Viscoacoustic wave propagation simulation in the earth

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 769-777 ◽  
Author(s):  
Jose M. Carcione ◽  
Dan Kosloff ◽  
Ronnie Kosloff
Keyword(s):  
Wave Propagation ◽  
Seismic Waves ◽  
Superposition Principle ◽  
Time Integration ◽  
Equation Of Motion ◽  
Strain History ◽  
Porous Rocks ◽  
Arrival Times ◽  
Realistic Description ◽  
Geometrical Effects

Anelasticity of earth materials produces significant changes in the amplitude and phase spectra of seismic waves. The anelastic properties of real materials, particularly of porous rocks, are described using the theory of linear viscoelasticity based on Boltzmann’s superposition principle. Wave‐propagation simulation with this model requires implementing the convolutional relation in the equation of motion. The choice of a viscoacoustic constitutive relation based on a spectrum of relaxation mechanisms allows a realistic description of the anelastic effects, and the introduction of memory variables obviates storing the entire strain history required by the time convolution. A pseudospectral time‐integration technique is used to solve the equation of motion. Applications of viscoacoustic modeling suggest the need for considering the correct attenuation‐dispersion effects for various fundamental seismic problems in anelastic earth models. Comparison of acoustic and viscoacoustic synthetic seismograms shows differences in the amplitudes and arrival times of the wave fields which are enhanced for particular combinations of anelastic and geometrical effects.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

Building Stiffness Estimation by Wave Traveling Times

2014 ◽  
Author(s):  
Jesús Morales-Valdez ◽  
Luis Alvarez-Icaza
Keyword(s):  
Wave Propagation ◽  
Modal Analysis ◽  
Single Layer ◽  
Original Formulation ◽  
Arrival Times ◽  
Identification Methods ◽  
Novel Technique ◽  
Wave Propagation Method ◽  
Local Technique ◽  
Interesting Alternative

A novel technique to estimate stiffness in buildings is presented. In contrast with most of the available work in the literature that resorts to diverse forms of modal analysis, this local technique is based on the propagation of a Ricker pulse through the structure and on measuring the wave arrival times at each story of the building, represented as a single layer in a multiple stratum model. These arrival times are later used to recuperate building stiffness at each story. Wave propagation is based on the Thomson-Haskell method, that allows to generalize the wave propagation method to multi-story buildings without significant changes to the original formulation. The number of calculated parameters is small in comparison with methods based on modal analysis. This technique provides and quick and easy methodology to assess building integrity and is an interesting alternative to verify results obtained by other identification methods. Simulation results for building with heterogeneous characteristics across the stories confirm the feasibility of the proposal.

A Smoothing Scheme for Seismic Wave Propagation Simulation with a Mixed FEM of Diffusionized Wave Equation

2021 ◽  
pp. 2150061
Author(s):  
Ryuta Imai ◽  
Naoki Kasui ◽  
Masayuki Yamada ◽  
Koji Hada ◽  
Hiroyuki Fujiwara
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Seismic Wave ◽  
Time Integration ◽  
Coupled System ◽  
Seismic Wave Propagation ◽  
Implicit Time ◽  
Integration Scheme ◽  
Weak Formulation ◽  
Mixed Fem

In this paper, we propose a smoothing scheme for seismic wave propagation simulation. The proposed scheme is based on a diffusionized wave equation with the fourth-order spatial derivative term. So, the solution requires higher regularity in the usual weak formulation. Reducing the diffusionized wave equation to a coupled system of diffusion equations yields a mixed FEM to ease the regularity. We mathematically explain how our scheme works for smoothing. We construct a semi-implicit time integration scheme and apply it to the wave equation. This numerical experiment reveals that our scheme is effective for filtering short wavelength components in seismic wave propagation simulation.

Seismic Rays

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Inverse Problem ◽  
Seismic Tomography ◽  
Seismic Waves ◽  
Seismic Station ◽  
Three Dimensional ◽  
Arrival Times ◽  
The Earth ◽  
Straight Lines ◽  
Ray Path ◽  
Uniform Composition

This chapter focuses on the underlying mathematics of seismic rays. Seismic waves caused by earthquakes and explosions are used in seismic tomography to create computer-generated, three-dimensional images of Earth's interior. If the Earth had a uniform composition and density, seismic rays would travel in straight lines. However, it is broadly layered, causing seismic rays to be refracted and reflected across boundaries. In order to calculate the speed along the wave's ray path, the time it takes for a seismic wave to arrive at a seismic station from an earthquake needs to be determined. Arrival times of different seismic waves allow scientists to define slower or faster regions deep in the Earth. The chapter first presents the relevant equations for seismic rays before discussing how rays are propagated in a spherical Earth. The Wiechert-Herglotz inverse problem is considered, along with the properties of X in a horizontally stratified Earth.

Azimuth and slowness anomalies of seismic waves measured on the central California seismographic array. Part I. Observations

1966 ◽  
Vol 56 (1) ◽  
pp. 223-239 ◽  
Author(s):  
Michio Otsuka
Keyword(s):  
Upper Mantle ◽  
Measurement Errors ◽  
Seismic Waves ◽  
Crust And Upper Mantle ◽  
Arrival Times ◽  
Central California ◽  
The North ◽  
Upper Mantle Structure ◽  
Coast Ranges ◽  
The University

abstract Arrays of seismographs are usually considered to be detectors which give enhanced signals from distant earthquakes. They also provide, however, a new way of learning more about the structure of the crust and upper mantle. The deviation of the seismic-wave surface from its expected configuration may be regarded as a consequence of non-homogeneous and anisotropic conditions in the earth. The operations of the University of California network of telemetry stations in the Coast Ranges of California provides an opportunity to discover the practicality of this approach. The situation of this network near the continental margin gives the study particular interest. The differences in arrival-times between array elements of coherent peaks or troughs of P and pP phases from 28 teleseisms in the period of 1963-1964 were read from the telemetry records of the central California seismographic array. The direction of approach and velocities of the wave fronts were then determined and compared with the great circle azimuths and with the apparent velocities calculated from the Jeffreys-Bullen tables. The observed anomalies in direction of approach and apparent velocites are found to be cyclic functions of the direction of the source. The amplitudes of these functions are almost 10 degrees in azimuth anomaly and 1.0 sec/deg in slowness anomaly. Error analyses show that the anomaly functions cannot be attributed to the measurement errors. The derived anomaly functions provide a powerful means of examining crustal and upper mantle structure under the array and perhaps at the source. Variations between subsets of the array indicate significant differences in structure between portions of the Coast Ranges to the north and to the south of Hollister.

scholarly journals Tsunami Intrusion and River Ice Movement

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1290 ◽  
Author(s):  
Jiajia Pan ◽  
Hung Tao Shen
Keyword(s):  
Wave Propagation ◽  
Tsunami Wave ◽  
Water Pressure ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Wave Model ◽  
Hybrid Technique ◽  
Ice Dynamics ◽  
Tsunami Waves ◽  
Surface Ice

A two-dimensional wave model coupled with ice dynamics is developed to evaluate ice effects on shallow water wave propagation on a beach and in a channel. The nonlinear Boussinesq equations with ice effects are derived and solved by the hybrid technique of the Godunov-type finite volume method and finite difference method with the third-order Runge–Kutta method for time integration. The shock capturing method enables the model to simulate complex flows over irregular topography. The model is capable of simulating wave propagations accurately, including non-hydrostatic water pressure and wave dispersions. The ice dynamic module utilizes a Lagrangian discrete parcel method, based on smoothed particle hydrodynamics. The Boussinesq wave model is validated with an analytical solution of water surface oscillation in a parabolic container, an analytical solitary wave propagation in a flat channel, and experimental data on tsunami wave propagations. The validated model is then applied to investigate the interaction between ice and tsunami wave propagation, in terms of ice attenuation on tsunami wave propagations over a beach, ice deposition on the beach driven by the tsunami wave, and ice jam formation and release in a coastal channel with the intrusion of the tsunami wave. The simulated results demonstrated the interactions between tsunami waves and surface ice, including the maximum run up, ice movement along the beach, and ice jamming in a channel.

Acoustic modeling in fluid‐saturated porous media

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 424-435 ◽  
Author(s):  
Siamak Hassanzadeh
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Seismic Waves ◽  
Single Phase ◽  
Reservoir Characterization ◽  
Acoustic Modeling ◽  
Fluid Viscosity ◽  
Acoustic Wave Propagation ◽  
Hydrocarbon Reservoir

An acoustic modeling method with possible application to enhanced hydrocarbon reservoir characterization is presented. The method involves numerical simulation of two‐dimensional (2‐D), low‐frequency transient acoustic‐wave propagation in porous media and is based on the explicit finite‐difference formulation of Biot’s system of equations in a fluid‐saturated poroacoustic medium. The scheme is second‐order accurate in space and time. Synthetic seismograms computed using this approach indicate that transient acoustic‐wave propagation in unbounded fluid‐filled porous media and in the presence of fluid viscosity closely mimics that in an equivalent nonporous (single‐phase) solid. However, in the presence of heterogeneities, such as layering, inclusions, and discontinuities, the results show that acoustic‐wave characteristics are affected by spatial variations in reservoir parameters such as porosity, permeability, and fluid content as well as the fluid‐solid interaction. The effects of permeability and fluid viscosity are discernible in dispersion and dissipation of the compressional wave, whereas porosity affects the compressional velocity as well. The results of this study suggest that no equivalent single‐phase model can adequately describe the effects of permeability and porosity on seismic waves propagating through heterogeneous fluid‐filled porous media.

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