Isometric method: Efficient tool for solving non-linear inverse problems

Málek, Jiří; Růžek, Bohuslav; Kolář, Petr

doi:10.1007/s11200-007-0028-1

Cited by 13 publications

(7 citation statements)

References 14 publications

(9 reference statements)

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“…Inversion is solved by the isometric method (IM). It is a fast algorithm developed by Málek et al (2005) and tested by Málek et al (2007). It combines features of several standard inverse methods, particularly the simplex method, Newton's least squares method and simulated annealing.…”

Section: Inversion Of Group Velocity Dispersion Curvesmentioning

confidence: 99%

Seismic waves velocities inferred from the surface waves dispersion in the Male Karpaty Mountains, Slovakia

Lukesova¹

2019

Acta Geodynamica Et Geomaterialia

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The study area of Western Carpathians belongs to one of the most seismically active regions in Slovakia, where the available velocity models are not precise enough for accurate location and determination of focal mechanism. To improve the uppermost part of the currently used models, seismic surface wave data from two blasts in the quarry Rohožník, recorded at the MKnet local seismic network, were analyzed. Group velocity dispersion curves of Rayleigh and Love waves were determined by the frequency-time analysis. A mean group velocity dispersion curve for Love and Rayleigh waves for the central part of the MKnet network was settled and consequently joint inversion, for the period range 0.9-2.7 s, was performed to obtain a 1-D velocity model using the isometric method. The 11-layered model extends to depth of 2.5 km and indicate increase of the velocities from the surface down to the depths of 0.9 km. Then, velocities slightly decrease. The minimum of the low-velocity zone is at the depth of 1.8 km after which the velocities moderately increase to the velocity of the halfspace with v P = 5.35 km/s and v S = 2.96 km/s.

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Section: Inversion Of Group Velocity Dispersion Curvesmentioning

confidence: 99%

Seismic waves velocities inferred from the surface waves dispersion in the Male Karpaty Mountains, Slovakia

Lukesova¹

2019

Acta Geodynamica Et Geomaterialia

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“…The transformations through similarity were also applied to other solutions for nonlinear inverse problems (Málek et al, 2007). The transformations through similarity are also commonly used in close range photogrammetry, in which the rotation angles are much larger in comparison to the traditional aerial survey (Jue, 2008).…”

Section: Photogrammetric Transformations In An Oblique Systemmentioning

confidence: 99%

New approach to isometric transformations in oblique local coordinate systems of reference

Stępień

Zalas

Ziębka

2017

Geodesy and Cartography

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Abstract:The research article describes a method of isometric transformation and determining an exterior orientation of a measurement instrument. The method is based on a designation of a "virtual" translation of two relative oblique orthogonal systems to a common, known in the both systems, point. The relative angle orientation of the systems does not change as each of the systems is moved along its axis. The next step is the designation of the three rotation angles (e.g. Tait-Bryan or Euler angles), transformation of the system convoluted at the calculated angles and moving the system to the initial position where the primary coordinate system was. This way eliminates movements of the systems from the calculations and makes it possible to calculate angles of mutual rotation angles of two orthogonal systems primarily involved in the movement. The research article covers laboratory calculations for simulated data. The accuracy of the results is 10 -6 m (10 -3 regarding the accuracy of the input data). This confi rmed the correctness of the assumed calculation method. In the following step the method was verifi ed under fi eld conditions, where the accuracy of the method raised to 0.003 m. The proposed method enabled to make the measurements with the oblique and uncentered instrument, e.g. total station instrument set over an unknown point. This is the reason why the method was named by the authors as Total Free Station -TFS. The method may be also used for isometric transformations for photogrammetric purposes.

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“…The isometric method (IM) is used for solving the inversion of dispersion curves. It is a fast inversion algorithm developed and tested by Málek et al (2005Málek et al ( , 2007. It combines the features of several standard inverse methods, particularly the simplex method, Newton's least-squares method and simulated annealing (Tarantola 1987).…”

Section: Surface Wave Phase Velocity Determinationmentioning

confidence: 99%

“…The inversion is performed by the isometric method (Málek et al . ). By combining these 1‐D velocity models, a pseudo 2‐D S‐wave velocity distribution across the fault is obtained.…”

Section: Introductionmentioning

confidence: 97%

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Combining surface waves and common methods for shallow geophysical survey

Gaždová

Kolínský

Vilhelm

et al. 2014

Near Surface Geophysics

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Geophysical data were acquired during a survey of the Hluboká Fault in the Czech Republic, Central Europe. The recorded surface waves are studied in the frequency range 8‐200 Hz. Phase velocity dispersion curves of Rayleigh and Love waves are determined from pairs of three‐component seismograms with a 5 m receiver spacing by means of a frequency‐time analysis along the profile. Rayleigh waves are analysed on the vertical (Z) and radial (R) components and Love waves on the transversal (T) component. Dispersion curves from the vertical component are then inverted to 1‐D S‐wave velocity models using the isometric method. A set of 1‐D S‐wave velocity models representing a pseudo 2‐D S‐wave velocity distribution along the profile is obtained. This velocity distribution is compared with the results of other geophysical methods and also with direct observation from a shallow paleoseismic trenching. A combination of the S‐wave velocities obtained from the surface wave analysis and P‐wave velocities from refraction tomography is used to estimate the Poisson ratio distribution. It is shown that the resolution capabilities of surface waves are comparable in this case with electric resistivity tomography in near surface medium and with P‐wave tomography in the depths exceeding approx. 15 metres.

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Isometric method: Efficient tool for solving non-linear inverse problems

Cited by 13 publications

References 14 publications

Seismic waves velocities inferred from the surface waves dispersion in the Male Karpaty Mountains, Slovakia

Seismic waves velocities inferred from the surface waves dispersion in the Male Karpaty Mountains, Slovakia

New approach to isometric transformations in oblique local coordinate systems of reference

Combining surface waves and common methods for shallow geophysical survey

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