Publications (revised 12 April 2010)
Kolář, P., 2010, Some possible correlations between electro magnetic emission and seismic activity during West Bohemia 2008 earthquake swarm, submited to Solid Earth (SE) http://www.solid-earth.net/, status: accepted for publication as a discussion paper in SED on 1 April, 2010
Kolář P. a B. Růžek, P. Adamová, 2009: Modelování seismického zdroje jako reálná testovací úloha pro nelineární inversní algoritmus, (in Czech) in Technical Computing Prague 2009, ISBN 978-80-7080-733-0, Praha, p.56 (abstrakt)
Růžek, B., P., Kolář and M. Kvasnička, 2009: Robust solver of a system of nonlinear equations, in Technical Computing Prague 2009, ISBN 978-80-7080-733-0, Praha, p.90 (abstrakt)
Kolář, P., 2008b, Reflect2 - semi-interaktivní nástroj pro heuristické zkoumání některých anomálií pozorovaných v seismogramech západočeských zemětřesení (představení verze 1). (in czech), in Technical Computing Prague 2008, Humusoft, ISBN 978-80-7080-692-0, Prague, p. 59, (abstrakt)
Kolář, P., 2008a, How much can we trust some moment tensors or an attempt of seismic moment error estimation - 2. data reinterpretation, methodology improvement. Acta Geodyn. et Geomater, Vol. 5, No. 1(149), 31 – 39 (abstrakt)
Vavryčuk, V., Bohnhoff, M., Jechumtálová, Z., Kolář, P. and Šílený, J., 2008, Non‑double‑couple mechanisms of induced micro‑earthquakes during the 2000 injection experiment at the KTB site, Germany: a result of tensile faulting or anisotropy of a rock?, Tectonophysics. Roč. 456, č. 1-2, p. 74-93. ISSN 0040-1951
Málek, J., Růžek, B. and Kolář, P., 2007, Isometric method: efficient tool for solving non-linear inverse problems, Studia Geophys. et Geodet., Vol. 51, No. 4, pp. 469 – 490
Kolář, P., 2007d, MEPL2 - an interactive‑batch tool for full seismic moment tensor potting, in Technical Computing Prague 2007, ISBN 978-80-7080-658-9, Prague, p. 76, (abstract)
Kolář, P., 2007c, Symbolical Numeric Process for error transformation, in Technical Computing Prague 2007, ISBN 978-80-7080-658-9, Prague, p. 77, (abstract)
Kolář, P.: 2007b: How much can we trust some moment tensors or an attempt of seismic moment error estimation, Acta Geodyn. et Geomater, Vol. 4, No. 2(146), 13 – 20 (abstract)
Kolář, P., 2007a: OP, Interactive seismic viewer “OP” – short review. Acta Geodyn. et Geomater, Vol. 4, No. 2(146), 21 -25 (abstract)
Kolář, P.: 2006b: Evaluation of Full Seismic Moment Tensor from Isotropic, CLVD and Double-Couple Components, Acta geodyn. et geomech, Vol.3, No.4 (144), pp. 1-3 (abstract)
Kolář, P.: 2006a: Interactive viewer of seismic signals - “OP”, (in Czech), in Technical Computing Prague 2006, ISBN 80-7080-616-8, pp. 51 (abstract)
Kolář P., 2005b: Interactive tool for demonstration of the effect of casual and acausal frequency filtering on seismic signals, Acta Geodyn. Geomater., 2, 4 (140), pp. 99-105 (abstract)
Kolář P., 2005a: Několik utilit pro komfortnější ovládání interaktivního grafického rozhraní (in czech), In: Technical Computing Prague 2005 – 13th Annual Conference Proceedings, Praha, ISBN 80-7080-577-3, pp. 58. (abstract)
Kolář, P. and Boušková A., 2003b: On some anomalies of vP/vS ratio of West Bohemia swarm 2000 – preliminary results, Acta Montana, 22 (129) ser. A, 51 – 57 (abstract)
Kolář, P., 2003a: Seismic source model form West Bohemia seismograms inversion - the method and preliminary results for ML2.0, Jan 17 1997 event, Acta Montana, 22 (129) ser. A, 33 – 49 (abstract)
Kolář, P., 2000b: Comparing tests of Several Non‑linear Inversion Methods on There Simple Synthetic Problems, Acta Montana, 15(116) ser. A, pp. 84 – 93 (abstract)
Kolář, P., 2000a: Two Attempts of Study of Seismic Source from Teleseismic Data by Simulated Annealig Non-linear Inversion, J. of Seism., 4, pp.197-213 (abstract)
Kolář, P., 1999: Energy of Seismic Waves Radiated by Finite Circular Source -Numerical Approach. Acta Montana, 14(114) ser. A, pp. 39 – 54 (abstract)
Kolář P., 1994:Simultaneous Determination of the Source Mechanism and the Seismic Wave Energy, Pageoph, 143, No.4, pp.654-671, (abstract)
Acta Geodyn. et Geomater, Vol. 5, No. 1(149), 31 – 39, 2008
How much can we trust some moment tensors or an attempt of seismic moment error estimation -2 data reinterpretation, methodology improvement
Geophysical Institute, Czech Acad. of Sci., Boční II, 141 Praha 4 – Spořilov
Non-liner inversion of ratio of (relative) P to S waves amplitudes of 3 selected KTB events was performed in Kolář (2007a) to determine moment tensors (MTs). Here further development of the method is presented: (i) re-calibration of the seismograms, (ii) re-interpretation of the S wave maximal amplitudes readings, (iii) a linear inversion of the (re-calibrated) amplitudes including MTs errors determination, and (iv) four methods of transformation of MT errors into errors of their decomposed parts. Generally, the new results confirm previous ones, however remain some open questions about MT errors transformation. New methodology is more accurate and data processing more user-friendly.
Keywords:seismic moment tensor inversion, error estimation, seismic moment tensor decomposition
Acta Geodyn. et Geomater, Vol. 4, No. 2(146), 13 – 20, 2007
How much can we trust some moment tensors or an attempt of seismic moment error estimation
Geophysical Institute, Czech Acad. of Sci., Boční II, 141 Praha 4 – Spořilov
During routine processing of selected events of an active KTB experiment it has appeared doubts concerning data reliability and consequently the reliability of results based on them. In the paper 3 events are studied in detail, full seismic moment tensors, as well as their errors, are determined (by non-linear inversion of P/SH waves ratios). It is shown that for the processed low constrained data moment tensor (MT) can be determined, however the relative error is of order of first tens of percent; the results also considerably depend on the way of data picking, used medium model, way of Cost function construction, etc. Any subsequent geophysical interpretation therefore should takes into account this uncertainty. MTs are finally decomposed into DC and non‑DC parts, MTs errors are also transformed.
Keywords: seismic moment tensor inversion, error estimation, seismic moment decomposition
Acta Geodyn. et Geomater, Vol. 4, No. 2(146), 21 -25, 2007
Interactive seismic viewer “OP” – short review
Geophysical Institute, Czech Acad. of Sci., Boční II, 141 Praha 4 – Spořilov
Abstract: We introduce an interactive seismic viewer “OP” (developed in MATLAB platform), primary designated for detailed processing of selected events. Few examples of graphical outlook are presented (main display window, particle motion diagram, etc.), available tools are briefly described, uncommon special tools (simultaneous display of original and filtered signal or time‑spatial correlation of seismogram components) are emphasized. Features of the viewer are discussed, some programming solutions are also mentioned.
Keywords: interactive seismic viewer, seismogram processing, MATLAB
Acta geodyn. et geomech, Vol.3, No.4 (144), pp. 1-3, 2006
Evaluation of Full Seismic Moment Tensor from Isotropic, CLVD and Double-Couple Components
Geophysical Institute, Czech Acad. of Sci.
Abstract: Formulas for full seismic moment tensor composition are present, i.e. moment tensor is express as a function of ISO, CLVD, DC, strike, dip, rake, where ISO is amount of isotropic part, CLVD is amount of compensated liner‑vector dipole and DC is amount of pure double couple. Two forms of final formulas are given: i, two matrixes multiplication, ii, extension of “classical” formulas for 6 independent moment tensor elements.
Keywords: evaluation of full seismic moment tensor, point source representation
Acta Geodyn. Geomater., Vol.2, No.4 (140), 99-105, 2005
INTERACTIVE TOOL FOR DEMONSTRATION OF THE EFFECT OF CAUSAL AND ACAUSAL FREQUENCY FILTERING ON SEISMIC SIGNALS
Geophysical Institute, Boční II, 141 37 Praha 4 – Spořilov
ABSTRACT: Although causal and acausal (zero-phase) frequency filtering are procedures routinely used in seismic signal processing, many users of respective software tools are not fully aware of at first glance subtle, but for the exact interpretation of the filtered time series significant, differences between the two methods. Typical effects are waveform distortions due to the non-linear phase response in the former case, and generation of spurious anticipatory signal components due to the acausality of the
process in the latter. In the present paper an interactive MATLAB program for the tutorial demonstration of the mentioned effects is described. The program allows processing of external (real) seismograms as well as internally generated synthetic
seismic signals. All parameters specifying the synthetic signal and the filter properties (type, order, corner-frequencies) can be entered interactively. The amplitude and phase responses of the filters and the results of the filtering procedure are displayed,
and the kinematic as well as dynamic parameters of the filtered signals such as onset times, time shifts, time differences and amplitudes can be picked with the cursor. Typical examples of causal vs. acausal filtering are given to demonstrate the performance of the program and the differences between the two approaches (there are presented two synthetic examples to illustrate basic filter behaviour and two examples of real seismograms analysis).
KEYWORDS: effect of causal and acausal filtration; seismic signal processing
Acta Montana, 22 (129) ser. A, 51 – 57,2003
On some anomalies of vP/vS ratio of West Bohemian swarm 2000 – preliminary results
Petr KOLÁŘ and Alena BOUŠKOVÁ
Abstract: Some irregularities of vP/vS ratio were observed in West Bohemia region during routine processing. In the present work we try to quantify these variations in 9 time phases of Swarm 2000. We seek for azimuthal dependence residua, which fit data better then a constant vP/vS value. The search of particular values is preformed by (Boender - Csendes) non-linear inversion method. We were able to distinguish such residua and to observe their time dependency (however with lower reliability). In addition we try to interpret observed anomalities of arrival of S waves in term of (horizontal) S waves velocity quazi‑anisotropy; the difference between max and min value was found to be about 1%, the maximum oriented in WSW - ENE direction. Our results can serve as an indication of composed geological structure and complexity of the processes in the area, which should be investigated in more detailed way.
Acta Montana, 22 (129) ser. A, 33 – 49, 2003
Seismic source model from West Bohemia seismograms inversion – the method and preliminary results for ML=2.0, Jan 17 1997 event
Key words: non-linear inversion, seismic source model, West Bohemia region
Summary: The aim of this work was to determine a source model by inversion of seismograms. An event of 1997 West Bohemia swarm was processed; Boender - Csendes non-linear inversion method (Boender et al., 1982, Csendes, 1988) was used for inversion of records from 7 closest stations. A source model composed of one or two point sub‑sources was considered, pure double couple optionally extended with non-double couple components. We supposed 1D medium model, optionally amended to reflecting interface situated closely to the source (horizontally or almost vertically oriented reflecting interface was considered). We were looking for optimal values of source parameters; we also tried to determine statistical reliability of each solution and made an attempt of inverted parameters error estimation. In general, the models with more inverted parameters yield better fit between observed and synthetic data, however with different statistical reliability.
In the comparison with the simple DC point source the model composed of two double-couple point sub‑sources (with different mechanisms and different source time function - STF) fit the data more satisfactory and with sufficient statistical significance. The influence of non-DC components as well as of reflecting interface(s) was found to be smaller or under statistical significance even if the fit itself improved also.
Acta Montana, 15(116) ser. A, pp. 84 – 93, 2000
Comparing tests of several non-linear inversion methods on three simple synthetic problems
Geophysical Institute, Academy of Sciences of Czech Republic
Abstract: Efficiency of several non-linear inversion methods (Simplex, Simulated Annealing with Simplex, Very Fast Simulated Annealing, Differential Evolution, Boender's method) is tested on three simple synthetic testing problems (multidimensional parabola, pseudo-location problem, quadratic function). We increase the number of inverted parameters and express efficiency in numbers of forward problem evaluations. As the testing problems are rather simple, the simplest method (the Simplex) yields the best result, more sophisticated methods reached the result with more effort. However, from a point of view of further exploitation of the inversion methods for real problems, the Boender’s method seems to be the most promising.
Keywords: Simplex, Simulated Annealing with Simplex, Very Fast Simulated Annealing, Differential Evolution, Boender's method, efficiency comparison.
Displayed with kind permission of Kluwer Academic Publishers
J. of Seism., 4, pp.197-213, 2000
TWO ATTEMPTS OF STUDY OF SEISMIC SOURCE FROM TELESEISMIC DATA BY SIMULATED ANNEALING NON-LINEAR INVERSION
Key words: cooling schedule, control parameters, seismic source inversion, simulated annealing, very fast simulated annealing,
SUMMARY: Two seismic source studies using teleseismic data are performed by Simulated Annealing (SA), a non-linear inversion method. The Very Fast Simulated Annealing (VFSA) algorithm is used and only teleseismic data are inverted. We have designed a fast and efficient way of multiple direct problem evaluation, which is based on pre-calculating of the elementary Green’s function. During the process we set the values of the inversion control parameters (temperature, number of iterations) and modified the cooling schedule. In the current version, the inversion seeks for the point source mechanism, the depth of the source, the scalar moment and the source time function (STF). The method is applied to two earthquakes: 18 Nov. 1992 in Greece, M5.9 and 14 Sep. 1995 in Mexico, M7.3. The calculation is performed on a simple 1D model of the structure. For the first earthquake the inversion recovered the solution fairly well; for the second the solution was less acceptable. However, we do not consider this fact to be a failure of the method, but a consequence of an inadequate model of the source and of the medium structure. A casual attempt of reliability determination was also performed; the obtained values of errors are reasonable, except for a few cases when the method failed.
Acta Montana, Series A No.14 (114), 39-54, 1999
Energy of Seismic Waves Radiated by Finite Circular Source - Numerical Approach
Geophysical Institute, Academy of Sciences of the Czech Republic
Summary:We used a method, which allowed determined energy radiated in seismic waves from a seismogram recorded at one station only. In present work we compared how the results can differ if final source was neglected and replaced by a point source. The investigation was performed by numerical experiments. To be able to evaluate synthetic seismograms we developed a suitable model of the kinematic finite circular source. We investigated the influence oftake-off angle,distance,rakeandrupture velocity. We found that omitting a finite source can affects a final seismic energy, but the difference is less than an order of magnitude. The influence of thetake-off anglewas found to be the most significant, the influence of other investigated parameters (distance,rake,rupture velocity) is of less importance. The dependency of determined energy ontake-off angleis monotonous in general, however some irregularities for S waves energy were discovered.
Pageoph, 143, No.4, pp.654-671, 1994
Simultaneous Determination of the Source Mechanism and the Seismic Wave Energy
Geophysical Institute, Boční II, Prague 4 - Spořilov, 141 31, Czech Republic
abbreviated title: Determination of the Mechanism and the Energy
Summary: It is necessary to know the source mechanism for the determination of the seismic energy of seismic waves from the seismogram recorded at one station. For sparse data (selected events of the 1985/86 WesternÄBohemia earthquake swarm) the source mechanisms can not be determined from P-wave first motions. Therefore, a new method of determining the source mechanism simultaneously with the energy calculated from observations at two stations has been developed. The method is described and tested. Advantages, disadvantages and the stability of the method are discussed.
Keywords: source mechanism determination, seismic energy.