Modeling of a constant <i>Q</i>: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique

Blanch, Joakim O.; Robertsson, Johan O. A.; Symes, William W.

doi:10.1190/1.1443744

Cited by 345 publications

(214 citation statements)

References 18 publications

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“…This was proposed by Emmerich & Korn (1987) and later became more popular as the 'τ -method' by Blanch et al (1995). The advantage of this method is that it results in only one inverse problem while finding the parameters for different Q is trivial due to the linearity of a j in Q −1 .…”

Section: Determination Of the Optimal Structural Parameters In Full-smentioning

confidence: 99%

“…The relation between the parameter sets in the Maxwell (a j and ω j ) and Zener body (τ j and τ σ j , the strain and stress relaxation times) representation can be found by comparing eq. (8) in Blanch et al (1995) and eq. (11) in Emmerich & Korn (1987):…”

Section: Preliminariesmentioning

confidence: 99%

“…Blanch et al (1995;'τ -method') leads to a logarithmic trend with the strongest effect in the high frequencies (blue), the correction (red) results in a behaviour very close to optimizing the exact relation (black) even for Q as low as 20 [on the global scale, the minimum value is ≈50 in the 3-D model QRLW8 by Gung & Romanowicz (2004)]. Errors are frequency-weighted, see text for details.…”

Section: Determination Of the Optimal Structural Parameters In Full-smentioning

confidence: 99%

“…It is common practice (Emmerich & Korn 1987;Blanch et al 1995;Komatitsch & Tromp 2002b;Graves & Day 2003;Kristek & Moczo 2003;Käser et al 2007;Savage et al 2010) to find the medium parametrization a j , ω j by choosing the relaxation frequencies ω j a priori, mostly logarithmically spaced in the frequency range of interest. Then, the a j can be found by sampling Q(ω) at a finite number of frequencies ω k and solving an overdetermined inverse problem.…”

Section: Optimization Criteria and Variablesmentioning

confidence: 99%

“…Blanch et al 1995;Käser et al 2007). Day (1998) suggested a method called the coarsegrained memory variable approach to redistribute the medium properties on the subwavelength scale such that it behaves the same for the wavefield, but is computationally significantly less expensive.…”

Section: Introductionmentioning

confidence: 99%

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Optimized viscoelastic wave propagation for weakly dissipative media

Driel

Nissen‐Meyer

2014

Geophysical Journal International

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S U M M A R YThe representation of viscoelastic media in the time domain becomes more challenging with greater bandwidth of the propagating waves and number of travelled wavelengths. With the continuously increasing computational power, more extreme parameter regimes become accessible, which requires the reassessment and improvement of the standard 'memory variable' methods to implement attenuation in time-domain seismic wave-propagation methods. In this paper, we propose a method to minimize the error in the wavefield for a fixed complexity of the anelastic medium. This method consists of defining an appropriate misfit criterion based on a first-order analysis of how errors in the discretized medium propagate into errors in the wavefield and a simulated annealing optimization scheme to find the globally optimal parametrization. Furthermore, we derive an analytical time-stepping scheme for the memory variables that encode the strain history of the medium. Then we develop the coarse grained memory variable approach for the spectral element method (SEM) and benchmark it using the 2.5-D code AxiSEM for global body waves up to 1 Hz. Showing very good agreement with a reference solution, it also leads to a speedup of a factor of 5 in the anelastic part of the code (factor 2 in total) in this 2.5-D approach. A factor of ≈15 (3 in total) can be expected for the 3-D case compared to conventional implementations.

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Section: Determination Of the Optimal Structural Parameters In Full-smentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Determination Of the Optimal Structural Parameters In Full-smentioning

confidence: 99%

Section: Optimization Criteria and Variablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimized viscoelastic wave propagation for weakly dissipative media

Driel

Nissen‐Meyer

2014

Geophysical Journal International

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Evolution of the oceanic lithosphere inferred from Po/So waves traveling in the Philippine Sea Plate

2015

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Po/So waves are characterized by their high-frequency content and long-duration travel over great distances (up to 3000km) through the oceanic lithosphere. Po/So waves are developed by the multiple forward scattering of P and S waves due to small-scale stochastic random heterogeneities. To study the nature of these heterogeneities, Po/So waves are analyzed in the Philippine Sea Plate, which consists of three regions with different lithospheric ages. In the Philippine Sea Plate, Po/So waves propagate in the youngest region (15 Ma) and propagate more effectively in older regions. We investigate the mechanism of this propagation efficiency using numerical finite difference method simulations of 2-D seismic wave propagation. The results of this study demonstrate that the increase in propagation efficiency of Po/So waves depends on the age of the oceanic lithosphere, and this relationship can be qualitatively explained by thickening of the oceanic lithosphere including small-scale heterogeneities and a reduction in the intrinsic attenuation. These small-scale heterogeneities may form continuously in oceanic lithosphere from the time of its formation at a spreading ridge, via the solidification of melts distributed in the asthenosphere.

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The Yığma Tepe of Pergamon: stratigraphic construction of a monumental tumulus from seismic refraction measurements

Mecking

Meinecke

Erkul

et al. 2020

Archaeological Prospection

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The monumental tumulus Yı gma Tepe is an important part of the cityscape of the ancient city of Pergamon. The tumulus construction is estimated in the Hellenistic period, the internal structure and exact purpose have been unknown so far. Its height of 32 m and diameter of 158 m make the deep interior of the tumulus practically inaccessible for excavations. Therefore, we applied a combination of geophysical measurements and archaeological sondages to explore the structure of the Yı gma Tepe. The investigations centre on P-wave refraction soundings. They were carried out to clarify the stratigraphic structure and soil composition as a prerequisite for a better understanding of construction techniques, building history and soil deposition.Interactive seismic raytracing, traveltime tomography and visco-elastic forward modelling were applied to derive a three-dimensional seismic velocity model, which was validated by excavations and soil analysis, historical records and additional geoelectric measurements. Our results reveal that the tumulus is composed of three layers, each about 10 m thick, separated by first-order seismic discontinuities which were locally verified. These layers form a stack of conical disks, the interfaces of which define two internal plateaus. The analysis of soil samples showed that the seismic velocity increase at the interfaces is likely to be caused by anthropogenic compaction applied to soils showing increased fractions of silt and clay. By combining topographic data with results from seismic and geoelectric sounding on the tumulus, the surrounding trench and the unaltered surrounding area, we show that the tumulus was built almost completely from the surrounding soils and that 17% of its original volume was displaced by destruction and erosion. Based on this mass balance the strongly destroyed and eroded original surface of the tumulus and its surrounding trench is reconstructed.

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Modeling of a constant Q: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique

Cited by 345 publications

References 18 publications

Optimized viscoelastic wave propagation for weakly dissipative media

Optimized viscoelastic wave propagation for weakly dissipative media

Evolution of the oceanic lithosphere inferred from Po/So waves traveling in the Philippine Sea Plate

The Yığma Tepe of Pergamon: stratigraphic construction of a monumental tumulus from seismic refraction measurements

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