Characterization of alpine rockslides using statistical analysis of seismic signals

Authors


Abstract

[1] Seismic data analysis is a powerful tool for remote characterization of rock slope failures. Here we develop quantitative estimates of fundamental rockslide properties (e.g., volume) based solely on data from an existing regional seismic network. We assembled a data set of twenty known rockslides in the central Alps (with volumes between 1,000 and 2,000,000 m3) and analyzed their corresponding seismograms. Common signal characteristics include emergent onsets, slowly decaying tails, and a triangular spectrogram shape. The main component of seismic energy is contained in frequencies below ∼3–4 Hz, while higher-frequency signals may be caused by block impacts. Location estimates were generated using automatic arrival time picks and resulted in a mean location error of 10.9 km. A linear relationship for the detection limit of a rockslide as a function of volume was identified for our seismic station network. To estimate rockslide volume, runout distance, drop height, potential energy, and Fahrböschung (angle of reach), we extracted five simple metrics from each seismogram: signal duration, peak value of the ground velocity envelope, velocity envelope area, risetime, and average ground velocity. Using multivariate linear regression, the combination of duration, peak envelope velocity, and envelope area best estimated event parameters, with r2 values ranging between 0.8 and 0.88. Three new rockslides were then used to validate our method, and volume, runout, drop height, and potential energy were estimated within the correct order of magnitude. When provided with a suitable data set of rockslide events, our method can be easily adapted to other regions and seismic networks.

1. Introduction

[2] Increasing access and settlement in alpine regions presents greater exposure to rock slope hazards for both people and infrastructure. Seismic data analysis offers a unique method for studying rock slope failures that is independent of and complementary to other data sources. One distinct advantage of seismic monitoring is the ability to detect remote events that might otherwise go unnoticed for weeks or months. This advantage applies even in relatively densely settled mountain regions such as the Alps. Often slope failures will occur high in tributary valleys or glaciated areas and may not be directly observed. Many valleys are also uninhabited during winter months. These circumstances make recognition of secondary hazards potentially critical, for example lake formation behind rockslide debris and possible outburst flooding. Analysis of seismic signals can also offer invaluable insights into event characteristics. Timing, a basic ingredient of trigger analysis, is easily determined from the seismic record [e.g., Tilling et al., 1975]. Aspects of event dynamics (such as the number of sub-events) may also be extracted from seismic signals, helping to understand the failure process from an independent viewpoint [e.g., Norris, 1994]. In addition, we demonstrate that it is possible to estimate physical event properties such as volume and runout distance from seismic signals. When combined with automated detection in a continuous seismic data stream, our estimation method allows rapid and centralized first analysis, in advance of more detailed field investigations.

[3] In this paper, we use the term ‘rockslide’ for all mass wasting events composed primarily of rock. This simplified usage encompasses different events that may be otherwise classified according to their dynamics, such as rock falls, rock slides, rock avalanches, and rock collapses. Rock falls, for example, are those events with a confirmed initial free-fall phase of one or a few main blocks. Rock slides by definition involve a component of translational sliding in their failure, but often the term is applied generically to mid-sized rock slope failures (e.g., ∼100,000 m3). Rock avalanches are characterized by an unusually long runout distance (for the given volume of material), while rock collapses have an unusually short runout distance and a failure mode often described as ‘crumbling’. Whenever the specific event type is relevant to our discussion it will be mentioned explicitly, otherwise the generic term ‘rockslide’ (one word) will be used to indicate all types of rock slope failures.

[4] For a sound interpretation of rockslide-generated seismic signals, knowledge of the responsible seismic sources and how their energy is transferred is essential. Rockslide seismicity is primarily generated by the impact of individual rock blocks on the ground as they fall, roll, flow, or tumble down the slope [Tilling et al., 1975]. Larger volume events can generally be detected at a greater distance from the source than smaller events. If two events have a similar volume, the event composed of relatively larger blocks may be detected at a greater distance. Unconsolidated deposits in the runout path related to previous mass movements can decrease signal amplitude [Cole et al., 2009]. In all cases, energy transfer into the ground is not efficient, but seems to be similar for both landslides and rockslides. Weichert et al. [1994] analyzed the ratio of seismic to potential energy for four different landslides and concluded that the seismic energy captures more of the potential energy for events with steeper detachment surfaces, while Kawakatsu [1989] found that volume estimates based on seismic energy underestimated the size of a landslide by a factor of five to ten. For rockslides, Vilajosana et al. [2008] estimated that the seismic energy (calculated using the ground velocity envelope, distance to event, phase velocity, and ground density) represents only about a quarter of the potential energy, while Deparis et al. [2008] found that the ratio of seismic to potential energy lies between 10−6 and 10−3. Event energy not captured in the seismic signal is presumably lost through attenuation and geometrical spreading, rock fragmentation, and heat generation.

[5] The individual components of a mass movement seismic signal are not easy to determine. Predominant frequencies are generally below 5 Hz, with higher frequencies present at the time of peak amplitudes. Suriñach et al. [2005] found that while landslide recordings show an initial increase in frequency with time, the effect was strongest when a landslide was moving directly toward a seismic station. This may be explained both by ground attenuation of high frequencies and by entrainment of material as the avalanche progresses, as block collisions within the moving mass could be responsible for the higher frequency energy [Cole et al., 2009]. While the first explanation is valid for all mass movement seismic sources, Weichert et al. [1994] proposed that rockslides may be distinguished from other signals by their relatively large long-period energy content, which remains visible at stations several hundred km from the event. Another distinguishing feature of rockslide seismograms may be related to the excitation of surface waves by shallow sources. Using particle motion analysis, Rayleigh waves were identified in the seismic record of the May 2006 Mount St. Helens rock fall [Moran et al., 2008] and of the July 1996 Yosemite National Park rock fall [Uhrhammer, 2009]. In general, seismic signals with an apparent velocity of ∼3.8 km/s indicate that the signal is likely composed primarily of surface or shear waves [Suwa et al., 2010; Lin et al., 2010]. These results may give another potential clue into rockslide dynamics, as smaller blocks are expected to generate more surface waves than larger blocks [Norris, 1994].

[6] Rock falls may be distinguished from other rock slope failures by their initial high-frequency content. Vilajosana et al. [2008] observed sharp energetic bands over the complete frequency spectrum for the impact phase of rock falls, which is similar to the signal from an explosion. Moore et al. [2007] analyzed seismic signals from single block falls and found that these consist of high-frequency bursts as the block strikes the slope. Deparis et al. [2008] used numerical simulation of block falls to show that an impact signal exhibits higher amplitude and also a greater proportion of high-frequency energy than the preceding detachment signal.

[7] Even when detailed source functions cannot be extracted from rockslide seismograms, the latter may still contain valuable information about the event and environment. Favreau et al. [2010] noted that the velocity amplitude of the vertical component of a rockslide seismic signal depends on the local topography and basal friction angle. Similarly, Schneider et al. [2010] found that the total frictional work rate, mainly a function of runout path morphology, is proportional to the absolute amplitude of the vertical seismogram component. Several attempts have also been made to correlate certain seismic metrics with rockslide event characteristics. For example, Norris [1994] observed a linear relationship between signal amplitude and source volume for block falls occurring on the same slope at Mount St. Helens. Tilling et al. [1975] identified that larger rock falls resulted in longer seismic signals, while Deparis et al. [2008] demonstrated a correlation between signal duration (projected to a common distance of 30 km) and the log of potential energy (r2 = 0.69). In their study, signal duration was also well-correlated with the log of runout distance (r2 = 0.61).

[8] Most previous analyses of rockslide seismicity were case studies focusing on a single event [e.g., La Rocca et al., 2004; Moran et al., 2008; Vilajosana et al., 2008; Favreau et al., 2010]. Other studies were commonly limited to a specific set of circumstances, properties, or event magnitude ranges (e.g., large block failures from one slope [Norris, 1994]). Finally, there is a noticeable gap in the scale of seismic observation, where most studies either focus on large rockslides distinguishable across the globe [e.g., Kanamori and Given, 1982; Favreau et al., 2010] or use purpose-built seismic networks within a few km of the source [e.g., La Rocca et al., 2004; Vilajosana et al., 2008]. In this manuscript we show that it is possible to obtain reliable information on a variety of intrinsic rockslide parameters from a single large data set spanning several event types and magnitudes, and that these can be efficiently derived from readily available data of pre-existing regional seismic networks.

[9] We have chosen Switzerland as our study region for two main reasons. First, the seismic infrastructure is excellent. The Swiss Seismological Service (or SED) operates a dense seismic network consisting mainly of broadband instruments, with an average distance of approximately 30 km between seismic stations in the inner alpine region. This network provides continuous real-time data in which earthquakes are detected automatically and uncertain events are flagged for personal confirmation. This procedure has already led to the discovery of a number of suspected, but often unconfirmed, rockslide seismic signals, which suggests that more systematic analysis of the continuous seismic record may prove valuable for the study of rockslides. The second advantage of Switzerland is the relative prevalence of rock slope failures. For our study we were able to compile a data set of 20 rockslide events from the past 15 years, spanning several orders of magnitude in volume and encompassing a number of different failure modes (e.g., falls and slides). In this context it is important also to note that our data set represents only a fraction of the known rockslides that occurred during this time. We had to discard many events due to a lack of basic information; often fundamental data such as the event date were poorly constrained, while detailed rockslide properties such as volume were recorded only for the most publicized events. Among other considerations, this lack of consistent basic data was an important factor motivating our study of rockslide seismicity.

[10] In this study, we parameterize rockslide seismic signals in our data set using five basic metrics: duration, peak value of the ground velocity envelope, velocity envelope area, average ground velocity, and risetime. Bivariate correlation analysis between rockslide parameters and seismic metrics is performed to determine how certain seismic metrics relate to specific properties of the events. The resulting relationships are then used in a multivariate linear regression, correlating rockslide properties with a combination of several seismic metrics. This last step results in a set of equations that can be used to quickly estimate key parameters of an unknown rockslide event. Our parameter estimates are based on analysis of the seismic record alone, laying the groundwork for automatic detection and classification of rockslide signals in a continuous seismic data stream. Since the relevant infrastructure has long been available in Switzerland (as in many parts of the world), rockslide detection and characterization may be conducted alongside automatic earthquake detection procedures already in place at virtually no extra cost. In this way, we work toward a centralized system of rockslide detection and characterization for Switzerland, which may also be adapted to other seismic networks and mountain ranges.

2. Data

2.1. Event Data

[11] We compiled a data set of 20 of the best known rockslide events in the Swiss Alps and neighboring regions that occurred during the last 15 years (Table 1), utilizing geological reports, newspaper articles, topographic maps, photographs and videos. Selection of events was based on the availability of basic information (timing, location, and volume) and on successful identification of a seismic signal that could be unambiguously attributed to each event. The events are well-distributed throughout the highest parts of the Swiss and French Alps and bordering regions (Figure 1). Most events in our data set were classified as either rock slides (Figure 2c) or rock falls (Figure 2a).

Figure 1.

Map of Switzerland showing rockslide locations and associated event numbers from Table 1 (circles), and seismic stations used in this study (triangles). Full station details can be found on the SED website (http://www.seismo.ethz.ch/monitor/index_EN).

Figure 2.

Photographs of three different rockslide events from our data set. (a) Kärpf rock fall [9]: two photographs showing the ridge before the rock fall (arrow indicates source area) and during impact of the main block [Louis, 2008]. (b) Thurwieser rock avalanche [15]: video still image showing movement of the main mass, seen as a black cloud (arrow) in center (video: ‘Italia 1’ television channel). (c) Tavanasa rock slide [14]: a sequence of video stills showing the source area before detachment, during collapse of the main mass (arrow), and the scarp after detachment with dust cloud from runout (video: M. Cathomen, personal communication, 2011).

Table 1. Rockslide Properties for All Events Used in This Studya
 NameDateTime UTCTypeLatitude/LongitudeElevation (m)AspectVolume (m3)Drop Height H (m)Runout L (m)Fahrböschung αLithologySubstrateStation Distance (km)Nearest Station
1Aguille Dru30-Jun-051:23rock fall45.932650°/6.952383°3660W265,0001280115048graniterock/ice15EMV
2Eiger13-Jul-0617:26rock fall46.597210°/8.053796°1600E85,00020026038limestonerock19HASLI
3Eiger13-Jul-0617:39rock fall46.597210°/8.053796°1600E20,00020026038limestonerock19HASLI
4Eiger26-Jul-0619:04rock fall46.597210°/8.053796°1600E1,00020026038limestonerock19HASLI
5Eiger18-Aug-0810:14rock fall46.597210°/8.053796°1600E46,00020026038limestonerock19HASLI
6Eiger18-Aug-0812:19rock fall46.597210°/8.053796°1600E4,00020026038limestonerock19HASLI
7Felsberg6-Jul-0121:25rock slide46.850930°/9.471686°1000S250,00047070034limestoneforest24DAVOS
8Kärpf29-Sep-0713:02rock fall46.917005°/9.090499°2650N3,00013015041quartz conglomeratesnow/rock9LLS
9Kärpf29-Sep-0713:16rock fall46.917005°/9.090499°2650N16,00021030035quartz conglomeratesnow/rock9LLS
10Kärpf12-Sep-1010:54rock fall46.916356°/9.088073°2650N3,00013018036quartz conglomeraterock9LLS
11Kärpf16-Aug-0812:11rock fall46.916356°/9.088073°2650N3,00013018036quartz conglomeraterock9LLS
12Medji21-Nov-0214:20rock slide46.167414°/7.787053°1600E70,00048080031granitic gneissrock20MMK
13Monte Rosa21-Apr-077:24rock avalanche45.932838°/7.879150°4050E300,0001900290033biotite-gneisssnow/ice/rock14MMK
14Tavanasa6-Jun-028:37rock slide46.750035°/9.066638°1160N90,00032055030quartz conglomeraterock/forest11LLS
15Thurwieser18-Sep-0411:42rock avalanche46.49321°/10.524940°3630S2,000,0001410260029dolomite/limestonerock/ice24FUORN
16Val Canaria27-Oct-096:29rock collapse46.536590°/8.639964°1500W360,00025021050gypsumrock8FUSIO
17Vicosoprano13-Jul-0213:02rock slide46.340378°/9.632916°2050N50,0001000130038graniterock21VDL
18Zuetribistock24-Jan-968:00rock slide46.846671°/8.954972°2200E470,000900107040limestonerock4LLS
19Zuetribistock4-Sep-962:42rock slide46.846671°/8.954972°2200E30,000900107040limestonerock4LLS
20Zuetribistock27-Sep-9715:30rock slide46.846671°/8.954972°2200E60,000900107040limestonerock4LLS

[12] Rockslide event volumes in our data set span three orders of magnitude, with the smallest having a volume of 1,000 m3 (Eiger [4]; note that the bracketed numbers refer to the specific events listed in Table 1) and the largest a volume of about 2,000,000 m3 (Thurwieser [15]). Although geological reports exist for a number of these rockslide events, volume information for most was taken from newspaper articles or estimated using pre- and post-event photographs, so uncertainties may reach 20% of the volumes listed in Table 1. In particular, only volume range estimates are given in relevant literature for the Zuetribistock events [19] and [20], and an average value was assumed for our study. Many other rockslide events, notably the ∼30 million m3 Randa rockslides of 1991, had to be discarded because no precise volume information for each of the individual sub-events is presently available.

[13] Rockslide drop heights (H) ranged from 130 m (Kärpf [8]–[11]) to 1900 m (Monte Rosa [13]). These values were measured from the top of the scarp to the outermost point of the debris deposit and thus have no relation to actual block fall height, even if the event was classified as a fall. Event runout distance (L) ranges from 150 m (Kärpf [9]) to 2900 m (Monte Rosa [13]) and was measured as the horizontal planimetric distance from the scarp to the outermost debris deposit and is not necessarily identical to actual path length. The Fahrböschung (or angle of reach; F = atan(H/L)) varied between 29° (Thurwieser [15], a rock avalanche) and 50° (Val Canaria [16], a collapse). Since the events in our data set are spread across the Central Alps, source lithologies varied considerably from granite ([1], [17]) and gneiss ([12], [13]), to limestone ([2]–[6], [15], [18]–[20]), quartz conglomerate ([8]–[11], [14]), and gypsum ([16]). The runout path substrate was generally rock, though in some cases snow, ice or forest were also present. For the Eiger, Kärpf, and Zuetribistock locations, we have several events from each slope in our data set. In these cases the geometric event parameters were identical or very similar while volumes could vary widely, providing good test cases for the quality of runout and drop height estimates.

[14] Figure 3 shows all rockslides in our data set plotted together with other known rock slope failures on the so-called Scheidegger plot, which correlates H/L with volume on a log-log scale [Scheidegger 1973] with a best fit of

equation image

Although the power law relationship may fail for small events (a few thousand m3), most rockslides in our study fit comfortably within one standard deviation of equation (1) or have scatter similar to the original events used by Scheidegger [1973]. This suggests that our data set is reasonably representative of most possible events below a volume of 2 million m3. One notable exception is Val Canaria [16] above the one standard deviation line, which was classified as a rock collapse in part due to its anomalously short runout distance (A. Pedrazzini, personal communication, 2009). Aguille Dru [1] is also an outlier in Figure 3, although the seismogram for this event reveals two distinct sub-events in rapid succession, and thus it should be plotted more accurately as two events with smaller (but unknown) volumes. The five lowest-volume events [4], [6], [8], [10], and [11] lie below one standard deviation. These are all classified as rock falls, and their distinct free-fall and impact dynamics may explain the anomalously low H/L values.

Figure 3.

Scheidegger plot showing general variation of the ratio of rockslide drop height (H) to runout distance (L) with event volume. Original set of events used by Scheidegger [1973] (gray) and those from this study (red) are shown. The number labels correspond to the events listed in Table 1.

2.2. Seismic Data

[15] The Swiss Seismological Service (Schweizerischer Erdbebendienst, SED) operates a network of continuously recording seismic stations throughout Switzerland (Figure 1). These are not distributed uniformly; notable clusters are located along the Swiss-German border, in southwest and southeast Switzerland, and in southern Switzerland near the new Gotthard railway tunnel. However, the alpine regions are covered relatively well and all our events occurred within 25 km of a seismic station. Seismic data from some Austrian, German and Italian stations close to the Swiss border are also included in the SED network. The network consists of a mixture of long-period, short-period, and extremely short-period instruments. Long-period seismometers were installed after the year 2000 and were used in our analysis of later events to capture the seismic response over the broadest possible frequency range. Earlier events, however, were only recorded on short-period instruments. To ensure that our seismic signals accurately represent true ground motion, the frequency response of the seismometers must be flat, i.e., the signal amplitude should not be exaggerated or damped in the analyzed frequency range. Our study uses only velocity signals from the different sensors, and therefore only response spectra in the velocity domain will be discussed. The short-period instruments used before 2002 were Willmore model MKIII(a) seismometers with a flat frequency response above 0.1 Hz [Usher et al., 1979]. From 2002 onward the short-period instruments are Lennartz LE-3D/5s with a flat frequency response between 0.2 and 50 Hz, Lennartz LE-3D/1s with a flat frequency response between 1 and 100 Hz (Lennartz electronics product manual), and on occasion Mark Products L4C geophones with a flat frequency response above 1 Hz [e.g., Bormann, 2002]. Streckeisen STS-2 seismometers are used as long-period instruments and have a flat frequency response between 0.0083 and 40 Hz [e.g., Bormann, 2002]. Select locations are also equipped with Trillium 40 seismometers, featuring a flat response between 0.025 and 50 Hz (Nanometrics product manual).

[16] To ensure that the frequency response was flat across all instruments used in this study and that data were directly comparable between stations, we filtered all rockslide seismic data using a 1–20 Hz band-pass filter. In this common frequency range, short-period and long-period seismometer recordings are not affected by instrument response and are comparable [Strollo et al., 2008]. Experimenting with the frequency band for a given station also revealed that filtering between 1 and 20 Hz does not result in a significant loss of information for rockslide seismograms, as most of the energy resides in this range. To account for different site conditions between seismic stations, site-specific velocity amplification factors for most stations in the SED network have been determined [Edwards et al., 2009]. Both average amplification factors and frequency-dependent amplification factors are available, which convert the station response to a common reference value. In the 1–20 Hz range, the frequency dependence of amplification is negligible, so the seismic signals used in our study were simply multiplied by the average site-specific amplification factor to obtain the corrected velocity amplitudes. Since many seismic metrics depend on absolute ground motion amplitudes, and since the amplification factors range from 0.3 to 3.5, stations lacking site correction coefficients were not used in our analysis.

[17] For amplitude analysis, ground velocity was preferred over acceleration or displacement since seismometers directly measure velocity and the chance of introducing processing errors is reduced. All seismic metrics used in our study were based on the computed envelope of ground velocity. This envelope in effect smoothes the signal and reduces the influence of spurious outliers, making metrics that depend on the timing of peak ground velocity more reliable (see also section 3.1). The seismic envelope has been successfully used in place of the actual signal in other applications, such as earthquake epicenter location [Husebye et al., 1998]. Our ground velocity envelope was calculated using the standard procedure [e.g., Farnbach, 1975]: first the absolute value of the Hilbert transform of the velocity seismogram was computed, then this signal was low-pass filtered using a cut-off frequency of 0.35 Hz. Finally, the resulting signal was time delayed by the normalized cut-off filter period to match the delay caused by the low-pass filter.

[18] To analyze the frequency content of rockslide seismic signals, spectrograms showing the frequency evolution with time were computed from the filtered ground velocity signal. The Hamming window length of the short-time Fourier transform was 128 samples, the FFT length 512 samples, and the window overlap 64 samples.

3. Method

3.1. Seismic Metrics

[19] To quantify differences between seismic signals, we use five seismic metrics that are extracted from each seismogram at every station: 1. signal duration (DUR), 2. peak value of the ground velocity envelope (ePGV), 3. velocity envelope area (EA), 4. risetime (RT), and 5. average ground velocity (AGV). Except for ePGV, all metrics depend on reliable signal arrival and cease time (i.e., amplitude drops below the noise level) estimates. For simplicity, we used only the vertical component of motion. Figure 4 presents an example overview of the different metrics overlain on the seismogram of the Eiger [5] event.

Figure 4.

Definition of the five seismic metrics used in this study, superimposed on the seismogram of the Eiger [5] rockslide from the nearest station (HASLI), 19 km distant.

[20] Duration was determined using a short-term/long-term sliding window average (STA/LTA) on the velocity time series. The average noise level (n) at the beginning of an event trace was used as a baseline value, and the maximum amplitude of the signal served as the starting point for the algorithm. Next a sliding window of 15 s length and a step size of 0.008 s (one sample) moved in the positive-time and negative-time direction toward the ends of the trace. The average value within the window was compared to the baseline value, and when it dropped below an empirically defined threshold of 1.3*n, a second sliding window, now with both length and step size of 0.008 s, was used to determine the precise signal arrival and cease times. Each duration estimate was then either accepted or rejected by manual inspection. Stations that did not clearly record the event were rejected, and in a few cases the duration pick was manually adjusted, e.g., if the noise window incorporated an unrelated high-amplitude signal. The determined arrival times of several events were plotted against station-event distance, and the resulting average P wave velocity was found to be 5.01 ± 1.2 km/s, within the reported range of P wave velocities in the upper crust beneath the Alps [Ye et al., 1995; Husen et al., 2003]. We also tested the more common 5–95% duration estimate with our data set, which uses the times of 5% and 95% of the total seismic energy released as cutoffs [e.g., Trifunac and Brady, 1975; Deparis et al., 2008]. Due to the gradual onset and signal decay, we found that our new method captured a greater proportion of the event signal compared to the 5–95% method. Duration estimates differed by factors of 2.5 to 5, highlighting the importance of the choice of method.

[21] One of the most commonly used seismic metrics is peak ground velocity (PGV), which often serves as a proxy for event magnitude [e.g., Trifunac and Brady, 1975] and shaking intensity [e.g., Wu and Kanamori, 2008]. PGV can be measured from the signal itself or from the velocity envelope. PGV from the seismic signal has more widespread use and is simple to determine, but may be overly sensitive to spurious outliers. Since another of our metrics (risetime, described below) depends on the timing of PGV, we decided to use PGV calculated from the seismic envelope (here called ePGV). Plotting values of ePGV versus PGV showed that both measures are comparable, however there were instances where the timing of ePGV and PGV differ by several seconds and ePGV was found to better fit the timing of maximum ground motion.

[22] The risetime (RT), or time from first arrival to the time of ePGV, is a metric that could conceivably be used to distinguish between different rockslide types. In a rock fall event, for example, we might expect the risetime to be relatively short (5–20% of total event duration), since the fall and impact would transfer the largest amount of energy into the ground. Conversely, rock avalanches could exhibit longer risetimes, since the maximum amplitude may be achieved by superposition of smaller seismic sources as the individual blocks move down the slope. Our fourth seismic metric is the area of the velocity envelope (EA) between the signal arrival and cease times. EA is a measure of total ground motion and should be related to the total event energy. As rockslide signals emerge gradually from background noise usually without a sudden onset, EA is not significantly influenced by uncertainties in the arrival/cease time picks. The final seismic metric is the average ground velocity (AGV), here defined as the ratio of EA to event duration. This metric may be useful in distinguishing between different event types, as a rock fall and a rock avalanche with the same event energy should have a similar EA, but could exhibit very different average ground velocities. In the former case, the seismic energy would be created primarily by the fall and impact, and the total duration may be shorter than in the latter case, leading to a greater AGV.

[23] Continuous seismic data are available only from the year 2000 onward. All events that occurred before 2000 are stored as standardized event files with a limited total duration. For some large events, e.g., the 1997 Brenva rock avalanche, these files did not capture the complete seismic signal and thus could not be included in the present analysis. Similarly, peak ground motion for some large rockslides was clipped at stations close to the event and again these could not be used. For a few events, the signal duration was only completely captured at stations within a certain radius due to the limited file size, and the remaining stations were discarded. All events used in our study were properly recorded on at least five stations.

[24] Since our seismic metrics were computed for all stations at which a given event was visible, the distance-dependency of seismic metrics due to signal attenuation, geometrical spreading, dispersion, and differential velocities within the upper crust could be analyzed. Station distance was fitted to each metric using seven different possible curve types (Table 2, with station distance as the independent variable). This procedure was performed for each event separately. Fitting was conducted by minimizing the squared error of the dependent variables and returned two best fit coefficients a and b as output. For each fitted curve and each event, the goodness-of-fit parameter r2 was calculated (r2 = 0 signifies no correlation, r2 = 1 reflects perfect correlation). Afterwards, the mean and standard deviation of curve coefficients a and b, as well as those of r2, were determined across all events. We assume that distance-dependency is primarily a function of the ground rather than of the event, and thus should exhibit similar behavior for all events. To identify the curve type that fit all events with the best possible r2, both the mean and the standard deviation of fit and of the slope parameter b were examined. A histogram analysis with 20 bins of slope parameters, normalized by the mean, and r2 for all events was also performed to better assess their distribution.

Table 2. Functions Used for Fitting Distance-Dependency Behavior and Bivariate Relationships Between Event Parameters and Seismic Metrics
NameFunction
Lineary = a + b*x
Log-xy = a + b*log10(x)
Log-ylog10(y) = a + b*x
Power lawlog10 (y) = a + b*log10(x)
1/xy = a + b/x
1/x2y = a + b/x2
1/x3y = a + b/x3

[25] Finally, we attempted to locate the rockslide events using the automatically determined arrival times. The pick uncertainty of ±1 s can be reliable enough for a first estimate, especially since we constrained the source location to be at the Earth surface. Locations were determined using a nonlinear location routine (‘snap’ from the SED) including a three-dimensional P wave velocity model of Switzerland [Husen et al., 2003]. The location routine followed a rigorous procedure: (1) Arrival times were automatically determined using the algorithm described at the beginning of this section. (2) Locations were computed using ‘snap’. (3) Residuals between the predicted and actual arrival times were analyzed, and all stations with residuals greater than any of the residuals of the closest five stations were eliminated. The arrival times of the five closest stations are generally the most reliable due to high signal to noise (S/N) ratios, and high residuals at large distances from the event indicate that those picks were not useful. (4) Steps 2 and 3 were repeated until one of the following conditions was met: either one of the five closest stations had the highest residual, or the total number of stations used dropped below ten. Because we expect a signal to be most prominent at stations close to the event, dropping a nearby station (here ‘nearby’ is arbitrarily defined as among the five closest stations) will usually result in a worse location estimate, even if that residual is high. The second condition ensures that we have a sufficient number of stations for reliable location analysis. The only exception was if the initial number of stations was already below ten at the beginning of the analysis, in which case no stations were eliminated. The number of stations finally used in the location estimates ranged between 5 and 31, with an average of 14.

3.2. Estimating Event Parameters

[26] Independent estimates of rockslide event parameters based only on seismogram characteristics may be invaluable for assessing new and unknown events. To this end, we used the five seismic metrics described in section 3.1 to estimate five event source parameters: volume (V), runout distance (L), drop height (H), potential energy (PE), and tangent of the Fahrböschung angle (F). We first performed bivariate correlation analyses between all 25 pairs of seismic metrics and event parameters to identify the best fit relationship for each, testing five different curve types. We then conducted a multivariate correlation analysis to find the best combination of seismic metrics that estimate a given event parameter.

[27] Each set of seismic metrics was first normalized by their mean value. For the initial bivariate analysis we then fitted each pair of seismic metrics and event parameters with linear, power law, and logarithmic curves (Table 2). The event parameter was always the dependent variable and plotted on the y axis, and the best fit was achieved by minimizing the y-value squared error. With the best fit a and b values, r2 was calculated and inspected to eliminate those curve types resulting in anomalously high values (r2 ∼0.99) forced by single event outliers, as using these curve types would not produce meaningful correlations. Of the remaining relationships, only those with the greatest r2 values for every parameter combination were used in further analysis.

[28] We then conducted a multivariate correlation analysis. To do so, we first created linear equations out of every correlation relationship used, so that the final outcome of our analysis would be a set of equations of the following form:

equation image

where smX are the different seismic metrics. With the resulting equations we can estimate a single event parameter using a combination of several seismic metrics; psmX are thus the slopes of each seismic metric. The previously determined best fit correlation relationships control whether the event parameters and seismic metrics appear in log or linear form.

[29] To arrive at equation (2), we solve the standard linear inverse problem [see e.g., Menke, 1989] for each event parameter:

equation image

where m is the model vector, G the data kernel, and d the data vector. The model vector has length M and contains the slopes for each seismic metric and the offset parameter. These quantities are unknown. The data vector is of length N, the number of events used in our analysis. It contains a given event parameter according to the bivariate analysis, e.g., for volume estimation d(k) = log10(Vk), k = 1:N. The data kernel is an MxN matrix composed of the seismic metrics for each event, e.g., G(k, 1) = log10(EAk), G(k, 2) = ePGVk for k = 1:N.

[30] We choose a mixed-determined solution to our problem since we do not know a priori how well each model parameter can be determined. The solution for the model vector is then given by:

equation image

where ɛ2 is the damping factor, which ensures a balance between the norm of the prediction error and the solution length. Here the prediction error is the difference between the actual data vector and the estimated data vector found using equation (3), while the norm of the solution length is a measure of how well the estimated model vector matches the assumed true model vector. The inverse problem was solved for the two event categories ‘all’ and ‘falls.’

4. Results

4.1. Identifying Rockslide Seismograms and Locating Events

[31] The seismic signature of a rockslide varies considerably between events (see Figure 5), however a few common characteristics can be identified. The event onset is generally emergent, i.e., the seismic amplitude increases gradually above the noise level to peak ground motion. The precise risetime can vary considerably from case to case: events with an initial free-fall phase show relatively sharp onsets and may not appear as emergent, while rock avalanches typically have a ‘cigar’ shaped envelope with peak amplitude reached after one minute or more. The initial detachment phase, usually lasting around 5 s based on timestamps of photographs and video, cannot be unambiguously identified in the seismic signals of our data set. For all event types, the signal decay time is generally quite long (on average about 70% of the total duration), with the signal gradually fading into the background noise.

Figure 5.

Three rockslide seismograms with corresponding time series and spectrogram views. (a) Kärpf [9], a rock fall with characteristic initial high-frequency burst around 112 s. (b) Time series of Monte Rosa [13] showing the typical ‘cigar’ shape of a rock avalanche. (c) Tavanasa [14] displaying a signal characteristic typical of a small rock slide, where the main difference compared to the Kärpf seismogram is the lack of an initial high-frequency spectral peak.

[32] Analysis of rockslide spectrograms revealed that the majority of seismic energy for our events lies below ∼3–4 Hz (Figure 5, darker areas represent higher energy). Average Fourier spectra computed over the total event durations also showed a drop-off of energy above 3–5 Hz, with no other consistent identifiable spectral peaks. We also investigated unfiltered seismograms and found that the majority of rockslide energy lies above ∼0.5 Hz. The upper frequency limit is generally between 10 and 20 Hz during the time of peak ground motion. Frequencies >3 Hz are typically present around the event onset and taper off toward the end of the seismic signal (Figures 5a–5c). For example, in the spectrogram shown in Figure 5a, the upper frequency limit of high energy decreases smoothly from ∼12 Hz at ∼115 s, to ∼2 Hz at ∼145 s, giving the spectrogram a triangular appearance. Some events exhibit a high-frequency region in the initial portion of the signal (for example Figure 5a at ∼114 s or Figure 5c at ∼53 s), while others show a smooth decrease in power for increasing frequency (e.g., Figure 5b).

[33] Analysis of particle motion showed that many rockslide events excited surface Rayleigh waves (Figure 6a), which are characterized by retrograde motion in the radial direction. Shear waves (both horizontal, i.e., SH-waves, and vertical, i.e., SV-waves) were also observed in some parts of the seismogram. Although specific wave types were not clearly identifiable in most portions of the seismic signals, we were able to observe a difference between event types. Most rock falls, with the exception of the small Eiger [4], [6] and Kärpf [8] events, showed Rayleigh wave components at the nearest station in the frequency band between 0.4 and 1.2 Hz. Of the six rockslide events registered at broadband stations, only Thurwieser [15] and Val Canaria [16] exhibited a short Rayleigh wave phase, the former between 0.1 and 1 Hz. For all other events, including the large rock avalanches, the nearest station generally only recorded a few seconds of SH or SV waves irrespective of filter limits, and the rest of the signal was not clearly interpretable.

Figure 6.

Aguille Dru [1] event. (a) Particle motion plots from the seismograms shown in part Figure 6b between 51 and 55 s and filtered between 0.1 and 1 Hz, showing a clear Rayleigh wave phase. (b) Nearest station (EMV) at 15 km distance showing two clear sub-events. (c) The same signal at station DAVOX 243 km distant, showing separation of both sub-events into two separate signals.

[34] Aguille Dru [1] was a large rock fall visible at all stations in the SED network, and while at the nearest station we could clearly observe signals of two sub-events (Figure 6b), at distant stations we found that the original signals had each split into two parts (Figure 6c). The travel velocity ratio between the two parts was ∼1.76, agreeing well with the typically assumed P- to S-wave velocity ratio, vp/vs = 1.73 [e.g., Lay and Wallace, 1995]. This suggests that the first parts of the signals consisted of P waves and the second parts of surface or shear waves, and thus the original signal must have included both wave types, even if these were not distinguishable in particle motion plots.

[35] Location estimates could be generated for most events in our data set, and the final results are listed in Table 3; three events did not register on a sufficient number of stations to perform these calculations. The average location error, or the distance between the actual and estimated location, was 10.9 km. The best location estimate was for the Zuetribistock [18] event with an error of 3.2 km, while the worst location estimate was for Monte Rosa [13] with an error of 34.8 km. The latter event featured a highly emergent signal and thus our arrival time picks were less reliable than for other events. Over the entire data set, RMS (residual mean squared error of predicted arrival times at every station used for the location estimate) were relatively large between 0.97 s and 8.34 s, reflecting difficulty in picking reliable arrival times for emergent signals.

Table 3. Location Errors for the 17 Events Recorded by at Least Four Seismic Stationsa
 EventLocation Error (km)RMS (sec)Gap (deg)Number of Stations
  • a

    RMS is the cumulative root mean squared error between the true and predicted event arrival times at every station. Gap is the station gap, i.e., the largest angle centered at the event in which no stations are present. The last column lists the number of stations used in the location routine.

1Aguille Dru8.13.1122831
2Eiger7.72.376821
3Eiger10.55.5909
4Eiger24.64.412510
5Eiger7.60.979023
6Eiger9.91.261028
7Felsberg14.21.661679
9Kärpf73.311635
12Medji9.34.621339
13Monte Rosa34.88.3411923
14Tavanasa11.43.541269
15Thurwieser6.45.9928312
16Val Canaria8.151356
17Vicosoprano11.31.531579
18Zuetribistock3.21.899620
19Zuetribistock5.92.516320
20Zuetribistock5.73.171595

[36] The observed distance-dependency of the five seismic metrics varied considerably. Results are briefly described here, and the calculated best fit coefficients listed in Table 4. The small Kärpf events [8]–[11] had to be excluded as they were only recorded at two stations. Variation of duration with event-station distance was not represented well by any curve type, the greatest average r2 being 0.38 ± 0.24 for a linear fit. In contrast, Deparis et al. [2008] found a direct power law relationship between seismic signal duration and distance, which was explained by dispersion and diffusion in the upper crust. However, their slope parameter varied between events by a factor of eight and, similar to the present study, their duration picks exhibited considerable scatter. Risetime distance-dependency was also best described by a linear curve (r2 = 0.48 ± 0.29), although the average slope was close to zero, indicating that there is no clear trend in risetime with distance. Distance relationships with ePGV (Figure 7), EA, and AGV were best described by power law curves (based on both mean r2 values and the standard deviation of the slope, normalized by the slope mean, across events), with each of the seismic metrics decreasing in magnitude with increasing distance. Here, the average r2 values were always above 0.8 with small standard deviations. Previous related studies have only investigated a decrease in peak signal amplitude with distance. For example, Tilling et al. [1975] noted a decrease of trace amplitudes with distance that was more pronounced than for earthquakes, and Deparis et al. [2008] identified an inverse power law attenuation relationship. Analyzing the rock ‘falls’ category separately, we found consistently lower r2 values (by between 0.04 and 0.15) for the distance-dependency relationships of each seismic metric.

Figure 7.

Distance-dependency for ePGV. (a) Best fit behavior for every event in our data set (thin lines) and the average distance-dependency behavior (bold line). (b) Distribution of r2 values across all events. The notable outlier is Eiger [4].

Table 4. Distance-Dependency Coefficients for Each Seismic Metrica
MetricCurve Typeμslopeσslopeμoffsetσoffsetμr2σr2
  • a

    Curve types are listed in Table 2, with distance on the x axis. The mean and standard deviation of the slopes (variable b in Table 2), offsets (variable a in Table 2), and r2 were computed across all events.

AGVpower law−1.0030.3273.2822.120.830.12
DURlinear−0.0810.15592.80558.1380.380.24
EApower law−1.0780.332−3.7452.3410.850.11
ePGVpower law−1.2010.4344.6240.9930.860.13
RTlinear0.0360.08133.15231.6460.480.29

[37] To determine the limits of rockslide detection distance as a function of event volume, we selected the farthest seismic station at which each event was detectable. An event was deemed detectable when we had selected the station for the distance-dependency analysis. The four largest events were detected throughout our station network and thus were not used in this analysis. The remaining results are shown on a plot of distance versus volume (Figure 8), where we can observe an upper detection limit described by

equation image

If, for a given event, a station plots in the lower right area below the dashed line (equation (5)), the seismic signal should be detectable. However, this result also appears to depend on event type: Figure 8 shows that rock falls are generally detectable at distances comparable to larger volume rockslides. The detection limit also depends on the station signal quality; if the noise level is high, the signal may be obscured, even though a station farther away with a lower noise level will still record it clearly.

Figure 8.

Maximum distance of event detection as a function of rockslide volume. For a given event volume, the seismic signal should be visible at all stations plotting beneath the dashed curve (i.e., within the shaded area).

4.2. Multivariate Linear Regression

[38] From the initial bivariate correlation analysis, we chose the best fit curve type for each pair of event and seismic metrics based on the greatest correlation coefficient (r2), disregarding results where a single outlier could force an alternative correlation. If two curves had the same r2 value, we selected the curve type based on visual inspection of the overall fit. Power law curves generally provided the best fit for almost every pair of variables; only risetime exhibited better correlation with each metric using a log-y curve. The chosen correlations for all event parameters are listed in Table 5 along with the best fit curve parameters. To display the full range of correlations for a given event parameter with each seismic metric, both the best and the worst correlation coefficients are listed. Volume and PE correlated best with DUR, while runout and drop height correlated best with ePGV; so we can conclude that most variation of our event parameters is described by DUR and ePGV. AGV was not well-correlated with any event parameter. Volume, runout, drop height, and PE all had correlation coefficients greater than 0.7 with the best fit seismic metric, suggesting that a first estimate of these event parameters could be obtained using only bivariate relationships. Fahrböschung was not well-correlated with any single seismic metric, suggesting that this summary parameter is not clearly reflected in the seismogram. As H and L possess similar correlations with the various seismic metrics, correlation may be lost for H/L and therefore Fahrböschung.

Table 5. Coefficients for Bivariate Correlations Between Event Parameters and Select Seismic Metricsa
Event ParameterSeismic MetricSlopeOffsetr2
  • a

    For each event parameter, the seismic metrics are listed that give both the best and worst predictions, with corresponding slope and offset for the best fit power law equation and r2 value.

VolumeDUR1.9651.1610.79
 AGV0.114.4010.25
Runout distanceePGV0.4691.2230.74
 AGV0.0722.5590.35
Drop heightePGV0.4351.2010.73
 AGV0.0682.440.35
Potential energyDUR2.7216.8010.81
 AGV0.17811.2310.3
FahrböschungePGV−0.034−0.0210.27
 AGV−0.004−0.1190.11

[39] To populate the data vector and kernel for the inverse analysis, risetime was kept in a linear form, while the logarithms of the other seismic metrics and event parameters were used. The damping factor of ε2 = 0.03 best minimized the combination of model and data error. All events were included in our inverse analysis. The combination of duration, peak ground velocity, and envelope area was found to perform best in estimating each rockslide event parameter. The equation for the different event parameters is then given by

equation image

with the slope (qi) and offset values listed in Table 6. The r2 and standard deviation values in Table 6 were calculated from the differences between the estimated and actual event parameters in log space.

Table 6. Coefficients for Equation (6) Determined From Multivariate Regression
CategoryEvent ParameterqdurqEAqePGVOffsetr2SDa
  • a

    Here SD is the standard deviation between actual and estimated log-scale values of the event parameter.

AllVolume1.4831−0.0520.5774−0.08850.850.336
 Runout distance0.4398−0.01080.35940.73730.800.151
 Drop height0.4472−0.00810.31810.74150.800.144
 Potential energy1.9425−0.0650.91054.94710.880.343
 Fahrböschung0.00740.0027−0.04130.00420.280.058
Falls onlyVolume1.0368−0.12481.1446−1.64270.940.178
 Runout distance0.3445−0.02280.29440.88560.850.082
 Drop height0.39460.02570.35470.51070.840.107
 Potential energy1.4355−0.15821.55443.04420.970.177
 Fahrböschung0.0501−0.00290.0603−0.37490.670.025

[40] Rockslide volume and runout estimates are among the most critical properties of an unknown and potentially hazardous event, so we focus further discussion on these two parameters. Figure 9 shows the volume and runout estimates obtained using equation (6) and the best fit coefficients from Table 6. On the x axis we plot the actual event parameters for each rockslide, while on the y axis we plot the estimated event parameters. For a perfect estimate, all events should lie on the line y = x, shown as a solid line in Figure 9. The dashed lines represent one standard deviation above and below the ‘perfect’ match line. The overall correlation between actual and estimated volume (Figure 9a) was found to have r2 = 0.85, and most events fit well within one standard deviation. The farthest outlier below one standard deviation is Val Canaria [16], the only rock collapse in our data set, whose distinct dynamics may be responsible for the poor fit. Other outliers were event numbers [4], [6], [7], [19], and [20], all of which are similar to events with better estimates. Because our event catalog contains a large range of event types, we conclude that the method presented here is able to produce a good first estimate of volume for an unknown rockslide event. Runout distance showed a slightly worse, but still suitable, correlation as compared to volume (Figure 9b, r2 = 0.8). Runout was overestimated for events [2], [5] and [16], and underestimated for events [13], [17] and [20]. With the exception of the Monte Rosa rock-ice avalanche [13], these events do not appear to be significantly different from any others in our data set. Most event types were situated within one standard deviation of the best fit line.

Figure 9.

(a) Volume and (b) runout estimates from multivariate regression analysis for all events. The actual event parameter (see Table 1) is plotted on the x axis, while the estimated event parameter from equation (6) and Table 6 is plotted on the y axis. The solid line represents a perfect estimate; one standard deviation above and below the line are also shown.

[41] Potential energy estimates exhibited improved correlation with actual values (r2 = 0.88) as compared to volume, but the event distribution was similar. Correlation between estimated and actual drop height was the same as for runout and the event distribution again appeared similar. Fahrböschung could not be estimated well. While actual Fahrböschung angles varied widely across events, the estimated values were all similar and even the best combination of seismic metrics resulted in an r2 value of only 0.28.

[42] Separate analysis of events in the ‘falls’ category (Figure 10) produced best parameter estimates from the combination of DUR, EA, and ePGV, similar to the preceding analysis of ‘all’ events. Correlation coefficients were slightly improved across all event parameters, and smaller standard deviations indicated that the parameters were better resolved for rock falls. For volume (Figure 10a) and potential energy, the r2 values increased significantly to 0.94 and 0.97, respectively, while runout (Figure 10b) and drop height had correlation coefficients of 0.85 and 0.84, respectively.

Figure 10.

(a) Volume and (b) runout estimates from multivariate regression for the ‘fall’ subset of events. The actual event parameter (see Table 1) is plotted on the x axis, while the estimated event parameter from equation (6) and Table 6 is plotted on the y axis. The solid line represents a perfect estimate; one standard deviation above and below the line are also shown.

5. Discussion

5.1. Rockslide Seismogram Content

[43] Certain fundamental parameters of an unknown rockslide event can be readily extracted from continuous seismic data. These are primarily the event timing and the number of sub-events. Determining event timing can be particularly important for rapid post-event hazard assessment, and is always relevant when attempting to identify rockslide triggering factors. Similarly, the number of sub-events that constitute a rock slope failure will significantly influence the runout dynamics and ultimately travel distance. A volume that fails as many sub-events (e.g., the 1991 Randa rockslides mentioned in section 2.1., see also section 5.4.) will generally have a shorter runout distance than the same volume that fails as one. The number of sub-events can usually be detected from continuous seismic data, especially if these sub-events occur within a few seconds or minutes of each other (e.g., Aguille Dru [1], see also Figure 6b).

[44] The emergent nature of rockslide seismograms can be physically explained by small failures and rapidly accelerating slope movement preceding detachment of the main mass, as commonly observed for many large mass movements and documented in photographs and videos. As the rock mass breaks up after initial failure, the individual blocks impact the ground along the runout path, which may generate the high-amplitude portion of the seismogram [Norris, 1994]. Risetime may also be influenced by progressive failure of different rock mass compartments [McSaveney, 2002] or by material entrainment [Suriñach et al., 2005], both of which lead to an increase in the moving mass and thus increasing amplitudes. The timing of peak amplitude in a rockslide seismogram would then be related to the time at which the greatest mass is in motion on the slope. As the duration of movement for an individual block may vary widely due to size, shape and relative position, some parts of the rockslide may have already stopped while others continue, generating a signal with gradually decreasing amplitude. Signal duration should thus be comparable to event duration [Norris, 1994; McSaveney, 2002] at local stations. Irregularities in the seismogram may be due in part to successive failures [McSaveney, 2002].

[45] High-frequency signals have been linked to block impacts [e.g., Moore et al., 2007; Deparis et al., 2008; Vilajosana et al., 2008]. For our Kärpf [9] event, a clear high-frequency signal around 4 Hz was visible on the vertical trace about 2 s before the main lower-frequency portion of the spectrogram (Figure 5a). Based on a series of photographs, we could identify that the rock mass failed as a single large block, subsequently disintegrating upon impact (Figure 2a), and we interpret the high-frequency portion of the signal as being caused by this impact. Similar relatively high-frequency signals between 4 and 8 Hz were also visible around the event onset for other events with presumed free-fall and impact phases. The presence of these high-frequency signals may thus offer important clues into the failure dynamics.

5.2. Estimating Event Properties

[46] The seismic metrics used in this study to best estimate event parameters were DUR, ePGV, and EA. Exchanging AGV for EA resulted in the same model parameters and correlation coefficients, however EA is less dependent on an accurate duration estimate. An erroneously longer duration, for example, will only include additional background noise in the EA value, which is generally much smaller than the actual signal, while an erroneously short duration will not include the tail ends of the signal, which are also typically small compared to the overall signal area. This result also indicated that our duration estimates were good in the context of overall uncertainty.

[47] While runout estimates showed good correlation with actual values (r2 = 0.8), the Eiger [2]–[6] and Zuetribistock [18]–[20] events stand out on Figure 9b. Since we assigned very similar runout values to all events occurring on the same slope, the estimated runout distances should converge to a single point. Instead we observed two vertical lines of points at around 180 m (Eiger events) and 1100 m (Zuetribistock events). This result may either be caused by an imprecise ‘actual’ runout value, since we often did not have detailed information on the individual events. On the other hand, a combination of basic seismic metrics may simply not be as useful for predicting runout (compared to volume or PE) across a large range of events. Although not shown here, the event distribution of drop height estimates appeared similar to that of runout, indicating that we have the same problem of either incorrect ‘actual’ drop height values or an unsuitable method.

[48] The rock ‘falls’ subset consisted of nine events, but on the runout plot in Figure 10b, Aguille Dru [1] shows a much greater value than other fall events. The same was true for drop height. Using least squared error methods gives undue importance to such outliers, and the current best fit equations could change significantly if we incorporate new medium- to large-sized rock fall events. On the other hand, while the equation parameters did change by omitting Aguille Dru [1], the resulting estimates for the Eiger and Kärpf events were very similar to those presented, and adding more events may not significantly alter our results. A maximum-likelihood method could improve our parameter estimates, recognizing outliers and additionally incorporating data from all available stations.

[49] To assess the relative contribution of different seismic metrics to a given event parameter estimate, we can compare the slope values from Table 6 for a specific seismic metric across different event parameters and categories. Direct comparison among seismic metrics is not possible, since we did not normalize the metrics used in the inverse analysis; this ensures that our method works for unknown seismic signals. In our analysis of the ‘all’ events category, the slope parameters for runout and drop height were similar to those for ‘fall’ events, suggesting that estimation of these parameters is not sensitive to failure mode. Results for volume and PE, however, differed significantly between the ‘falls’ and ‘all’ event categories. For rock falls, ePGV was more important while duration was less important in assessing volume and PE. This finding agrees with observations of other authors, for example, Moore et al. [2007] who observed high-amplitude, high-frequency spikes in the seismic signal of rock falls, and Deparis et al. [2008] who generated synthetic seismograms of block falls showing high-amplitude, high-frequency signals. If a rock fall seismogram is strongly influenced by the initial impact, this would validate the relationship to peak ground velocity discovered in our work. EA also contributed more to volume and PE estimates in the ‘falls’ category, while in the ‘all’ category the slope parameter for EA was close to zero. If EA is a proxy for event dynamics (in this study the difference between strong first impacts of rock falls versus more gradual mass release of rock slides), then this seismic metric would be unsuitable for estimating volume and PE when all events are grouped together. When analyzing distinct event types, however, EA may be a reliable indicator of event volume and PE.

[50] Results discussed above highlighted differences in seismic signals generated by rock falls and other rockslide types. We therefore expect that other types of mass movements may have different seismogram characteristics and result in unreliable parameter estimates using our method. We were able to test this hypothesis on a pair of moraine slumps consisting of unconsolidated glacial till. The two moraine landslides occurred in May 2005 and May 2009 from the Stieregg slope opposite the Eiger rockslides listed in Table 1. The 2005 event had a total volume of 500,000 m3 [Balmer, 2005] with a runout distance of 400 m and drop height of 140 m. The 2009 event had a volume of 300,000 m3 [Petroni, 2009] with a runout distance of 300 m and drop height of 140 m. While the seismic signals of both moraine slumps superficially resembled those of rockslides, the signal amplitude was much lower than would be expected for a rock event of comparable volume. Consequently, the event parameter estimates from our analysis were a poor match to the actual values. For the 2005 event, equation (6) yielded a volume estimate of 30,000 m3, with a runout of 370 m and drop height of 290 m. The 2009 event volume was estimated to be 50,000 m3, with a runout of 500 m and drop height of 380 m. Volume estimates for the moraine slope failures were lower than the actual values by an order of magnitude.

5.3. Improving Rockslide Parameter Estimates

[51] Our rockslide location estimates are useful as a first rough approximation, but to actually pinpoint an unknown event to a specific alpine valley requires better location accuracy. The large RMS values, reflecting difficulty in picking reliable arrival times, indicate that the problem may be ill-posed for the given station coverage and arrival time uncertainties. However, one event, Monte Rosa [13], had the most adverse effect on our results. This was a large rock-ice avalanche with a cigar-shaped seismogram and extremely emergent onset, making the arrival time picks unreliable and giving a particularly poor location estimate. The same regression analysis without the Monte Rosa event reduced the average location error to 7.9 km, and then distance to the nearest seismic station exerted the greatest influence on overall location mismatch (r2 = 0.20, versus r2 = 0.06 with Monte Rosa). Distance to the nearest station affects the accuracy of our arrival time picks, since a signal at a closer station will typically have a higher S/N ratio and the arrival times can be more clearly distinguished in emergent signals. Minimum station-event distance can be improved with a more evenly distributed station network, which is an actively ongoing task of the SED. A less costly way to improve location estimates would be to improve our event arrival time picks, for example by analyzing initial particle motions or spectral arrival times.

[52] At the present time, our ability to estimate rockslide locations may not be overly useful to local geologists. Although our method for locating rockslides is crude, we were able to locate a series of unknown rockslides within the correct area. The events in question occurred in Italy near the Swiss border; no information was available in Switzerland, and all documentation eventually uncovered was written in Italian. For these events, our location estimate provided the first clue to guide further investigation, and led to our eventual discovery of the actual events about one year after their occurrence. Clearly these were known to the local geologists, but effective information transfer stopped at geographical borders. Correctly locating rockslides can both improve scientific research and allow for rapid secondary hazard assessment. As such we hope our results will motivate future research.

[53] Our inverse analysis was performed using seismic metrics extracted from only the nearest station to every event. This means that the station-event distance varied considerably between 1 and 25 km throughout all events in our data set. Because attenuation and geometrical spreading in the upper crust typically decrease seismic amplitudes, and dispersion and differential wave velocities increase signal duration with increasing distance, the variable station-event distance in our study might pose a problem. To investigate this possibility we used an empirical distance-dependency method to extrapolate all seismic metrics to a common station-event distance of 30 km. Since attenuation and dispersion are expected to be path-dependent in alpine terrain, we used the individual distance dependencies determined for each event separately. We then repeated the bivariate and multivariate analyses. The same combination of seismic metrics (ePGV, EA, and DUR) resulted in the best correlations, but the r2 values themselves were consistently lower by 5–9% compared to those using the nearest station metrics. Although distance-adjusted seismic metrics should in theory correct for attenuation, geometrical spreading, and dispersion, and thereby provide improved event parameter estimates, it appears that our distance-dependency estimates are not sufficiently accurate. An alternative solution to this problem might be provided by using maximum-likelihood methods similar to strong motion earthquake analysis, and using a nonlinear relationship between metric amplitude and station-event distance [e.g., Joyner and Boore, 1993].

[54] Although generating meaningful event parameter estimates for all rockslide types was the main goal of this study, we also analyzed the rock ‘falls’ subset of events to investigate whether specific event types have common distinguishing seismic characteristics. In this case, an equation tailored for falls alone led to improved parameter estimation because the defining characteristics of rock falls could be taken into account. However, by using only the subset of rock falls, we significantly reduced the total number of events used in the analysis, and a smaller number of samples can often lead to greater correlation values. Conversely, in the distance-dependency relationships the ‘falls’ subset performed worse than for all events. In both cases, the difference may be due to the ‘falls’ category containing events from only three distinct slopes (two for the distance-dependency analysis), and the results may therefore be influenced by site-specific errors. Adding more rock fall events as they occur may validate our present conclusion of improved event parameter estimates for ‘falls’ alone.

5.4. Validation of Rockslide Parameter Estimates

[55] Although our multivariate regression (equation (6)) worked well for the assembled data set, the real measure of viability is prediction of event parameters for new, previously uncharacterized rockslides. We were able to test our estimates on two events that occurred at Richitobelfall (Switzerland) on November 26 and 27, 2010. During the first event, a large block detached from a ledge and fell about 200 m before impacting the ground. The second event occurred one day later at the same location, and was likely composed of material destabilized by the initial failure; it presumably also experienced some amount of free-fall. Approximate event volumes were reported in newspaper articles two days later as 60,000 m3 and 40,000 m3 [Clavadetscher, 2010]. Analyzing post-event photographs and DEMs, we measured a runout distance of ∼550 m and total drop height of ∼440 m. Using equation (6) with the coefficients developed for ‘all’ events resulted in volume estimates of 66,000 m3 and 54,000 m3 for the two failures, respectively. Considering that the range of volume estimates at ±1 standard deviation was about 35,000 m3 to 70,000 m3, the predicted values fit the observed volumes well. As the reported event volumes were most likely only rough field estimates, it is especially important to note that the actual and estimated relative sizes are consistent, i.e., the first rock fall was larger by our estimates. The predicted runout and drop height values also match the actual measurements reasonably well, with estimated runouts of 680 and 660 m and estimated drop heights of 490 and 470 m.

[56] Two other rockslide events served as additional validation, although the results are less conclusive. One event associated with the large Randa rockslides of 1991 (see section 2.1) occurred on May 22, 1991. The detailed event dynamics are unknown, and the total volume was reported only as “a few 100,000 m3” by Schindler et al. [1993]. We measured a runout distance of 1050 m and a drop height of 790 m from photographs and DEMs. Equation (6) yielded a predicted volume of 300,000 m3, which is the correct range considering the uncertainty of the original statement. The estimated runout was 1260 m and the estimated drop height was 890 m, both relatively close to the measured values. The third site used for validation is the Formazza rockslide that occurred on the Italian-Swiss border on April 19, 2009. This rockslide was composed of three distinct sub-events, but only the total volume was reported as ∼500,000 m3 by the local geologist [Coluccino, 2009]. We used photographs of the scarp to estimate a runout distance of 1000 m and a drop height of 650 m, although these are maximum possible values and probably differed between sub-events. Our event parameter estimates obtained from equation (6) yielded predicted volumes for the three sub-events of 175,000 m3, 90,000 m3, and 180,000 m3, summing to a total volume of about 450,000 m3. Runout was estimated to be 1000 m, 650 m, and 960 m, while drop height was estimated to be 720 m, 490 m, and 700 m, respectively. Most of our estimates are encouragingly close to actual values. In particular, our estimates for the two larger sub-events, which were likely responsible for the maximum debris runout seen in the photographs, are in good agreement with the measured runout and drop height.

[57] Together, these three examples show that our ability to estimate key parameters of an unknown rockslide event (using equation (6) with the coefficients in Table 6) is thus far promising for events of different volumes. The station-event distances in these test cases ranged between 8 and 17 km, so again the practice of using only the nearest station resulted in good estimates. However, if a growing number of future rockslides are not well-predicted by equation (6), we can easily adapt the coefficients in Table 6. Even if this should not be the case, uncertainties associated with our estimates will remain high using the current method. To hone our parameter estimates further, we will likely need to incorporate other important rockslide parameters such as runout path substrate and morphology. Improved, time-dependent seismic metrics based on spectral or polarization properties might also result in better event parameter estimates. However, one clear advantage of our method is its simplicity. While the coefficients listed in Table 6 are specific to the SED station network, they can easily be adapted to other regions and seismic networks. The seismic metrics used are easy to compute, and rockslide parameter estimates for unknown events can be generated within a matter of minutes.

6. Conclusion

[58] After assembling a data set of twenty rockslide events in the central Alps, we analyzed the associated seismic signals and observed that rockslide seismograms share a number of common characteristics across a wide range of failure types and volumes. The time series seismic signals have an irregular envelope with emergent onsets and slowly decaying tails. The main component of seismic energy is typically contained in frequencies below ∼3–4 Hz, and the spectrogram generally exhibits a triangular shape, with higher frequencies decaying earlier. High-frequency signals between 3 and 10 Hz may be caused by the impact of large blocks on the ground. Although most portions of a rockslide seismic signal show no clear polarization, we could identify evidence for both body and surface waves, with Rayleigh waves being more prominent in seismic signals from events having an initial free-fall phase.

[59] The amplitude of seismic signals decreases with distance according to a power law relationship, although our analysis indicates that this distance dependency is influenced by regional complexity such as topography in alpine settings. The detection limit for a rockslide event of specific volume was identified for our station network (equation (5)), which also depends on the quality of the signal at each seismic station. Our rock ‘falls’ subset, containing events with an initial free-fall phase, exhibits similar detection distances to rockslides of larger volume, indicating that the detection limit may depend on the excited wave types. Location estimates were generated using automatic arrival time picks calculated from sliding window averages, and input into a standard earthquake locating routine. The resulting location mismatch is 10.9 km on average, which will need to be improved with better arrival time picks in order to more precisely locate unknown events.

[60] We extracted five simple metrics from each rockslide seismogram: signal duration (DUR); peak value of the ground velocity envelope (ePGV); velocity envelope area (EA); risetime (RT); and average ground velocity (AGV). Using these seismic metrics we attempted to estimate five fundamental rockslide event parameters: volume, runout, drop height, potential energy, and Fahrböschung. Bivariate analysis revealed that event parameters can be reasonably well predicted using either DUR or ePGV. Employing multivariate linear regression, we were able to improve our estimates of event parameters using the combination of DUR, ePGV, and EA. In particular, the correlation coefficient between actual and estimated volume was r2 = 0.85. Runout distance, drop height, and potential energy were also well-resolved; only Fahrböschung (angle of reach) could not be predicted using our seismic metrics. We also performed the same analysis on a subset of nine events consisting of rock ‘falls.’ The best fit combination of seismic metrics was again DUR, ePGV and EA, and correlations between estimated and actual event parameters were consistently improved compared to the analysis with ‘all’ events.

[61] We have also assessed the relative contributions of the best three seismic metrics used for event parameter estimates between the ‘all’ and ‘falls’ event categories. In the ‘falls’ subset, ePGV is more important in estimating volume compared to the analysis with ‘all’ events, indicating that peak seismic amplitude may be related to the magnitude of the impact of material on the ground. Finally, EA is a small contributor when estimating volume in the analysis using all events and a much larger contributor in the ‘falls’ subset analysis, indicating that envelope area may be useful in distinguishing event types.

[62] Three rockslides not included in our regression analyses were used to validate the method of event parameter estimation. All volume estimates were found to be reasonably close to actual values, well within the correct order of magnitude with consistent relative sizes. While predicted runout distances were slightly greater than actual distances, they provided a good first estimate. Our method for estimating rockslide parameters from seismic signals may be improved by taking into account other factors, for example, attenuation related to topography. However, one clear advantage of our present method is its simplicity. The seismic metrics used are simple to compute, and approximate parameter estimates for new events can be generated within a matter of minutes. Provided that a suitable data set of rockslide events is available, our method can also be easily adapted to other regions and seismic networks.

Acknowledgments

[63] The authors would like to thank Florian Amann, Nicholas Deichmann, Donat Fäh, Stephan Husen, Hans Rudolf Keusen, and Bruno Petroni for valuable data as well as helpful and interesting discussions. Jaqueline Caplan-Auerbach and two anonymous reviewers provided valuable reviews that helped improve this manuscript.

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