Extracting the Response of the Bay Bridge, California, from the Application of Multichannel Deconvolution to Earthquake-Induced Shaking

2020 ◽  
Vol 110 (2) ◽  
pp. 556-564 ◽  
Author(s):  
Jing Jian ◽  
Roel Snieder ◽  
Nori Nakata
Keyword(s):  
Structural Response ◽  
Transverse Motion ◽  
Response Functions ◽  
Structural Units ◽  
Deconvolution Problem ◽  
Engineered Structures ◽  
Ill Posed ◽  
Multichannel Deconvolution ◽  
The Waves ◽  
Western Half

ABSTRACT Engineered structures, such as bridges, are excited by earthquakes at the base of the towers and the endpoint of decks. The different structural units of bridges, such as the towers and decks, are coupled. We extract the response of the towers and decks of the Bay Bridge in California from the motion of the bridge that is caused by earthquakes. This constitutes a multichannel deconvolution problem, which is, in general, ill-posed. We use the redundancy of the western half of the Bay Bridge, with near-identical towers and decks, to estimate the response of the upper towers, lower towers, and decks, from the transverse motion recorded in the bridge after four earthquakes. The extracted response functions for the four earthquakes show consistent wave arrivals that correspond to the waves that propagate through the towers and the decks. This method can, in principle, be used to monitor changes in the structural response.

Polarization and coherence of 5 to 30 Hz seismic wave fields at a hard-rock site and their relevance to velocity heterogeneities in the crust

1990 ◽  
Vol 80 (2) ◽  
pp. 430-449 ◽  
Author(s):  
William Menke ◽  
Arthur L. Lerner-Lam ◽  
Bruce Dubendorff ◽  
Javier Pacheco
Keyword(s):  
Hard Rock ◽  
Scale Effects ◽  
Spatial Coherence ◽  
Compressional Wave ◽  
P Wave ◽  
Transverse Motion ◽  
S Wave ◽  
Chemical Explosions ◽  
Aperture Arrays ◽  
The Waves

Abstract Except for its very onset, the P wave of earthquakes and chemical explosions observed at two narrow-aperture arrays on hard-rock sites in the Adirondack Mountains have a nearly random polarization. The amount of energy on the vertical, radial, and transverse components is about equal over the frequency range 5 to 30 Hz, for the entire seismogram. The spatial coherence of the seismograms is approximately exp(−cfΔx), where c is in the range 0.4 to 0.7 km−1Hz−1, f is frequency and Δx is the distance between array elements. Vertical, radial, and transverse components were quite coherent over the aperture of the array, indicating that the transverse motion of the compressional wave is a property of relatively large (106 m3) volumes of rock, and not just an anomaly caused by a malfunctioning instrument, poor instrument-rock coupling, or out-crop-scale effects. The spatial coherence is approximately independent of component, epicentral azimuth and range, and whether P- or S-wave coda is being considered, at least for propagation distances between 5 and 170 km. These results imply a strongly and three-dimensionally heterogeneous crust, with near-receiver scattering in the uppermost crust controlling the coherence properties of the waves.

scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

Deconvolution of X-ray diffraction profiles by using series expansion

2000 ◽  
Vol 33 (2) ◽  
pp. 259-266 ◽  
Author(s):  
F. Sánchez-Bajo ◽  
F. L. Cumbrera
Keyword(s):  
Series Expansion ◽  
Random Noise ◽  
Hermite Polynomials ◽  
Linear Integral Equation ◽  
X Ray Diffraction ◽  
Basic Step ◽  
X Ray ◽  
Deconvolution Problem ◽  
Ill Posed ◽  
Linear Integral

The deconvolution of X-ray diffraction profiles is a basic step in order to obtain reliable results on the microstructure of crystalline powder (crystallite size, lattice microstrain,etc.). A procedure for unfolding the linear integral equationh=g finvolved in the kinematical theory of X-ray diffraction is proposed. This technique is based on the series expansion of the `pure' profile,f. The method has been tested with a simulated instrument-broadened profile overlaid with random noise by using Hermite polynomials and Fourier series, and applied to the deconvolution of the (111) peak of a sample of 9-YSZ. In both cases, the effects of the `ill-posed' nature of this deconvolution problem were minimized, especially when using the zero-order regularization combined with the series expansion.

Identification of the Dynamic Properties of Mechanical Joints

2013 ◽  
Vol 468 ◽  
pp. 114-118
Author(s):  
Tie Neng Guo ◽  
Ting Yu Wu ◽  
Xiao Lei Song
Keyword(s):  
Dynamic Properties ◽  
Measured Data ◽  
Reduction Technique ◽  
Response Functions ◽  
Theoretical Derivation ◽  
Mechanical Joints ◽  
Frequency Selection ◽  
Ill Posed ◽  
Noise Frequency ◽  
High Degree

The frequency response functions (FRFs) are frequently used to identify dynamic properties of the mechanical joints. However, the ill-posed problems of the system are caused by the contamination of measurement noise even if it is processed by reduction technique. In order to solve this problem, put the noised FRFs into identification equations to theoretical derivation, explained the degree of influence on the identified results by noised FRFs in theory. In order to make the identified results represent real properties of the joints, an improved FRFs method was developed based on subtraction term frequency selection, in which the measured data were processed could get high degree of anti-noise frequency before parameters identification. This method avoids the occurrence of ill-posed problems. The results of simulation show that the proposed method can solve the ill-posed problems, thus significantly improve the accuracy of identification.

Peri-Ultrasound Modeling of Dynamic Response of an Interface Crack Showing Wave Scattering and Crack Propagation

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
Mohammad Hadi Hafezi ◽  
Tribikram Kundu
Keyword(s):  
Crack Propagation ◽  
Interface Crack ◽  
Pure Shear ◽  
Structural Response ◽  
Shear Loading ◽  
Modeling Tools ◽  
Modeling Tool ◽  
Numerical Predictions ◽  
The Waves ◽  
Cracked Structure

A cracked structure made of two different elastic materials having a Griffith crack at the interface is analyzed when it is subjected to pure shear loading and ultrasonic loading. The waves generated by the applied load and the crack propagation resulted from the shear loading are investigated. Peri-ultrasound modeling tool is used for this analysis. A comparison between experimental results and numerical predictions shows a very good matching between the two. Furthermore, the increase in nonlinear ultrasonic response in presence of the interface crack could also be modeled by this technique. The computed results show that when the interface crack propagates, then it breaks the interface at one end of the crack and breaks the material with lower elastic modulus at the other end. The unique feature of this peridynamics-based modeling tool is that it gives a complete picture of the structural response when it is loaded—it shows how elastic waves propagate in the structure and are scattered by the crack, how the crack surfaces open up, and then how crack starts to propagate. Different modeling tools are not needed to model these various phenomena.

scholarly journals Identification of linear response functions from arbitrary perturbation experiments in the presence of noise – Part I. Method development and toy model demonstration

2021 ◽  
Author(s):  
Guilherme L. Torres Mendonça ◽  
Julia Pongratz ◽  
Christian H. Reick
Keyword(s):  
Response Function ◽  
Noise Level ◽  
Linear Response ◽  
Method Development ◽  
Control Experiment ◽  
Regularization Parameter ◽  
Response Functions ◽  
Perturbation Experiment ◽  
Ill Posed ◽  
Proper Estimation

Abstract. Existent methods to identify linear response functions from data require tailored perturbation experiments, e.g. impulse or step experiments. And if the system is noisy, these experiments need to be repeated several times to obtain a good statistics. In contrast, for the method developed here, data from only a single perturbation experiment at arbitrary perturbation is sufficient if in addition data from an unperturbed (control) experiment is available. To identify the linear response function for this ill-posed problem we invoke regularization theory. The main novelty of our method lies in the determination of the level of background noise needed for a proper estimation of the regularization parameter: This is achieved by comparing the frequency spectrum of the perturbation experiment with that of the additional control experiment. The resulting noise level estimate can be further improved for linear response functions known to be monotonic. The robustness of our method and its advantages are investigated by means of a toy model. We discuss in detail the dependence of the identified response function on the quality of the data (signal-to-noise ratio) and on possible nonlinear contributions to the response. The method development presented here prepares in particular for the identification of carbon-cycle response functions in Part II of this study. But the core of our method, namely our new approach to obtain the noise level for a proper estimation of the regularization parameter, may find applications in solving also other types of linear ill-posed problems.

scholarly journals Identification of linear response functions from arbitrary perturbation experiments in the presence of noise – Part 1: Method development and toy model demonstration

2021 ◽  
Vol 28 (4) ◽  
pp. 501-532
Author(s):  
Guilherme L. Torres Mendonça ◽  
Julia Pongratz ◽  
Christian H. Reick
Keyword(s):  
Response Function ◽  
Noise Level ◽  
Linear Response ◽  
Method Development ◽  
Control Experiment ◽  
Regularization Parameter ◽  
Response Functions ◽  
Perturbation Experiment ◽  
Ill Posed ◽  
Proper Estimation

Abstract. Existent methods to identify linear response functions from data require tailored perturbation experiments, e.g., impulse or step experiments, and if the system is noisy, these experiments need to be repeated several times to obtain good statistics. In contrast, for the method developed here, data from only a single perturbation experiment at arbitrary perturbation are sufficient if in addition data from an unperturbed (control) experiment are available. To identify the linear response function for this ill-posed problem, we invoke regularization theory. The main novelty of our method lies in the determination of the level of background noise needed for a proper estimation of the regularization parameter: this is achieved by comparing the frequency spectrum of the perturbation experiment with that of the additional control experiment. The resulting noise-level estimate can be further improved for linear response functions known to be monotonic. The robustness of our method and its advantages are investigated by means of a toy model. We discuss in detail the dependence of the identified response function on the quality of the data (signal-to-noise ratio) and on possible nonlinear contributions to the response. The method development presented here prepares in particular for the identification of carbon cycle response functions in Part 2 of this study (Torres Mendonça et al., 2021a). However, the core of our method, namely our new approach to obtaining the noise level for a proper estimation of the regularization parameter, may find applications in also solving other types of linear ill-posed problems.

The use of the conjugate‐gradient algorithm in the computation of predictive deconvolution operators

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2752-2758 ◽  
Author(s):  
Fulton Koehler ◽  
M. Turhan Taner
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Single Channel ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Time Varying ◽  
Simple Formulation ◽  
Deconvolution Problem ◽  
Levinson Algorithm ◽  
Multichannel Deconvolution

A number of excellent papers have been published since the introduction of deconvolution by Robinson in the middle 1950s. The application of the Wiener‐Levinson algorithm makes deconvolution a practical and vital part of today’s digital seismic data processing. We review the original formulation of deconvolution, develop the solution from another perspective, and demonstrate a general and rigorous solution that could be implemented. By “general” we mean a deterministic time‐varying and multichannel operator design, and by “rigorous” we mean the straightforward least‐squares error solution without simplifying to a Toeplitz matrix. Also we show that the conjugate‐gradient algorithm used in conjunction with the least‐squares problem leads to a satisfactory simplification; that in the computation of the operators, the square matrix involved in the normal equations need not be computed. Furthermore, the product of this matrix with a column matrix can be obtained directly from the data as a result of two cascaded simple convolutions. The time‐varying deconvolution problem is shown to be equivalent to the multichannel deconvolution problem. Hence, with one simple formulation and associated programming, the procedure can be utilized for time‐constant single‐channel and multichannel deconvolution and time‐varying single‐channel and multichannel deconvolution.

scholarly journals Optimisation in the regularisation ill-posed problems

1986 ◽  
Vol 28 (1) ◽  
pp. 114-133 ◽  
Author(s):  
A. R. Davies ◽  
R. S. Anderssen
Keyword(s):  
Maximum Likelihood ◽  
Tikhonov Regularization ◽  
Cross Validation ◽  
Discrepancy Principle ◽  
Asymptotic Estimates ◽  
Deconvolution Problem ◽  
Ill Posed ◽  
The Relationship ◽  
Asymptotic Analyses ◽  
Selection Of

We survey the role played by optimization in the choice of parameters for Tikhonov regularization of first-kind integral equations. Asymptotic analyses are presented for a selection of practical optimizing methods applied to a model deconvolution problem. These methods include the discrepancy principle, cross-validation and maximum likelihood. The relationship between optimality and regularity is emphasized. New bounds on the constants appearing in asymptotic estimates are presented.

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