An autoregressive filter model for constant Q attenuation

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 749-758 ◽  
Author(s):  
Lon A. McCarley
Keyword(s):  
Seismic Waves ◽  
Seismic Wave Propagation ◽  
Good Representation ◽  
Minimum Phase ◽  
Inverse Filter ◽  
Low Frequencies ◽  
Filter Model ◽  
Sonic Log ◽  
Wavelet Response ◽  
Filter Response

The Earth’s filter response to seismic wave propagation can be approximated by constant Q attenuation and is dispersive or minimum phase. A finite‐length autoregressive (AR) filter model is a good representation for constant Q attenuation with minimum phase. Coefficients of the AR filter are the Wiener‐Levinson inverse filter coefficients for the sampled constant Q auto‐correlation. Conventional spike deconvolution approximates fairly well the inverse filter on this ground if the minimum‐phase attenuation law holds true. Wavelet response to attenuation was analyzed using the AR filter model. The amplitude of the filtered impulse response decreases at nearly 1/t, where t is traveltime, and is sensitive to the loss of low frequencies. The wavelets’ peak amplitude is fractionally time delayed with .92/Q. Velocity dispersion of seismic waves should not contribute to the mis‐tie observed between the conventional check shot and the borehole sonic log when the first arrivals are picked the same way.

scholarly journals Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

2015 ◽  
Vol 9 (1) ◽  
pp. 367-384 ◽  
Author(s):  
A. Diez ◽  
O. Eisen
Keyword(s):  
Seismic Waves ◽  
Dynamic Behaviour ◽  
Ice Core ◽  
Ice Cores ◽  
Seismic Wave Propagation ◽  
Elasticity Tensor ◽  
Reflection Coefficients ◽  
Seismic Velocities ◽  
Crystal Anisotropy ◽  
Elasticity Tensors

Abstract. A preferred orientation of the anisotropic ice crystals influences the viscosity of the ice bulk and the dynamic behaviour of glaciers and ice sheets. Knowledge about the distribution of crystal anisotropy is mainly provided by crystal orientation fabric (COF) data from ice cores. However, the developed anisotropic fabric influences not only the flow behaviour of ice but also the propagation of seismic waves. Two effects are important: (i) sudden changes in COF lead to englacial reflections, and (ii) the anisotropic fabric induces an angle dependency on the seismic velocities and, thus, recorded travel times. A framework is presented here to connect COF data from ice cores with the elasticity tensor to determine seismic velocities and reflection coefficients for cone and girdle fabrics. We connect the microscopic anisotropy of the crystals with the macroscopic anisotropy of the ice mass, observable with seismic methods. Elasticity tensors for different fabrics are calculated and used to investigate the influence of the anisotropic ice fabric on seismic velocities and reflection coefficients, englacially as well as for the ice–bed contact. Hence, it is possible to remotely determine the bulk ice anisotropy.

scholarly journals Vertical to Horizontal Spectral Ratio (VHSR) Response of Seismic Wave Propagation in a Homogeneous Elastic – Poroelastic Medium Using The Spectral Finite Element Method

2021 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Sudarmaji Saroji ◽  
Budi Eka Nurcahya ◽  
Nivan Ramadhan Sugiantoro
Keyword(s):  
Finite Element Method ◽  
Elastic Medium ◽  
Seismic Waves ◽  
Low Frequency ◽  
Seismic Wave Propagation ◽  
P Wave ◽  
Poroelastic Medium ◽  
Compressional Waves ◽  
Spectral Finite Element Method ◽  
Spectral Finite Element

<p>Numerical modeling of 2D seismic wave propagation using spectral finite element method to estimate the response of seismic waves passing through the poroelastic medium from a hydrocarbon reservoir has been carried out. A hybrid simple model of the elastic - poroelastic - elastic with a mesoscopic scale element size of about 50cm was created. Seismic waves which was in the form of the ricker function are generated on the first elastic medium, propagated into the poroelastic medium and then transmitted to the second elastic medium. Pororoelastic medium is bearing hydrocarbon fluid in the form of gas, oil or water. Vertical and horizontal component of velocity seismograms are recorded on all mediums. Seismograms which are recorded in the poroelastic and second elastic medium show the existence of slow P compressional waves following fast P compressional waves that do not appear on the seismogram of the first elastic medium. The slow P wave is generated when the fast P wave enters the interface of the elastic - poroelastic boundary, propagated in the poroelastic medium and is transmited to the second elastic medium. The curves of Vertical to horizontal spectrum ratio (VHSR) which are observed from seismograms recorded in the poroelastic and the second elastic medium show that the peak of VHSR values at low frequency correlated with the fluid of poroelastic reservoir. The highest VHSR value at the low frequency which is recorded on the seismogram is above the 2.5 Hz frequency for reservoirs containing gas and oil in the second elastic medium, while for the medium containing water is the highest VHSR value is below the 2.5 Hz frequency.</p>

Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches

2020 ◽  
Vol 224 (2) ◽  
pp. 1443-1463
Author(s):  
Victor Mensah ◽  
Arturo Hidalgo
Keyword(s):  
Seismic Wave ◽  
Fourth Order ◽  
Seismic Waves ◽  
Time Discretization ◽  
Seismic Wave Propagation ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Fluid Saturation ◽  
Runge Kutta ◽  
Saturated Medium

SUMMARY The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterize the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the active attenuation parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, quality factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite-volume scheme with a second order Runge–Kutta approximation for the time discretization and a fourth order accurate finite-difference scheme with a fourth order Runge–Kutta approximation for the time discretization. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.

PROPOSED ATTENUATION‐DISPERSION PAIR FOR SEISMIC WAVES

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 456-461 ◽  
Author(s):  
J. E. White ◽  
D. J. Walsh
Keyword(s):  
Experimental Data ◽  
Seismic Waves ◽  
Numerical Application ◽  
Low Frequencies ◽  
One Dimensional ◽  
Lumped Element ◽  
Resistive Element ◽  
The Hilbert Transform ◽  
Attenuation And Dispersion ◽  
Mathematical Behavior

Several papers in recent years have dealt with the causality‐imposed relation between attenuation and dispersion for waves in lossy solids, with emphasis on seismic waves. While the published formulas for dispersion within a particular frequency band are supported by experimental evidence within that band, the mathematical behavior of these expressions outside the band, particularly at low frequencies, is physically unacceptable. In the present paper, one‐dimensional seismic waves are modeled as propagation along a simple lumped‐element transmission line, leading to expressions for attenuation and velocity as functions of frequency which not only satisfy the experimental data available, but exhibit no objectionable behavior outside the range of available data. This is achieved by introducing a resistive element whose value is inversely proportional to frequency. Numerical application of the Hilbert transform shows the condition of causality to be satisfied by this model quite accurately.

scholarly journals 2D full-waveform modeling of seismic waves in layered karstic media

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. T25-T34 ◽  
Author(s):  
Yingcai Zheng ◽  
Adel H. Malallah ◽  
Michael C. Fehler ◽  
Hao Hu
Keyword(s):  
Seismic Waves ◽  
Finite Size ◽  
Spectral Element ◽  
Seismic Wave Propagation ◽  
Complex Model ◽  
Waveform Modeling ◽  
Frequency Space ◽  
Full Waveform ◽  
Matrix Scheme ◽  
Element Method

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent [Formula: see text] can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels.

Structure and mobility of the crust and mantle in the vicinity of island arcs

1968 ◽  
Vol 5 (4) ◽  
pp. 985-991 ◽  
Author(s):  
Jack Oliver ◽  
Bryan Isacks
Keyword(s):  
Upper Mantle ◽  
Seismic Waves ◽  
Current Knowledge ◽  
Average Rate ◽  
Seismic Wave Propagation ◽  
Rift System ◽  
Island Arcs ◽  
Deep Earthquake ◽  
Anomalous Zone ◽  
The World

A detailed study of seismic wave propagation in the Fiji-Tonga region shows that there exists in the upper mantle an anomalous zone whose thickness is about 100 km and whose upper surface is approximately defined by the zone of seismic foci extending to depths of about 700 km. Attenuation of seismic waves within the zone is anomalously low and velocities are high. Other island arcs appear to be associated with similar zones.The anomalous zone in Tonga can be interpreted as the westernmost portion of a block of lithosphere that has been thrust, or dragged, or has settled beneath the island arc. Such mobility of the lithosphere suggests a key role in geotectonics for this layer of strength and raises a number of possible new solutions to long standing problems. For example, assuming that deep earthquake zones throughout the world are a measure of the amount of underthrusting during the last 107 years, an average rate of spreading over the entire worldwide rift system can be obtained as a check, but not a proof, of the hypothesis. The half-velocity obtained is 1.3 cm/year and is reasonable in light of current knowledge.

SEISMIC WAVES COUPLED TO SONIC BOOMS

Geophysics ◽  
1962 ◽  
Vol 27 (4) ◽  
pp. 528-530 ◽  
Author(s):  
Jack Oliver ◽  
Bryan Isacks
Keyword(s):  
New Jersey ◽  
Continental Shelf ◽  
Seismic Waves ◽  
Low Frequencies ◽  
Sonic Booms ◽  
Sea Floor

Air‐coupled seismic waves of low frequencies were excited by aircraft‐generated sonic booms and detected by a hydrophone at moderate depth and a geophone on the sea floor. The experiments were conducted on the continental shelf off New Jersey.

On: “Proposed Attenuation‐Dispersion Pair for Seismic Waves” by J. E. White and D. J. Walsh (GEOPHYSICS, June 1972, p. 456–461)

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 423-425 ◽  
Author(s):  
Ellis Strick
Keyword(s):  
Power Law ◽  
Seismic Waves ◽  
Low Frequency ◽  
Dispersion Relations ◽  
Minimum Phase ◽  
Power Law Model ◽  
Phase Property ◽  
Propagation Function ◽  
Complex Propagation ◽  
Frequency Behavior

In their paper, White and Walsh claim dispersion relations based upon an assumed minimum‐phase property of rock lead to such drastic low‐frequency behavior that any complex propagation function based upon dispersion relations is unacceptable. Since my power‐law model (Strick, 1967, 1970a) was placed in such a category, my response is as follows.

A NOTE ON THE PROPAGATION OF SEISMIC WAVES

Geophysics ◽  
1937 ◽  
Vol 2 (4) ◽  
pp. 319-328 ◽  
Author(s):  
Morris Muskat
Keyword(s):  
Wave Propagation ◽  
Power Series ◽  
Conventional Method ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Seismic Wave Propagation ◽  
Time Distance

It is suggested that in the computation of theoretical time‐distance curves for seismic wave propagation a more tractable form of analysis is obtained if the depth is expressed as a power series in the velocity than when the converse but more conventional method is used. Several illustrations of this procedure are given.

3D Nonlinear Ground‐Motion Simulation Using a Physics‐Based Method for the Kinburn Basin

2019 ◽  
Author(s):  
Amin Esmaeilzadeh ◽  
Dariush Motazedian ◽  
Jim Hunter
Keyword(s):  
Shear Wave ◽  
Ground Motion ◽  
Seismic Waves ◽  
Peak Ground Velocity ◽  
Ground Acceleration ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Nonlinear Viscoelastic ◽  
Finite Fault

Abstract We used a finite‐difference modeling method, developed by Olsen–Day–Cui, to simulate nonlinear‐viscoelastic basin effects in a spectral frequency range of 0.1–1 Hz in the Kinburn bedrock topographic basin, Ottawa, Canada, for large earthquakes. The geotechnical and geological features of the study area are unique: loose, postglacial sediments with very low shear‐wave velocities (<200  m/s) overlying very firm bedrock with high shear‐wave velocities (>2000  m/s). Comparing records and simulated velocity time series showed regular viscoelastic simulations could model the ground motions at the rock and soil sites in the Kinburn basin for the Ladysmith earthquake, a local earthquake occurred on 17 May 2013 with Mw 4.7 (MN 5.2). The Ladysmith earthquake was scaled to provide a strong level of shaking for investigating the nonlinear behavior of soil; therefore, a new nonlinear‐viscoelastic subroutine was introduced to the program. A modeled stress–strain relationship associated with ground‐motion modeling in the Kinburn basin using a scaled Ladysmith earthquake event of Mw 7.5 followed Masing’s rules. Using nonlinear‐viscoelastic ground‐motion simulations significantly reduced the amplitude of the horizontal component of the Fourier spectrum at low frequencies and the predicted peak ground acceleration and peak ground velocity values compared with regular linear viscoelastic simulations; hence, the lower soil amplification of seismic waves and the frequency and amplitude spectral content were altered by the nonlinear soil behavior. In addition, using a finite‐fault model to simulate an earthquake with Mw 7.5 was necessary to predict the higher levels of stresses and strains, which were generated in the basin. Using a finite‐fault source for the nonlinear‐viscoelastic simulation caused decreases in the horizontal components because of the shear modulus reduction and increase of damping.

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