...Hanjie Song; Yingjie Gao; Jinhai Zhang; Zhenxing Yao ABSTRACT The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation...

...Daniela Amazonas; Jessé C. Costa; Jörg Schleicher; Reynam Pestana Abstract Seismic migration by downward continuation using the one-way wave-equation approximations has two shortcomings: imaging steep-dip reflectors and handling evanescent waves. Complex Padé approximations allow a better treatment...

...Figure 3. (a) Response of the Padé approximant for an isolated pole modeling a thin vertical sheet of infinite depth extent at the magnetic pole (i.e., θ = π /2 in equation 7). (b) Forward model of an isolated pole. The remaining panels show the Padé approximants for (c) a thin sheet...

...Figure 5. Optimization of the one-term real Padé approximation. (a) Color-coded image evaluating θ m for all the possible values of a and b . The black dot indicates the point with the highest angle. (b) Approximation of the real part. ...

... such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power...

...Figure 1. The plots show three examples of the Padé approximation of the averaged polarization coefficient ⟨ P p ⟩ in the frequency range between 1 MHz and 1 GHz. (a and b) The real and imaginary parts of ⟨ P p ⟩ with α = β = 3.5 , respectively. (c...

... solutions are given by expansions in η and θ with coefficients extracted from solving linear first-order partial differential equations. Pade approximations are used to enhance the accuracy of the representation by predicting the behavior of the higher-order terms of the expansion. A simplification...

... can be determined by the Pade approximation. Our test computations show, however, that this approximation generally is of poor quality. Therefore, we suggest a new approach which is based on the rheological model of the generalized Maxwell body, which has a modulus of the desired rational form. We...

... paraxial approximation.Absorption properties are compared analytically and numerically. Our numerical results confirm that the L infinity or Chebychev-Pade approximations are best for wide-angle absorption and that the Chebychev or least-squares approximations are best for uniform absorption over a wide...

...Kun Xu; George A. McMechan ABSTRACT To improve the computational efficiency for the solution of the 3D Helmholtz equation in the frequency-space domain, high-order compact forms of finite differences are preferred. We applied a pointwise Padé approximation to develop a 3D 27-point fourth-order...

.... A possible solution to these problems is the complex Padé approximation, which avoids problems with evanescent waves by rotating the branch cut of the complex square root. We have applied this approximation to the acoustic wave equation for vertical transversely isotropic media to derive more stable FD...

... with four-way splitting is applied. Fourth-order Padé approximation is unsatisfactory in anelliptic media for large propagation angles with respect to the vertical direction. Therefore, a method of coefficient optimization is developed in conjunction with a method of choosing an adequate homogeneous...

... response. The filtering can be approximated in the wavenumber domain by, for example, power series, Chebyshev polynonomial fitting, Pade approximants, or continued fraction expansions. The filters must then be Fourier transformed back to the frequency–space domain, where the resulting filter is convolved...