Time functions appropriate for deep earthquakes

1974 ◽  
Vol 64 (5) ◽  
pp. 1419-1427 ◽  
Author(s):  
L. J. Burdick ◽  
D. V. Helmberger
Keyword(s):  
Time Domain ◽  
Time History ◽  
Dislocation Theory ◽  
S Wave ◽  
P Waves ◽  
Multiple Events ◽  
Deep Earthquakes ◽  
Deep Focus ◽  
The Time Domain ◽  
Wave Shapes

Abstract The seismic signatures of isolated body phases from many deep-focus earthquakes were analyzed in the time domain. Most shocks were found to be multiple events when examined in detail. The time history derived from P waves for single events predict synthetic S-wave shapes that match the observations, indicating compatibility with shear dislocation theory. Several other features of source functions in the time domain have been brought to light.

Full‐wave acoustic logging: synthetic microseismograms and frequency‐wavenumber analysis

Geophysics ◽  
1985 ◽  
Vol 50 (11) ◽  
pp. 1756-1778 ◽  
Author(s):  
Denis P. Schmitt ◽  
Michel Bouchon
Keyword(s):  
Wave Field ◽  
Time Domain ◽  
Displacement Vector ◽  
Fluid Velocity ◽  
Scattered Wave ◽  
Close Relation ◽  
Spectral Energy ◽  
S Wave ◽  
Resonance Frequencies ◽  
The Time Domain

The discrete wavenumber method is used to compute synthetic full‐waveform acoustic logs in axisymmetric multilayered boreholes and to perform the frequency‐wavenumber analysis of the radiated wave field. The stress‐displacement vector is propagated through the layers using a numerically improved formulation of the Thomson‐Haskell method. In the time domain, all the trapped and interface modes overlap. On the contrary, the representations of the spectral energy density of the scattered wave field in the frequency axial‐wavenumber domain, for various radial positions of observation, allow the recognition and identification of the different wave types as well as their repartition of energy. In particular, these diagrams show the close relation between the resonance frequencies of the borehole and the significant low‐frequency energy of the pseudo‐Rayleigh modes. They also facilitate the interpretation of some of the physical phenomena which occur during the propagation in a complex borehole environment. We present the configurations of a well‐bonded and unbonded cased hole, an invaded zone, and a mudcake. For all of these models, we consider a “fast” formation in which the S-wave velocity is higher than the bore fluid velocity and a “slow” formation. The presence of an elastic tool at the center of the borehole is also investigated. The associated microseismograms, computed for a series of source‐receiver spacings, characterize in the time domain the observations previously made.

A non-linear model for elastic hysteresis in the time domain: Computational procedure

2020 ◽  
pp. 095440622098202
Author(s):  
MMS Dwaikat ◽  
C Spitas ◽  
V Spitas
Keyword(s):  
Time Domain ◽  
Mechanical Energy ◽  
Numerical Procedure ◽  
Time History ◽  
Computational Procedure ◽  
Continuous Systems ◽  
Full Time ◽  
Proposed Model ◽  
History Of ◽  
The Time Domain

Hysteretic damping of a material or structure loaded within its elastic region is the dissipation of mechanical energy at a rate independent of the frequency of vibration while at the same time directly proportional to the square of the displacement. Generally, reproducing this frequency-independent damping can be computationally complex and requires prior knowledge of the system’s natural frequencies or the full time history of the system’s response. In this paper, a new model and numerical procedure are proposed whereby hysteretic material damping is achieved in the time domain. The proposed procedure is developed based on modifying the viscous model through a correction factor calculated exclusively using the local response. The superiority of the proposed approach lies in its ability to capture material hysteresis without any knowledge of the eigen- or modal frequencies of the system and without knowledge of the past time history of the system’s response or the characteristics of any excitation forces. A numerical procedure is also presented for implementing the proposed model in vibration analysis. The simplicity of the approach enables its generalisation to continuous systems and to systems of multi-degrees of freedom as demonstrated herein. The proposed model is presented as a correction to the viscous damping model which makes it attractive to implement into commercial finite element package using user-defined element subroutines as demonstrated in this study.

Impact of FPSO Heading on Fatigue Design in Non-Collinear Environments

2002 ◽  
Author(s):  
Christina D. Nordstrom ◽  
Peter B. Lacey ◽  
Bob Grant ◽  
Derek D. Hee
Keyword(s):  
Time Domain ◽  
First Principles ◽  
Fatigue Cracks ◽  
Time History ◽  
Geographic Location ◽  
Analysis Procedure ◽  
Fatigue Design ◽  
Operational Life ◽  
Structural Details ◽  
The Time Domain

To achieve confidence in continuous 20+ year FPSO service without fatigue cracks leading to costly repair offshore or in dry-dock, ExxonMobil has developed a prescriptive Fatigue Methodology Specification (FMS, ref. 5) for new-build FPSOs. An important FMS requirement for turret-moored FPSOs is to determine relative wave headings in non-collinear wind, current and wave environments using a first-principles approach. Based on initial review with FPSO designers, this FMS requirement may pose a significant challenge because appropriately defined met-ocean criteria and efficient analytical design tools are not readily available. To date, FPSO designers typically account for weather-vaning in non-collinear environments by assuming a distribution of relative wave headings based on experience. For example, one assumption is to use 0 degrees (head seas) for 70% of the time and within ±30 degrees off the bow for the remaining 30%. In certain environments, this assumption can lead to a non-conservative fatigue design for hull structural details that are sensitive to beam seas, and an overly conservative fatigue design for details sensitive to head seas. ExxonMobil contracted Moffat & Nichol to develop a time-domain procedure to predict mean FPSO headings by considering wave, wind and current induced loads on the FPSO hull and topsides throughout the FPSO’s 20+ year operational life. A key element of this methodology is a directional representation of met-ocean data, including waves, winds and currents for every 3- or 6-hour sea-state. We have implemented our heading analysis procedure in robust software, which includes processing of the 20+ year met-ocean data in the time domain. Once the FPSO heading time history is known, fatigue lives at critical structural connections are predicted using the spectral fatigue method prescribed in the FMS. To demonstrate the heading methodology and assess its efficiency for project use, an example analysis was performed for an FPSO at a specific geographic location, where relatively strong currents exist. Comparison of predicted FPSO headings and fatigue lives with those using the existing industry practices confirmed the need for a first principles based heading methodology for FPSO fatigue design. The heading and fatigue analysis procedure described here can lead to more accurate, robust fatigue designs for FPSOs in non-collinear environments.

Reconstruction of the Force Applied to a Plate in the Time Domain From Sound Pressure Measurements

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Chuan-Xing Bi ◽  
Long Hu ◽  
Yong-Bin Zhang ◽  
Xiao-Zheng Zhang
Keyword(s):  
Time Domain ◽  
Sound Pressure ◽  
Microphone Array ◽  
Near Field ◽  
Impulse Response Function ◽  
Time History ◽  
Pressure Measurements ◽  
Concentrated Force ◽  
Vibration Responses ◽  
The Time Domain

Abstract This paper provides a non-contact approach to reconstruct the distributed or concentrated force applied to a plate in the time domain. This approach is based on sound pressure measurements and is realized by coupling the techniques of real-time near-field acoustic holography (RT-NAH) and force reconstruction. A microphone array is used to measure the sound pressures in the near field of the plate. The measured sound pressures are taken as the inputs of the RT-NAH to reconstruct the vibration responses, including the normal acceleration, velocity, and displacement, on the surface of the plate. With the reconstructed vibration responses, the equation of motion governing the forced vibration can be further processed to reconstruct the force applied to the plate in the time domain. In the process of reconstructing the vibration responses, a displacement–pressure impulse response function is derived for the first time and is used in the RT-NAH. Results of numerical simulations as well as experiments demonstrate that the proposed approach can identify the location of the force accurately and reconstruct the time history of the force effectively, thereby helping to diagnose the mechanical cause of the radiated noise.

Direct Hang-Off Model to Evaluate Fatigue Damage at Riser Hang-Off

2013 ◽  
Author(s):  
Yucheng Hou ◽  
Jiabei Yuan ◽  
Yanqiu Zhang ◽  
Zhimin Tan ◽  
Terry Sheldrake
Keyword(s):  
Dynamic Simulation ◽  
Fatigue Damage ◽  
Time Domain ◽  
Damage Assessment ◽  
Global Analysis ◽  
Time History ◽  
Fatigue Analysis ◽  
Analysis Software ◽  
External Function ◽  
The Time Domain

Fatigue damage assessment at the flexible riser hang-off location, where the pipe frequently endures maximum tension and curvature variations, is key to verify design integrity for service life. Traditionally, the fatigue analysis is performed in a separate local structure model, as the commercial global analysis software lacks the capability of handling the local behavior of the riser structural component, which is dependent on materials and manufacturing processes. During global fatigue analysis, the riser configuration is built with pinned connected at the hang-off point. The resulting tension and angle responses at the hang-off location, are then input to a local model to perform the stress and fatigue analysis, where the detailed pipe layer structure and bend stiffener are modeled. This traditional approach is conservative, time costly and is often limited to regular wave approach. Wellstream developed an external function to work with specialized commercial riser dynamic analysis software. The external function simulates the detailed behaviour of flexible pipe structure components and the resulting bending hysteresis during dynamic simulation in the time domain. Therefore, the stress time history of the tensile armour becomes available at the end of global simulation in the time domain and is ready for fatigue damage assessment by rain flow counting. This paper presents a study case where the fatigue assessment is performed directly at the hang-off region within the riser global dynamic simulation. The riser hang-off is situated at the top of the I-tube and a bend stiffener is fixed at the bottom of the I-tube. I-tube and pipe section are precisely modeled as pipe-in-pipe facility, where the interaction of riser/I-tube can be captured.

Time-domain asymptotics. I General theory for double integrals

1994 ◽  
Vol 446 (1927) ◽  
pp. 341-360 ◽  
Keyword(s):  
Time Domain ◽  
Source Function ◽  
Saddle Points ◽  
Time History ◽  
Integral Transforms ◽  
Stationary Points ◽  
Limiting Behaviour ◽  
The Time Domain ◽  
The Hilbert Transform ◽  
Double Integrals

A technique is described for obtaining asymptotic formulae for the time-domain waveforms associated with double integrals of rapidly-varying isolated pulses. The method is an extension of the theory of the time-domain asymptotics of single integrals given by C. J. Chapman ( Proc. R. Soc. Lond. A 437, 25–40 (1992)), and represents a generalization of the method of stationary phase to integrals with non-sinusoidal integrands. Stationary points of the phase function in the domain of integration each give rise to a particular waveform shape in the time-history of the solution; the waveforms associated with interior extrema and saddle points are proportional to the original source function and the Hilbert transform of the source function respectively. Boundary stationary points also give rise to distinctive waveforms, proportional to fractional integral transforms of the source function. The transitional case of the coalescence of two interior stationary points is considered in some detail; an asymptotic formula describing the coalescence is found, and the limiting behaviour of this formula after coalescence is calculated, i. e. the residual waveform after the annihilation of the stationary points. Asymptotic and numerical results are compared for an example integral, and good agreement is found even for moderate values of the asymptotic parameter.

scholarly journals The normal distribution fitting method for frequency distribution characteristics of peak arrival time of earthquake

2020 ◽  
Vol 29 ◽  
pp. 2633366X2092141
Author(s):  
Xu Han ◽  
Yunan Liu ◽  
Lihua Wang
Keyword(s):  
Energy Distribution ◽  
Time Domain ◽  
Seismic Waves ◽  
Arrival Time ◽  
Time History ◽  
Distribution Characteristics ◽  
Acceleration Time ◽  
Acceleration Time History ◽  
Fitting Method ◽  
The Time Domain

The physical meaning of phase difference controls the occurrence time of peak values of triangular series, which can be abbreviated as peak arrival time. This article describes a method for deducing the correspondence between the energy distribution characteristics in the time domain and the peak arrival time. The variation laws of acceleration time–history curve of natural seismic wave can be transformed into its energy distribution characteristics in time domain. Based on the needs of seismic engineering, this article proposes a conversion formula to describe the relationship between the peak arrival time and the energy distribution characteristics in the time domain. To ensure that the variation laws of acceleration time–history curve of artificial seismic waves are more consistent with those of natural seismic waves, a normal-fitting annealing algorithm is proposed based on the normal-fitting method. The proposed method not only considers the frequency distribution characteristics of the peak arrival time comprehensively but also optimizes the fitting parameters according to the actual situation. The results of all the experimental cases verify the rationality and reliability of the proposed method.

scholarly journals Seismic gaps and intraplate seismicity around Rodrigues Ridge (Indian Ocean) from time-domain array analysis

2020 ◽  
Author(s):  
Manvendra Singh ◽  
Georg Rümpker
Keyword(s):  
Time Domain ◽  
Velocity Model ◽  
Surface Expression ◽  
Array Analysis ◽  
Intraplate Earthquakes ◽  
Earthquake Catalogues ◽  
P Waves ◽  
Global Networks ◽  
Reunion Plume ◽  
The Time Domain

Abstract. Rodrigues Ridge connects the Reunion hotspot track with the Central Indian Ridge (CIR) and has been suggested to represent the surface expression of a sub-lithospheric flow channel. From global earthquake catalogues, the seismicity in the region has been associated mainly with events related to the fracture zones at the CIR. However, some segments of the CIR appear void of seismic events. Here, we report on the seismicity recorded at a temporary array of ten seismic stations operating on Rodrigues Island from September 2014 to June 2016. The array analysis was performed in the time domain – by time shifting and stacking of the complete waveforms. Event distances were estimated based on a 1-D velocity model and the travel-time differences between S- and P-waves arrivals. We detected and located 63 new events, which were not reported by the global networks. Most of the events (51) are located off the CIR and can be classified as intraplate earthquakes. Local magnitudes varied between 1.3 and 3.5. Four seismic clusters were observed along with a distinguishable swarm of earthquakes that occurred to the west of the spreading segment of the CIR during the period from March to April 2015. The Rodrigues Ridge appeared aseismic during the period of operation. The lack of seismic activity along both Rodrigues Ridge and the sections of the CIR to the east of Rodrigues may be explained by partially-molten upper-mantle material, possibly in relation to the proposed material flow between the Reunion plume and the CIR.

scholarly journals A New Elastoplastic Time-History Analysis Method for Frame Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Qianqian Liang ◽  
Chen Zhao ◽  
Jun Hu
Keyword(s):  
Periodic Point ◽  
Time Domain ◽  
Response Spectrum ◽  
Time History ◽  
Specific Yield ◽  
Seismic Load ◽  
Structural Systems ◽  
History Analysis ◽  
The Time Domain ◽  
Fracture Stiffness

This study aimed to analyze the formation and application of the time-domain elastoplastic response spectrum. The elastoplastic response spectrum in the time domain was computed according to the trilinear force-restoring model. The time-domain elastoplastic response spectrum corresponded to a specific yield strength coefficient, fracture stiffness, and yield stiffness. However, the force-restoring models corresponding to different structural systems and the states of the structural systems at different moments were not the same. Therefore, the dynamic characteristics of a particular periodic point corresponding to a particular structure were meaningful for the elastoplastic response spectrum. In addition, the curve in the time-domain dimension along the periodic point truly reflected the real-time response of the structure when the structure encountered a seismic load.

SCATTERING OF ELASTIC WAVES FROM DEPTH‐DEPENDENT INHOMOGENEITIES

Geophysics ◽  
1976 ◽  
Vol 41 (3) ◽  
pp. 441-458 ◽  
Author(s):  
Paul G. Richards ◽  
Clint W. Frasier
Keyword(s):  
Time Domain ◽  
Elastic Waves ◽  
P Waves ◽  
Simple Method ◽  
Transmitted Waves ◽  
Short Period ◽  
Scattering Of Elastic Waves ◽  
The Time Domain ◽  
Thick Crust ◽  
Zero Frequency

We have studied scattered pulse shapes by modeling inhomogeneities as a sequence of infinitesimally thin homogeneous layers. With oblique incidence of plane P or SV waves, the reflected‐converted‐transmitted waves are obtained by taking the calculus limit for the sum of primary interactions of the incident wave with all layer boundaries. The resulting scattered waves thus present themselves naturally in the time domain. For an incident impulse, the scattered pulse shape is merely an analytic function of the depth from which scatter has taken place within the inhomogeneity. The direct application of this simple method appears to be new, and we have found it remarkably accurate when compared with methods in which higher‐order boundary interactions are also retained (i.e., Haskell methods and an adaptation in the time domain which also keeps all multiples). In specific studies of P-waves incident (up to 30 degrees away from the vertical) upon a 5 km thick crust‐mantle transition, between materials having impedance ratio 1:2.8, we find the scattered pulse shapes are given adequately by our theory, for the passband of short‐period seismometers. Indeed, the theory remains remarkably accurate even for long periods, being in error by only 8 per cent at zero frequency.

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