scholarly journals Traveltime inversion for 2‐D anomaly structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1481-1487 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Optimization Problem ◽  
Inversion Method ◽  
Unknown Parameters ◽  
New Approach ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Highly Nonlinear ◽  
Small Set ◽  
A Cell ◽  
Parametric Functions

This work presents a traveltime inversion method that uses parametric functions to represent 2‐D anomaly structures. These functions are described by a small set of unknown parameters which in turn are obtained after solving a highly nonlinear optimization problem via simulated annealing (SA). The procedure favors neither smooth nor high contrasting anomalies and keeps the number of unknowns very small so as to make the problem tractable using SA. Yet the strategy allows one to accommodate a large class of velocity models. Results indicate that this new approach typically yields better images than a standard linearized inversion based on a cell parameterization scheme.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

2021 ◽  
Vol 225 (2) ◽  
pp. 1020-1031
Author(s):  
Huachen Yang ◽  
Jianzhong Zhang ◽  
Kai Ren ◽  
Changbo Wang
Keyword(s):  
Turning Points ◽  
Analytical Formula ◽  
Velocity Model ◽  
Western China ◽  
Inversion Method ◽  
Mountain Area ◽  
Traveltime Inversion ◽  
Static Correction ◽  
Velocity Models ◽  
First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

scholarly journals Simultaneous simulation and optimization of multiple dividing wall columns

2021 ◽  
Author(s):  
Tobias Seidel ◽  
Lena-Marie Ränger ◽  
Thomas Grützner ◽  
Michael Bortz
Keyword(s):  
Optimization Problem ◽  
Calculation Procedure ◽  
Process Variables ◽  
Fast Calculation ◽  
New Approach ◽  
Simulation And Optimization ◽  
Highly Nonlinear ◽  
Commercial Process ◽  
Model Equations ◽  
Process Simulator

In this work we present a new approach that we use to simulate and optimize multiple dividing wall columns at the same time. Instead of considering all model equations as constraints and all process variables as optimization variables in a large and highly nonlinear optimization problem we only incorporate a subset of the model equations as constraints and a subset of the process variables as optimization variables. The remaining process variables are calculated from this subset by a robust and fast calculation procedure. This calculation procedure also ensures that the remaining model equations are satisfied. A comparison with the commercial process simulator Aspen Plus shows that with the new approach multiple dividing wall columns can be optimized more stable and better solutions are found. Moreover the time needed to find an optimal design decreases significantly.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

Modeling of Shape Memory Alloy Actuators Using Matlab and dSpace Platform

2010 ◽  
Vol 166-167 ◽  
pp. 149-154
Author(s):  
Ioan Adrian Cosma ◽  
Vistrian Măties ◽  
Ciprian Lapusan ◽  
Rares Ciprian Mîndru
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Dynamic Model ◽  
Dynamic Equations ◽  
Control Technique ◽  
Positioning System ◽  
Unknown Parameters ◽  
New Approach ◽  
Model Based Control ◽  
Input And Output

The aim of the paper is to describe an approach for modeling the dynamic behavior of a positioning system actuated by two shape memory alloy springs, placed in opposition. The mathematical analysis of the system in order to develop the dynamic model is difficult in this case because of the unknown parameters within the dynamic equations (thermodynamics, change in austenite fraction) and therefore a new approach is presented. Thus, a positioning system is considered, and its behavior is determined using Matlab Software, D-space platform and an optical sensor, which analyses the position/velocity of the moving cart. The dynamic model of the system is determined in order to develop a further model based control technique. The model is generated using system identification toolbox within Matlab and input and output (response) of the considered system.

Velocity models for routine earthquake monitoring at volcanoes: from deterministic to Bayesian

2021 ◽  
Author(s):  
Jeremy Pesicek ◽  
Trond Ryberg ◽  
Roger Machacca ◽  
Jaime Raigosa
Keyword(s):  
Velocity Structure ◽  
Full Range ◽  
Earthquake Location ◽  
Monitoring Networks ◽  
Unknown Parameters ◽  
Widespread Application ◽  
Starting Values ◽  
Velocity Models ◽  
Earthquake Locations ◽  
Station Corrections

<p>Earthquake location is a primary function of volcano observatories worldwide and the resulting catalogs of seismicity are integral to interpretations and forecasts of volcanic activity.  Ensuring earthquake location accuracy is therefore of critical importance.  However, accurate earthquake locations require accurate velocity models, which are not always available.  In addition, difficulties involved in applying traditional velocity modeling methods often mean that earthquake locations are computed at volcanoes using velocity models not specific to the local volcano.   </p><p>Traditional linearized methods that jointly invert for earthquake locations, velocity structure, and station corrections depend critically on having reasonable starting values for the unknown parameters, which are then iteratively updated to minimize the data misfit.  However, these deterministic methods are susceptible to local minima and divergence, issues exacerbated by sparse seismic networks and/or poor data quality common at volcanoes.  In cases where independent prior constraints on local velocity structure are not available, these methods may result in systematic errors in velocity models and hypocenters, especially if the full range of possible starting values is not explored.  Furthermore, such solutions depend on subjective choices for model regularization and parameterization.</p><p>In contrast, Bayesian methods promise to avoid all these pitfalls.  Although these methods traditionally have been difficult to implement due to additional computational burdens, the increasing use and availability of High-Performance Computing resources mean widespread application of these methods is no longer prohibitively expensive.  In this presentation, we apply a Bayesian, hierarchical, trans-dimensional Markov chain Monte Carlo method to jointly solve for hypocentral parameters, 1D velocity structure, and station corrections using data from monitoring networks of varying quality at several volcanoes in the U.S. and South America.  We compare the results with those from a more traditional deterministic approach and show that the resulting velocity models produce more accurate earthquake locations.  Finally, we chart a path forward for more widespread adoption of the Bayesian approach, which may improve catalogs of volcanic seismicity at observatories worldwide. </p>

Spectral Efficiency Self-Optimization through Dynamic User Clustering and Beam Steering

2016 ◽  
pp. 137-155
Author(s):  
Md Salik Parwez ◽  
Hasan Farooq ◽  
Ali Imran ◽  
Hazem Refai
Keyword(s):  
Spectral Efficiency ◽  
Large Scale ◽  
Optimization Problem ◽  
Focal Point ◽  
Beam Steering ◽  
Clustering Algorithms ◽  
Performance Comparison ◽  
Base Stations ◽  
User Clustering ◽  
A Cell

This paper presents a novel scheme for spectral efficiency (SE) optimization through clustering of users. By clustering users with respect to their geographical concentration we propose a solution for dynamic steering of antenna beam, i.e., antenna azimuth and tilt optimization with respect to the most focal point in a cell that would maximize overall SE in the system. The proposed framework thus introduces the notion of elastic cells that can be potential component of 5G networks. The proposed scheme decomposes large-scale system-wide optimization problem into small-scale local sub-problems and thus provides a low complexity solution for dynamic system wide optimization. Every sub-problem involves clustering of users to determine focal point of the cell for given user distribution in time and space, and determining new values of azimuth and tilt that would optimize the overall system SE performance. To this end, we propose three user clustering algorithms to transform a given user distribution into the focal points that can be used in optimization; the first is based on received signal to interference ratio (SIR) at the user; the second is based on received signal level (RSL) at the user; the third and final one is based on relative distances of users from the base stations. We also formulate and solve an optimization problem to determine optimal radii of clusters. The performances of proposed algorithms are evaluated through system level simulations. Performance comparison against benchmark where no elastic cell deployed, shows that a gain in spectral efficiency of up to 25% is possible depending upon user distribution in a cell.

scholarly journals Control Force Recalculation for Balancing Problems

2019 ◽  
Vol 19 (05) ◽  
pp. 1941010
Author(s):  
Bálint Bodor ◽  
László Bencsik ◽  
Tamás Insperger
Keyword(s):  
Optimization Problem ◽  
Control Mechanism ◽  
Numerical Differentiation ◽  
Open Loop ◽  
Second Step ◽  
Control Force ◽  
New Approach ◽  
Numerical Errors ◽  
Linearized System ◽  
Control Forces

Understanding the mechanism of human balancing is a scientifically challenging task. In order to describe the nature of the underlying control mechanism, the control force has to be determined experimentally. A main feature of balancing tasks is that the open-loop system is unstable. Therefore, reconstruction of the trajectories using the measured control force is difficult, since measurement inaccuracies, noise and numerical errors increase exponentially with time. In order to overcome this problem, a new approach is proposed in this paper. In the presented technique, first the solution of the linearized system is used. As a second step, an optimization problem is solved which is based on a variational principle. A main advantage of the method is that there is no need for the numerical differentiation of the measured data for the calculation of the control forces, which is the main source of the numerical errors. The method is demonstrated in case of a human stick balancing.

scholarly journals An efficient wavefield inversion for transversely isotropic media with a vertical axis of symmetry

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R195-R206 ◽  
Author(s):  
Chao Song ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Optimization Problem ◽  
Source Function ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Trade Off ◽  
Transversely Isotropic Media ◽  
Highly Nonlinear ◽  
Isotropic Media ◽  
Axis Of Symmetry

Conventional full-waveform inversion (FWI) aims at retrieving a high-resolution velocity model directly from the wavefields measured at the sensor locations resulting in a highly nonlinear optimization problem. Due to the high nonlinearity of FWI (manifested in one form in the cycle-skipping problem), it is easy to fall into local minima. Considering that the earth is truly anisotropic, a multiparameter inversion imposes additional challenges in exacerbating the null-space problem and the parameter trade-off issue. We have formulated an optimization problem to reconstruct the wavefield in an efficient matter with background models by using an enhanced source function (which includes secondary sources) in combination with fitting the data. In this two-term optimization problem to fit the wavefield to the data and to the background wave equation, the inversion for the wavefield is linear. Because we keep the modeling operator stationary within each frequency, we only need one matrix inversion per frequency. The inversion for the anisotropic parameters is handled in a separate optimization using the wavefield and the enhanced source function. Because the velocity is the dominant parameter controlling the wave propagation, it is updated first. Thus, this reduces undesired updates for anisotropic parameters due to the velocity update leakage. We find the effectiveness of this approach in reducing parameter trade-off with a distinct Gaussian anomaly model. We find that in using the parameterization [Formula: see text], and [Formula: see text] to describe the transversely isotropic media with a vertical axis of symmetry model in the inversion, we end up with high resolution and minimal trade-off compared to conventional parameterizations for the anisotropic Marmousi model. Application on 2D real data also indicates the validity of our method.

scholarly journals A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 60
Author(s):  
Stanislaus Maier-Paape ◽  
Andreas Platen ◽  
Qiji Jim Zhu
Keyword(s):  
General Framework ◽  
Optimization Problem ◽  
Risk Measure ◽  
Efficient Frontier ◽  
Portfolio Theory ◽  
Trading Strategies ◽  
Performance Criteria ◽  
Market Model ◽  
Constant Weight ◽  
New Approach

This is Part III of a series of papers which focus on a general framework for portfolio theory. Here, we extend a general framework for portfolio theory in a one-period financial market as introduced in Part I [Maier-Paape and Zhu, Risks 2018, 6(2), 53] to multi-period markets. This extension is reasonable for applications. More importantly, we take a new approach, the “modular portfolio theory”, which is built from the interaction among four related modules: (a) multi period market model; (b) trading strategies; (c) risk and utility functions (performance criteria); and (d) the optimization problem (efficient frontier and efficient portfolio). An important concept that allows dealing with the more general framework discussed here is a trading strategy generating function. This concept limits the discussion to a special class of manageable trading strategies, which is still wide enough to cover many frequently used trading strategies, for instance “constant weight” (fixed fraction). As application, we discuss the utility function of compounded return and the risk measure of relative log drawdowns.

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