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Reply to Comments on “ Separation of Qi, Qs from 1 passive data at Mt. Vesuvius: A reappraisal of the
seismic attenuation estimates” by Ugalde, A. and Carcole, E
Edoardo del Pezzo, Francesca Bianco, Lucia Zaccarelli
To cite this version:
Edoardo del Pezzo, Francesca Bianco, Lucia Zaccarelli. Reply to Comments on “ Separation of Qi, Qs from 1 passive data at Mt. Vesuvius: A reappraisal of the seismic attenuation estimates” by Ugalde, A. and Carcole, E. Physics of the Earth and Planetary Interiors, Elsevier, 2009, 173 (1-2), pp.195.
�10.1016/j.pepi.2008.10.002�. �hal-00532181�
Accepted Manuscript
Title: Reply to Comments on “ Separation of Qi, Qs from 1 passive data at Mt. Vesuvius: A reappraisal of the seismic attenuation estimates” by Ugalde, A. and Carcole, E Authors: Edoardo Del Pezzo, Francesca Bianco, Lucia Zaccarelli
PII: S0031-9201(08)00295-1
DOI: doi:10.1016/j.pepi.2008.10.002 Reference: PEPI 5079
To appear in: Physics of the Earth and Planetary Interiors Received date: 10-9-2008
Accepted date: 1-10-2008
Please cite this article as: Del Pezzo, E., Bianco, F., Zaccarelli, L., Reply to Comments on “ Separation of Qi, Qs from 1 passive data at Mt. Vesuvius: A reappraisal of the seismic attenuation estimates” by Ugalde, A. and Carcole, E, Physics of the Earth and Planetary Interiors (2008), doi:10.1016/j.pepi.2008.10.002
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Page 1 of 5
Accepted Manuscript
Reply to Comments on " Separation of Qi and
1
Qs from 1 passive data at Mt. Vesuvius: A
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reappraisal of the seismic attenuation
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estimates" by Ugalde, A. and Carcolé , E.
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Edoardo Del Pezzo, Francesca Bianco and Lucia Zaccarelli
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INGV sezione di Napoli Osservatorio Vesuviano
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Key words: seismic scattering, elastic attenuation
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1 Introduction
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The paper by Del Pezzo et al. (2006) , hereafter named DPBZ, deals with the
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estimate of the seismic attenuation in the high frequency range for the volcanic
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area of Mt. Vesuvius. In particular DPBZ use a method based on the …t of the
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observed local earthquake coda envelopes to the radiative transfer classical
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equation (see Sato and Fehler, 1998 for a wide and exhaustive review on this
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argument) in terms of the intrinsic attenuation and the scattering attenuation
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coe¢ cients.
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Ugalde and Carcolé in their comment (hereafter named UC) discuss two points
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of DPBZ that we summarize here in their essence:
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a) Two approximations of the exact solution of the 3-D radiative transfer
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model have been calculated, that discussed by Zeng (1991) - hereafter Z91 -
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expressed by Formula (5) of UC, and that by Paaschens (1997) - hereafter P97
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- expressed by Formula (6) of UC. UC show that P97 is more accurate than
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Z91, which is instead used in DPBZ.
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b) DPBZ obtain the separated estimates of intrinsic- and scattering-attenuation
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coe¢ cients, respectively i and s, …rst stacking the normalized energy en-
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velopes (starting at 2T s lapse time) and then …tting the experimental data
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with the normalized (in the same way) theoretical curve. UC disagree with
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this procedure. Their opinion is that DPBZ should have inverted the single
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energy envelopes and then have averaged the results obtained.
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Preprint submitted to Elsevier 10 September 2008
Testo
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Accepted Manuscript
In the following we reply to points a) and b) in two separate sections.
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2 Reply to point a)
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UC show that P97 is more accurate than Z91. This is true, with no doubts at
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all. At the time DPBZ was written (2005) the authors were not informed of
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P97, being P97 published on a General Physics Journal in a sector di¤erent
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from that of Seismology. The authors of DPBZ are grateful to A. Ugalde and
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E. Carcolè for having informed that the approximation described in P97 is
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better than that in Z91; accordingly they already changed the formula in Z91
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with that in P97 in their Matlab …les for a possible use in their future works.
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However, due to the assumptions that are at the base of DPBZ as well as
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to the data scatter produced by the high level of background seismic noise
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in their study, the separated estimates of intrinsic- and scattering-attenuation
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coe¢ cients, respectively i and s, are a¤ected by an uncertainty (see Figure 7
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of DPBZ) that results so high that the use of P97 instead of Z91 is practically
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ine¤ective. In addition, but only for the sake of precision (or in other words
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to be scholastic), in DPBZ the authors use theoretical curves normalized at
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12 seconds lapse time to …t their data. In the plot of Figures 1 and 2 of UC
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the percent ratio between the absolute P97 and Z91 instead of the normalized
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values used in DPBZ is reported. In the present reply we plot in Fig. 1 the
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percent ratio between the normalized P97 and Z91, estimated for the values
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of i and s estimated by DPBZ for Mt. Vesuvius. Due to the normalization,
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the bias is much lower than that calculated by UC.
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3 Reply to point b)
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We generate two vectors of normally distributed values ik and sk in the
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error range determined in DPBZ for the estimate of i and s (at 3 Hz, see
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Fig. 7 of DPBZ) and a vector of uniformly distributed (between 0.5 and 5
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km) synthetic values of source station distances, rk, k 2 [0; 1000] ; roughly
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corresponding to the real distribution of measured source-BKE distances for
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the seismicity at Mt. Vesuvius. Then, for each value of k we calculated the
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theoretical energy envelopes using Formula (6) of UC for ik , sk and rk. For
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these synthetical envelopes we eventually calculate the stack in the same way
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as described in DPBZ. Indicating the average of ik , sk and rk respectively
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with i , s and r we plot in Fig. 2 the energy envelope calculated using
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Formula (7) of UC for i , s and r and the stacked envelope of the synthetic
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traces. The two quantity are practically coincident in the range of lapse time
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used for the analysis done at Mt. Vesuvius by DPBZ.
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2
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4 Figure Captions
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Figure 1 - Percent ratio between Z91 and P97 ( 100 (1 (EZeng/ EP aasschens);
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continuous line) and between Z91-normalized and P91-normalized (100 (1
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(EZengN/ EP aasschensN), dashed line) as a function of lapse time, in the lapse
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time interval between 3.6 and 12 s, used by DPBZ.
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Figure 2 - Normalized energy envelope calculated for the average (dashed) and
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stack of the energy envelopes (continuous). The vertical bar mark the lapse
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time at which DPBZ start their analysis.
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5 References
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References
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Del Pezzo, E., Bianco, F., Zaccarelli, L. (2006) Separation of Qi and Qs
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from passive data at Mt. Vesuvius: a reappraisal of the sismic attenuation
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estimates, Physics of the Earth and Pl. Int., 159, 202-212
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Paasschens, J.C.J. (1997) Solution of the time dependent Boltzmann equation,
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Phys. Rev. E. 56, 1135-1141
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Sato, H. and Fehler, M. (1998) Seismic wave propagation and scattering in
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the heterogeneous earth. Springer and Verlag, New York.
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Zeng, Y. (1991) Compact solutions for multiple scattered wave energy in time
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domain, Bull. Seism. Soc. Am 81, 1022-1029
84
3
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Accepted Manuscript
2 4 6 8 10 12
Lapse time (s)
0 1 2 3 4 5
Percen t ratio
100*[1-(EZeng / EPaasschens)]
100*[1-(EZengN / EPaasschensN)]
Figure 1
Figure 1
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Accepted Manuscript
4 6 8 10 12 14
Lapse time (s) 1
10 100
Normalized energy envelope
Energy Envelope for the average parameters Average (Stack) of the energy envelopes
Figure 2
Figure 2
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