end points, while the middle control points and weights have been computed using definition of parallel curves. As a result, offsets of rational and nonrational trigonometric Bezier curves have been approximated by rational ´ cubic trigonometric Bezier curve. An error between exact and approxi- ´ mated offset curves have also been computed to show the efficacy of the method.

Offset approximation of polygons on an ellipsoid

We present an approximation method for offset curves of polygons on an oblate ellipsoid using implicit algebraic surfaces. The polygon on the ellipsoid is given by a set of vertices, i.e. points on the ellipsoid. The edges are the shortest geodesic paths connecting two consecutive points. The offset curve of the polygon consists of two parts. The offset curve of an edge is the set of points that are at the same distance from each point on the edge, in the normal direction of the edge. The offset curve of a vertex is the set of points that are at the same geodesic distance from the vertex. Our offset approximation method uses plane section curves for offset curves of edges and prolate ellipsoids for offset curves of vertices. Since our offset approximation curve is constructed from implicit algebraic surfaces, it is easy to check whether a given point on the oblate ellipsoid has intruded into the inside of the offset curve. Moreover our method achieves extremely small approximation errors. We apply our method to numerical examples on the Earth.

Inversion for Geofluid Discrimination Based on Poroelasticity and AVO Inversion

Geofluid discrimination plays an important role in reservoir characterization and prospect identification. Compared with other fluid indicators, the effective pore-fluid bulk modulus is more sensitive to the property of fluid contained in reservoirs. We combine the empirical relations with deterministic models to form a new kind of linearized relationship between the mixed fluid/rock term and the fluid modulus. On the one hand, the linearized relationship can decouple the fluid bulk modulus from the mixed fluid/rock term; on the other hand, the decoupled terms are more stable especially in low-porosity situations compared with previous approaches. In terms of the new linearized equation of the fluid modulus, we derive a novel linearized amplitude variation with offset (AVO) approximation to avoid the complicated nonlinear relationship between the fluid modulus and the reflectivity series. Convoluting this linearized AVO approximation with seismic wavelets, the forward modeling is constructed to combine the prestack seismic records with the fluid modulus. Meanwhile, we introduce the Bayesian inference with multivariable Cauchy prior to the fluid modulus inversion for a stable and high-resolution solution. Model examples demonstrate the accuracy of the proposed linearized AVO approximation compared with the exact Zoeppritz equation and Aki-Richards approximate equation. The synthetic and field data tests illustrate the accuracy and feasibility of the proposed fluid modulus inversion approach for geofluid discrimination.

Matrix-fluid decoupling-based joint PP-PS-wave seismic inversion for fluid identification

Seismic fluid identification is the main goal of current prestack seismic inversion. Various kinds of fluid indicators are used for fluid detection in industry today. However, the existing methods cannot always provide reliable fluid prediction owing to the insensitivity to fluid response and the lack of converted wave constraints. The equivalent fluid bulk modulus is an effective fluid factor based on matrix-fluid decoupling, which can provide persuasive evidence for fluid detection. Combining poroelasticity theory and matrix-fluid decoupling theory, we have deduced a new PS-wave linear amplitude versus offset approximation equation that provides estimations of equivalent fluid bulk modulus, rigidity, porosity, and density. Then, the joint inversion of PP- and PS-waves based on matrix-fluid decoupling was executed in a Bayesian framework with constraints from rock physics and well-log data obtaining elastic parameter estimation of high precision directly. We tested the new method on a synthetic example and field multicomponent data, and the results indicated that the estimated fluid factor matched with well-data interpretation and geology information because of adding converted wave information and avoiding indirect inversion error. This demonstrated that the new method can enhance the quality of fluid detection and provide reliable geophysical evidence for reservoir characterization.

A digital dual-modulation control for single-phase UPS inverters

ABSTRACTA trip-point modulation strategy is proposed for single-phase uninterruptible power supply inverters with an LC filter, which operates simultaneously with pulse-width modulation, named dual-modulation (DM) control. Current estimation and offset current approximation are used conjointly to facilitate the proposed control law. It is shown analytically that the DM control leads to reduced total harmonic distortion (THD) and gains fast transient-state recovery. The simulation and experimental results demonstrate significant amelioration to THD and dynamic state compared to proportional–integral–derivative control under both linear and non-linear loads.

Bayesian linearized petrophysical AVO inversion

Seismic reservoir characterization aims to provide a 3D model of rock and fluid properties based on measured seismic data. Petrophysical properties, such as porosity, mineral volumes, and water saturation, are related to elastic properties, such as velocity and impedance, through a rock-physics model. Elastic attributes can be obtained from seismic data through seismic modeling. Estimation of the properties of interest is an inverse problem; however, if the forward model is nonlinear, computationally demanding inversion algorithms should be adopted. We have developed a linearized forward model, based on a convolutional model and a new amplitude variation with offset approximation that combined Gray’s linearization of the reflectivity coefficients with Gassmann’s equation and Nur’s critical porosity model. Physical relations between the saturated elastic moduli and the matrix elastic moduli, fluid bulk modulus, and porosity are almost linear, and the model linearization can be obtained by computing the first-order Taylor series approximation. The inversion method for the estimation of the reservoir properties of interest is then developed in the Bayesian framework. If we assume that the distributions of the prior model and error term are Gaussian, then the explicit analytical solution of the posterior distribution of rock and fluid properties can be analytically derived. Our method has first been validated on synthetic seismic data and then applied to a 2D seismic section extracted from a real data set acquired in the Norwegian Sea.

Theoretical performance of mid wavelength HgCdTe(1 0 0) heterostructure infrared detectors

The paper presents a theoretical study of the p+BpnN+ design based on HgCdTe(100) layers, which significantly improves the performance of detectors optimized for the mid-wave infrared spectral range. p+BpnN+ design combines the concept of a high impedance photoconductor with double layer hetero-junction device. Zero valence band offset approximation throughout the p+Bpn heterostructure allows flow of only minority holes generated in the absorber, what in a combination with n-N+ exclusion junction provides the Auger suppression. Modeling shows that by applying a low doping active layer, it is possible to achieve an order of magnitude lower dark current densities than those determined by “Rule 07”. A key to its success is a reduction of Shockley-Read-Hall centers associated with native defects, residual impurities and misfit dislocations. Reduction of metal site vacancies below 1012cm−3 and dislocation density to 105cm−2 allow to achieve a background limited performance at 250K. If the background radiation can be reduced, operation with a three- or four-stage thermo-electric-cooler may be possible.

A Novel Method of Offset Approximation along the Normal Direction with High Precision

A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of normal, and thus could reflect the approximate performance more properly. The approximation is completely independent of the original curve parameterization, and thus could ensure the stability of the approximation result. Experimental results show that the proposed algorithm is reasonable and effective.

A new method approximating offset curve by Bézier curve using parallel derivative curves

In this paper, we present a new method for the offset approximation of an n-th degree Bezier curve by an \(n+1\)-th degree Bezier curve using parallel derivative curves. Our method is based on the Gauss map approximation of the n-th degree Bezier curve by the \(n+1\)-th degree Bezier curve whose derivative curve is parallel to that of the n-th degree Bezier curve. Thus, the convolution of the Gauss map approximation curve and n-th Bezier curve is a polynomial of degree \(n+1\), which is our offset approximation of the n-th degree Bezier curve. Our approximation method has two advantages. One is that the offset approximation method yields a non-rational (polynomial) curve which is obtained by the simple sum of two Bezier curves. The other is that the offset approximation curve satisfying the endpoint interpolation of the given offset curve automatically has the same tangent lines as the offset curve at both endpoints. We illustrate our offset approximation method with some numerical examples.

Offset Approximation of Hybrid Hyperbolic Polynomial Curves

In this paper, two methods for approximation of offset curves of H-Bezier curves and H-B spline curves are presented, which are based on the approximation of shifting control points and norm of parametric speed. Firstly, after calculating the perturbed vectors, the offset curve can be obtained by shifting the control points of the base curve. Then, both the Chebyshev approximation and optimal trigonometric polynomials approximation of parametric speed of base curve are presented, and two approximation functions of offset curves are also obtained. Finally, some examples are used to demonstrate their practicality.

Comparison of Offset Approximation Methods of Conics with Explicit Error Bounds

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

An algorithm for [formula omitted] offset approximation based on circle approximation by [formula omitted] quadratic spline

We present a method for G2 approximation of offset curves using G2 quadratic spline approximation of circular arc. An algorithm for the approximation method is presented and is applied to some numerical examples.

Bayesian inversion for effective pore-fluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation

Fluid indicators estimated from seismic data play important roles in reservoir characterization and prospect identification. Traditionally, there are a variety of fluid indicators proposed, but they are very likely to provide ambiguous results for fluid identification due to the fact that their sensitivity is dependent upon the mixed effect of pore fluid and rock porosity. To raise the sensitivity of fluid indication, we used the effective pore-fluid bulk modulus as a fluid indicator. Starting with the poroelastic amplitude variation with offset (AVO) theory and the corresponding rock-physics model with the homogeneous sorting trend, we derived a new AVO approximation that allowed us to estimate the effective pore-fluid bulk modulus in a direct fashion. The inversion for the fluid indicator is formulated in Bayesian framework with the Cauchy distribution as a prior constraint. We tested the method on synthetic data and analyzed the feasibility and stability of the inversion. A field data example shows that the effective pore-fluid bulk modulus can reduce the ambiguity caused by the rock porosity and improve the quality of fluid discrimination in a clastic reservoir. Further research needs to be done on the reservoirs that do not fit the rock-physics model without a sorting trend.

Circle approximation using LN Bézier curves of even degree and its application

We present an approximation method of circular arcs using linear-normal (LN) Bézier curves of even degree, four and higher. Our method achieves Gm continuity for endpoint interpolation of a circular arc by a LN Bézier curve of degree 2m, for m=2,3. We also present the exact Hausdorff distance between the circular arc and the approximating LN Bézier curve. We show that the LN curve has an approximation order of 2m+2, for m=2,3. Our approximation method can be applied to offset approximation, so obtaining a rational Bézier curve as an offset approximant. We derive an algorithm for offset approximation based on the LN circle approximation and illustrate our method with some numerical examples.

Azimuthal reflectivity inversion

Seismic fracture prediction is becoming a more important exploration and development problem with the growing focus on unconventional reservoirs. A non-linear inversion technique is presented to estimate layer-based fracture parameters and velocities based on azimuthal reflectivity data. The earth model assumes a single set of vertical fractures per layer parameterized in terms of linear slip parameters - the normal and tangential fracture weaknesses - and fracture strike. In addition, the background P-wave and S-wave impedances are estimated. Either the exact Zoeppritz equation or some linearization thereof is used in a convolutional modelling scheme to estimate seismic amplitude data. The inverse problem is solved in a nonlinear fashion using simulated annealing. The new technique has several advantages over performing azimuthal amplitude versus angle analysis (AVAz). The reflectivity calculation used in the new technique is more theoretically correct, allowing for the symmetry plane to change as a function of layer. The 90 degree ambiguity in estimating the symmetry plane typical of the near offset approximation also disappears. Further, there is an improvement in the isotropic parameter estimates compared to isotropic inversion since the bias introduced by neglecting anisotropy has been removed by incorporating it into the forward model. The azimuthal inversion is demonstrated on both synthetic and real seismic data.

Approximation of planar offset curves with globally bounded error for B-spline NC tool paths

The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and the approximation error is guaranteed within a given tolerance over the entire curve. However, the existing methods utilising global error control approximate the offsets of 2D free-form curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by segmenting the curve at appropriate knot values. The proposed new approach is more efficient, and the resulting offset approximations are more accurate, with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, which have the potential for other applications in industry.

A Direct Approach for Loop Subdivision Surface Offset Approximation

A novel and direct approach for Loop subdivision surface offset approximation is proposed. Instead of solving a linear equation system previously, the main idea is to convert the Loop subdivision surface offset approximation into updating the vertices of original triangular mesh iteratively by using progressive interpolation (PI) method. Generated smooth subdivision surfaces interpolate the original mesh control points and preserve the sharp features. Then triangular mesh offset method can be utilized to obtain Loop subdivision surface offset approximation. The proposed method has the advantages of both local and global methods. The meshes considered here can be either closed or open. Some typical examples are illustrated to demonstrate the efficiency of the proposed approach in the end.