A recursive method for the separation of upgoing and downgoing waves of vertical seismic profiling data

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2206-2218 ◽  
Author(s):  
F. Aminzadeh
Keyword(s):  
Time Domain ◽  
Fourier Transforms ◽  
A Priori ◽  
Computational Time ◽  
Linear Filter ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Starting Point ◽  
Vsp Data ◽  
The Time Domain

An important part of the processing of vertical seismic profiling (VSP) data is the separation of upgoing and downgoing waves. I introduce a new method for separation based on a time‐domain recursive linear filter. The separation method uses an approximation to an optimal, frequency‐domain, nonlinear filter solution as the starting point. The time‐domain recursive linear (approximate) filter converges to the optimal (exact) solution. Since the computation is in the time domain and since this filter is linear, some of the temporal aliasing and other problems resulting from the forward and inverse Fourier transforms are avoided. Specifically, instability for some frequencies (spectral singularities) is not experienced here. This method uses a priori information of the opposite stepouts of the upgoing and downgoing waves. Equal spacing between borehole measurement points is not required. Further, the computational time may be controlled according to the desired accuracy. An important feature of this method is that it locates the reflecting boundaries of the subsurface. Having located the homogeneous layers, it allows variable‐length windows of traces for separation, which eliminates the undesirable effects of smearing and extending wave fields beyond their origins. Also, knowledge of acoustic impedances for accurate implementation of the optimum filter is no longer required.

First-break vertical seismic profiling tomography for Vinton Salt Dome

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. U29-U36 ◽  
Author(s):  
Hua-wei Zhou
Keyword(s):  
A Priori ◽  
Salt Dome ◽  
Data Set ◽  
Velocity Anisotropy ◽  
Seismic Profiling ◽  
Velocity Models ◽  
Vertical Seismic Profiling ◽  
Vsp Data ◽  
Multiscale Inversion ◽  
Sonic Logs

Building laterally depth-varying velocity models for vertical seismic profiling (VSP) imaging is challenging because of the narrow ray-angle coverage of VSP data, especially if only first arrivals are used. This study explores the potential of a new deformable-layer tomography (DLT) for building velocity models with a VSP data set acquired over the Vinton salt dome in southwestern Louisiana. The DLT method uses first breaks to constrain the geometry of velocity interfaces from an initial model of flat, constant-velocity layers parameterized using a priori geologic and geophysical information. A progressive multiscale inversion loop gradually updates the interface geometry. The final solution model, containing 3D geometry, is well supported by resolution and reliability tests and closely matches the long-wavelength trends of area sonic logs. The presence of velocity anisotropy is also indicated.

High Dimensional Harmonic Balance Analysis for Dynamic Piecewise Aeroelastic Systems

2008 ◽  
Author(s):  
Liping Liu ◽  
Earl H. Dowell
Keyword(s):  
Frequency Domain ◽  
Limit Cycle ◽  
Time Domain ◽  
Harmonic Balance ◽  
Solution Method ◽  
Computational Time ◽  
High Dimensional ◽  
Aeroelastic System ◽  
Time Marching ◽  
The Time Domain

This paper describes the extension and application of a novel solution method for the periodic nonlinear oscillations of an aeroelastic system. This solution method is a very attractive alternative to time marching algorithms in that it is much faster and may track unstable as well as stable limit cycles. The method is employed to analyze the nonlinear aeroelastic response of a two dimensional airfoil including a control surface with freeplay placed in an incompressible flow. The mathematical model for this piecewise aeroelastic system is initially formulated as a set of first order ordinary differential equations. A frequency domain solution for the limit cycle oscillations is derived by a novel high dimensional harmonic balance (HDHB) method. By an inverse Fourier transformation, the system in the frequency domain is then converted into the time domain. Finally, the airfoil motions are obtained by solving the system in the time domain for only one period of limit cycle oscillation. This process can be easily implemented into computer programs without going through the complex algebraic manipulations for the nonlinearities typical of a more conventional harmonic balance solution method. The solutions found using this new HDHB method have been shown to be the same as those found using a more traditional time marching (e.g. Runge-Kutta) approach and also a conventional harmonic balance approach in the frequency domain with a considerable computational time saving.

Calculate Formation Velocity from Vertical Seismic Profiling Data

2014 ◽  
Vol 599-601 ◽  
pp. 639-642
Author(s):  
Jun Zhou ◽  
Chun Hui Xie ◽  
Peng Yang
Keyword(s):  
Random Errors ◽  
Seismic Profiling ◽  
Interval Velocity ◽  
Vertical Seismic Profiling ◽  
Long Offset ◽  
Vsp Data ◽  
Velocity Information

Extracting interval velocity is one of important applications of VSP data. Also, imaging of VSP data requires accurate velocity information. Two kinds of algorithms on the assumption of straight-ray and curve-ray are employed to calculate interval velocity respectively. Comparison of the extracted velocity from the two methods above with real velocity shows that both methods are suitable for VSP data recorded in the vicinity of well, while the algorithm derived from straight-ray fails in the long-offset. Moreover, the curve-ray is more reliable when there are some random errors due to the first arrivals picking.

scholarly journals Active Power Measurement Based on Multiwavelet Transforms

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiao-Bing Zhang ◽  
Yun-Hui Li ◽  
Xiao-Meng Cui
Keyword(s):  
Time Domain ◽  
Fourier Transforms ◽  
Active Power ◽  
New Method ◽  
Power Measurement ◽  
The Time Domain ◽  
Better Than

This paper discusses a new method for calculating active power in the multiwavelet domain. When the voltage and current waveforms are analyzed using multiwavelet, the active power can be calculated by simply adding the products of the multiwavelet coefficients without having to reconstruct the signals back to the time domain first and then using the traditional integration. From the simulation result, we can see that the results using multiwavelet are better than the ones using wavelet and Fourier Transforms no matter which prefilter is used.

scholarly journals A new iterative solver for the time-harmonic wave equation

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E57-E63 ◽  
Author(s):  
C. D. Riyanti ◽  
Y. A. Erlangga ◽  
R.-E. Plessix ◽  
W. A. Mulder ◽  
C. Vuik ◽  
...  
Keyword(s):  
Wave Equation ◽  
Linear System ◽  
Time Domain ◽  
Multigrid Method ◽  
Harmonic Wave ◽  
Computational Time ◽  
Full Time ◽  
Iterative Solver ◽  
Time Harmonic ◽  
The Time Domain

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In three dimensions, direct methods cannot be used for problems of practical sizes because the computational time and the amount of memory required become too large. Iterative methods are an alternative. These methods are often based on a conjugate gradient iterative scheme with a preconditioner that accelerates its convergence. The iterative solution of the time-harmonic wave equation has long been a notoriously difficult problem in numerical analysis. Recently, a new preconditioner based on a strongly damped wave equation has heralded a breakthrough. The solution of the linear system associated with the preconditioner is approximated by another iterative method, the multigrid method. The multigrid method fails for the original wave equation but performs well on the damped version. The performance of the new iterative solver is investigated on a number of 2D test problems. The results suggest that the number of required iterations increases linearly with frequency, even for a strongly heterogeneous model where earlier iterative schemes fail to converge. Complexity analysis shows that the new iterative solver is still slower than a time-domain solver to generate a full time series. We compare the time-domain numeric results obtained using the new iterative solver with those using the direct solver and conclude that they agree very well quantitatively. The new iterative solver can be applied straightforwardly to 3D problems.

scholarly journals Lay-up Optimization of Laminated Composites Using a Modified Branch and Bound Method

2018 ◽  
Vol 12 (1) ◽  
pp. 138-150 ◽  
Author(s):  
Giacomo Canale ◽  
Paul M. Weaver ◽  
Felice Rubino ◽  
Angelo Maligno ◽  
Roberto Citarella
Keyword(s):  
Branch And Bound ◽  
A Priori ◽  
Computational Effort ◽  
Branch And Bound Algorithm ◽  
Computational Time ◽  
Stacking Sequence ◽  
Branch And Bound Method ◽  
Starting Point ◽  
Global Optima ◽  
Laminate Thickness

Background:Composite materials are widely used in the aerospace, marine and automotive industries. One of their main advantages is that their stacking sequence can be tailored to maximise/minimise a specific structural performance. Efficient and non-computational-expensive algorithms are always needed to find the optimum stacking sequence of a composite laminate whose thickness is either to be minimised or may be kept constant (i.e.the thickness and the plies orientation percentages are pre-determined; the problem of the optimisation is therefore permutational).Objective:A modified branch and bound algorithm is proposed here and used to determine the stacking sequence for single and multi-objective optimisation problems. Laminate thickness and orientation percentages are either variables or determined a priori (the optimisation problem is therefore permutational). Computational time is drastically reduced when compared with other meta-heuristic techniques.Methods:The proposed method is a branch and bound algorithm, modified from the original work proposed by Kim and Hwang [10]. The main novelty is the starting point of the optimisation sequence: a laminate formed by “Ideal” layers, described in this paper.Results:The modified branch and bound has been first tested with a laminate having fixed thickness and a fixed percentage of layer orientation. Three different problems have been investigated: maximisation of natural frequencies, minimisation of tip deflection and maximisation of buckling critical load. The algorithm has been also tested, secondly, for a problem of weight minimisation subjected to buckling and strength constraints.Conclusion:The MBB has been shown to give good fidelity and significant computational advantages compared with a GA. Despite the simplicity of the structures in the numerical examples, it is anticipated that the MBB can be used to determine lay-ups in multi-part structures. The method was used to determine stacking sequences for several problems. The modified branch and bound method was shown to determine good laminate designs and offer significant efficiency savings.A “Good Design” is here defined as a solution producing “Near Global Optima” fitness values by minimising the computational effort. It was shown that for a single objective without ply competition, global optima were obtained.

The Development and Application of a Time-Domain Harmonic Balance Flow Solver

2012 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Unsteady Flows ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Time ◽  
Test Cases ◽  
Flow Solver ◽  
The Time Domain ◽  
Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

On: “Vertical seismic profiling: Separation of upgoing and downgoing acoustic waves in a stratified medium” by B. Seeman and L. Horowicz (GEOPHYSICS, 48, 555–568, May 1983)

Geophysics ◽  
1986 ◽  
Vol 51 (5) ◽  
pp. 1148-1149
Author(s):  
S. D. Stainsby ◽  
M. H. Worthington
Keyword(s):  
Acoustic Waves ◽  
Sampling Interval ◽  
Stratified Medium ◽  
Time Shift ◽  
Reference Level ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Cutoff Frequencies ◽  
The Earth ◽  
Vsp Data

Seeman and Horowicz devised an elegant procedure for the separation of upgoing and downgoing waves in VSP data. Their method is based upon a least‐squares solution of the frequency‐domain equations which relate the upgoing and downgoing signals at a reference level to the observed signals at other levels in the Earth. The coefficients of these equations are time‐shift operations. Unfortunately, for frequencies [Formula: see text] where δt is the vertical time sampling interval, the denominator of the solution equations is zero. For this reason the authors only applied the method over a passband: [Formula: see text] where the cutoff frequencies [Formula: see text] and [Formula: see text] are chosen to reflect the useful frequency band of the signal.

Sign in / Sign up

Export Citation Format

Share Document