Effect of source spectrum on seismic attenuation measurements using the pulse‐broadening method

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1520-1526 ◽  
Author(s):  
Hsi‐Ping Liu
Keyword(s):  
Wave Propagation ◽  
Internal Friction ◽  
Rise Time ◽  
Delta Function ◽  
Seismic Attenuation ◽  
Time Function ◽  
Source Spectrum ◽  
Source Time Function ◽  
Band Limited ◽  
D Wave

Numerical examples of one‐dimensional (1-D) wave propagation, using realistic source time functions in an anelastic material characterized by frequency‐independent internal friction, demonstrate that (a) the source time function strongly influences the dependencies of initial rise time τ and pulse width w on internal friction [Formula: see text] and distance x; (b) in general, τ and w have different functional dependencies on [Formula: see text] and x; and (c) the slope ∂τ/∂x for particle displacement computed for a band‐limited source time function can be either greater than or less than the corresponding value computed for a delta‐function displacement source time function. Result (a) corroborates the result for τ given by Blair and Spathis, which implies that the commonly used linear rise time and distance relation, [Formula: see text], where T is the traveltime and C a source‐independent constant, is an oversimplification of 1-D anelastic wave propagation; the source spectrum must be considered when inferring seismic attenuation from changes in rise time. Result (c) contradicts the assertion by Blair and Spathis that ∂τ/∂x of wave trains generated by a band‐limited source time function is always less than the corresponding value generated by a delta‐function source time function. By matching first arrival times and rise times obtained by modeling 1-D wave propagation in an anelastic medium to those obtained in the field, seismic attenuation can be determined.

scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

2013 ◽  
Vol 5 (2) ◽  
pp. 1125-1162 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

scholarly journals Pemodelan Tsunami Sederhana dengan Menggunakan Persamaan Differensial Parsial

2018 ◽  
Vol 8 (1) ◽  
pp. 26
Author(s):  
Indriati Retno Palupi ◽  
Wiji Raharjo ◽  
Eko Wibowo ◽  
Hafiz Hamdalah
Keyword(s):  
Differential Equation ◽  
Fluid Dynamics ◽  
Partial Differential Equation ◽  
Wave Propagation ◽  
Taylor Expansion ◽  
Tsunami Wave ◽  
Time Function ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Space And Time

One way to solve fluid dynamics problem is using partial differential equation. By using Taylor expansion, fluid dynamics can be applied simply. For the example is tsunami wave. It is include to hyperbolic partial differential equation, tsunami wave propagation can describe in space and time function by using Euler FTCS (Forward Time Central Space) formula.

The 14 September 1995 (M = 7.3) Copala, Mexico, earthquake: A source study using teleseismic, regional, and local data

1997 ◽  
Vol 87 (4) ◽  
pp. 999-1010
Author(s):  
F. Courboulex ◽  
M. A. Santoyo ◽  
J. F. Pacheco ◽  
S. K. Singh
Keyword(s):  
Time Window ◽  
Time Function ◽  
Source Process ◽  
Source Time Function ◽  
Nonlinear Method ◽  
Local Data ◽  
Plate Interface ◽  
Linear Inversion ◽  
Field Source ◽  
Mexico Earthquake

Abstract We analyze source characteristics of the 14 September 1995, Copala, Mexico, earthquake (M = 7.3) using teleseismic, regional, and local seismograms. In the analysis of the teleseismic and the regional seismic waves, we apply the empirical Green's function (EGF) technique. The recording of an appropriate aftershock is taken as the EGF and is used to deconvolve the mainshock seismogram, thus obtaining an apparent far-field source-time function at each station. The deconvolution has been done using surface waves. For teleseismic data, we apply a spectral deconvolution method that enables us to obtain 37 apparent source-time functions (ASTFs) at 29 stations. In the analysis of the regional broadband seismograms, we use two different aftershocks as EGF, and the deconvolution is performed in the time domain with a nonlinear method, imposing a positivity constraint, and the best azimuth for the directivity vector is obtained through a grid-search approach. We also analyze two near-source accelerograms. The traces are inverted for the slip distribution over the fault plane by applying a linear inversion technique. With the aid of a time-window analysis, we obtain an independent estimation of the source-time function and a more detailed description of the source process. The analysis of the three datasets permits us to deduce the main characteristics of the source process. The rupture initiated at a depth of 16 km and propagated in two directions: updip along the plate interface toward 165° N and toward 70° N. The source duration was between 12 and 14 sec, with the maximum of energy release occurring 8 sec after the initiation of the rupture. The estimated rupture dimension of 35 × 45 km is about one-fourth of the aftershock area. The average dislocation over the fault was 1.4 m (with a maximum dislocation of 4.1 m located 10 km south of the hypocenter), which gives roughly 1 MPa as the average static stress drop.

Verification of UDEC Modeling 1-D Wave Propagation in Rocks

2011 ◽  
Vol 90-93 ◽  
pp. 1998-2001
Author(s):  
Wei Dong Lei ◽  
Xue Feng He ◽  
Rui Chen
Keyword(s):  
Wave Propagation ◽  
Analytical Solution ◽  
Transmission Coefficient ◽  
Method Of Characteristics ◽  
Rock Joint ◽  
Rock Joints ◽  
Dynamic Problems ◽  
The Method Of Characteristics ◽  
Elastic Rock ◽  
D Wave

Three cases for 1-D wave propagation in ideal elastic rock, through single rock joint and multiple parallel rock joints are used to verify 1-D wave propagation in rocks. For the case for 1-D wave propagation through single rock joint, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the analytical solution. For 1-D wave propagation through multiple parallel joints, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the method of characteristics. For all these cases, UDEC results agree well with results from the analytical solutions and the method of characteristics. From these verification studies, it can be concluded that UDEC is capable of modeling 1-D dynamic problems in rocks.

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