Seismic recording of small zero frequency displacement from moderate events

1. Introduction

[2] Since mid sixties Press [1965] stressed the importance of analyzing the low and zero frequency displacement associated with seismic events as invaluable information for deriving a complete image of source properties and strain features. Indications on the final seismic moment and slip distribution are provided by the static offset, while possible relatively slow strain release and postseismic relaxation can be evidenced starting from precise coseismic observations. Generally, such measures are accomplished by using strainmeters or geodetic instruments. In recent times, with the large use of high dynamic broadband digital instruments, seismic recordings have also been successfully used to recover the static displacement associated with large earthquakes either from double integration of close strong motion recordings [see Boore et al., 2002, and references therein] or from very broadband seismometer recordings. The June, 9, 1994, 660 km deep earthquake (M_w = 8.3) produced a well visible static offset of 6 mm [Zhu, 2003] at the very broadband STS-2 instruments of the BANJO temporary array, about 600 km away. This favorable circumstance resulted from the large magnitude, allowing good quality recordings, and the considerable hypocentral depth, which prevented the development of energetic surface waves and the arrival of strong multiple phases that could possibly mask the permanent displacement. In the case of the Bolivian event, near-field component of ground motion could be detected even at teleseismic distances. In fact, Vidale et al. [1995] observed near-field effects recorded at Californian stations, in terms of a small offset following the P wave pulse and representing the initial part of the expected ramp-like displacement between P and S waves.

[3] As for moderate magnitude events, only dynamic effects of near- and intermediate-field have been observed on seismic instruments. A nice example is described by Kanamori et al. [1990], who observed a clear ramp between P and S arrivals for a M_L = 4.9 event at the distance of 3.9 km, on a STS-1 instrument waveforms. It should be noticed that, these observations are very important for rapid characterization of the source [Uhrhammer, 1993]. However, except for the observation of Uhrhammer et al. [1999] (M_w = 5.1 earthquake recorded at 12 km from the source), no recognition of static offset for moderate events has been reported yet. The lack of observation is mainly due to the small amplitude of the permanent displacement, often superimposed by late arrivals, surface waves, and low period noise, and to difficulties in removing the instrument response, usually resulting in a baseline drift which hinders a reliable measure of the static offset. In this work, we attempt at an estimate of the permanent displacement from seismic broadband recordings of a couple of moderate magnitude crustal events, about 50 km away from the source.

2. Data Analysis and Results

[4] We analyzed the broadband waveforms of two southern Italy earthquakes recorded at the STS-2 instrument of the MedNet station CII (Table 1 and Figure 1). Due to the relatively large hypocentral depth, the contribution from surface waves and crustal multiples at local distance is smaller than what would be for a shallow crust event.

[5] As pointed out by Zhu [2003], the STS-2 has a flat velocity response above 8.3 mHz, which falls below 60 dB only at about 2 mHz, i.e. 500 s, far beyond the expected duration of the transient phase for moderate magnitude events. This means that the static offset has already fully developed when the instrument restoring force makes the velocity again to oscillate around zero.

[6] When dealing with the lower end of the spectrum, the removal of the instrument response is crucial. In the case of the Bolivian earthquake Jiao et al. [1995] estimated a subsidence of 2 cm at the BANJO array stations. On the other hand, Ekström [1995] showed that the normal mode prediction is only 6 mm and suggested that the discrepancy could possibly derive from the instabilities inherent in the deconvolution process. More recently, Zhu [2003] proposed a technique to recover the ground displacement from broadband seismic recordings which proved to be very effective. He applied the procedure to the same data used by Jiao et al. [1995] obtaining a static offset much closer to the prediction and more reliable waveforms. In particular, the deconvolved displacement evidenced an overshoot closely following the direct S wave arrival corresponding to Rayleigh waves just starting to develop at 600 km away, as expected for a 630 km deep earthquake, but missing in the data showed by Jiao et al. [1995].

[7] The technique, described in detail in the paper of Zhu [2003], is based on the application of a time domain recursive filter in order to remove the instrument response. This produces only negligible difference up to 1 Hz with respect to the exact response, but ensures stable signals, not altering the long period part of the spectrum.

[8] We applied this procedure to the data and then obtained the displacement by simple integration (Figure 2). The sampling rate is 0.05 s. All the waveforms display a large drift that makes the estimate of the permanent displacement very problematic and even masks earthquake signals. Again following Zhu [2003], we assumed that both the pre- and post-transient signal could be approximated by the same nth-order polynomial, with the addition of a constant term for the latter, representing the static displacement. The best fitting coefficients are searched by a least square inversion. Thus, the procedure returns n + 1 coefficients plus the static offset which is a direct result of the inversion. Corrected ground motion is then computed by subtracting the polynomial from the deconvolved displacement. By using a 4th-order polynomial for both events we obtained the waveforms displayed in Figures 3 and 4.

3. Discussion

[9] The retrieved ground motion for the two events displays well resolved and stable offsets on the horizontal components. No clear static displacement can be distinguished on the vertical components, being very small as expected due to source mechanism (see below). In addition to static offset, we remark that the distinct ramp between the first P and S arrivals and the presence of transversal motion before the first S arrival are unequivocal effects of near-field contribution (Figures 3a and 4a).

[10] For both events, the static offsets range approximately from 0.31 to 0.60 mm on the horizontal components, while much smaller (about one order of magnitude) coseismic permanent displacement results on the vertical, though not measurable with some confidence, due to long period noise. These numbers are well below the usual geodetic resolution, generally on the order of 1 centimeter and a few millimeters at best.

[11] In order to check our results, we computed reflectivity synthetic seismograms (Figures 3 and 4) for point sources embedded in a three layered crust over a halfspace (Table 2). We derived moment tensor and centroid depth by applying the technique for broadband waveform inversion routinely in automated use at the National Research Institute for Earth Science and Disaster Prevention (NIED - Tsukuba, Japan) and the Berkeley Seismological Laboratory (UC Berkeley - CA, USA) [e.g., Fukuyama and Dreger, 2000]. By inverting single station displacement waveforms in the frequency range 0.02 ÷ 0.05 Hz, we obtained the focal mechanisms displayed in Figure 1 and listed in Table 3. The difference between the hypocentral (Table 1) and centroid depths is mainly to be ascribed to the prevalent updip propagation of the sources, as evidenced by images of the coseismic slip [Vallée and Di Luccio, 2005].

[12] Incidentally, we notice that a 22 km deep source for the first event (Δ = 50.5 km) produces, respectively on the east and north components, permanent offset about 90% and 10% of what predicted for a source depth of 11 km.

[13] The computed predictions are in excellent agreement with the corrected displacement waveforms, well reproducing all the main features of the recorded waveforms, in particular for the near-field effects, and further validating our estimate of the static offsets. Our results also evidence that, at CII, the whole permanent displacement developed within 50 seconds from the first P wave arrival and no additional, possibly aseismic, offset occurred in the following minutes.

[14] In general, tilt could affect the observed displacement, with effects mostly visible on the horizontal components and almost negligible on the vertical. Due to the lack of other recording sites close to CII and taking advantage of the above validated synthetics, we quantified the theoretical tilt by computing synthetic seismograms at a couple of locations around CII. By using the relationship between displacement and a permanent tilt for a mechanical pendulum seismometer suggested by Rodgers [1968], we obtained a corresponding apparent offset of 0.02 mm. This is less than 10% of the smallest horizontal offset observed at CII.

[15] According to Vallée and Di Luccio [2005], the rupture occurred on a W-E oriented plane with horizontal dimension of about 8 km. Unfortunately, even though the source geometry and the station azimuth are particularly favourable, the epicentral distance is about 4 times the fault length and there is no chance of discriminating the source plane from the estimated static offset. In fact, we checked this possibility. We sketched each conjugate plane by using three 11 km deep point sources aligned along the strike, with a 4 km spacing, and obtained synthetic seismograms for each plane by summing the contributions from the three sources (Figure 5). The very small difference between the surface permanent displacement predicted for the two planes prevents any discrimination of the actual fault plane from the analysis of the coseismic static offset.

[16] We also investigated the largest aftershocks, all with magnitude below M_w = 4.6, but the small amplitude, relative to the long period noise, did not allow reliable estimate of the surface static displacement.

4. Conclusions

[17] In this work we described the use of modern, high dynamic, broadband stations to measure the coseismic surface permanent displacement produced by moderate magnitude events. The example of the 2002 Molise earthquakes demonstrates that stable and reliable estimate can be obtained in excellent agreement with synthetic predictions. The resulting values ensure the possibility of evaluating the coseismic static offset for very small displacement, on the order of tenths of millimeters, well below usual resolution of geodetic instruments. This indicates the great potential of high dynamic broadband instruments in providing estimates of the surface coseismic static displacement. A dense seismometer network could then be used to integrate the geodetic measurements in order to image the surface displacement field and, for closely spaced stations, provide estimates for the coseismic strain.