Defining Seismogenic Sources

from Historical Earthquake Felt Reports

Paolo Gasperini*, Filippo Bernardini#, Gianluca Valensise# and Enzo Boschi*#
*Dipartimento di Fisica, Settore di Geofisica, Università di Bologna

#Istituto Nazionale di Geofisica, Roma

Submitted to Bull. Seism. Soc. Am.

(Revised version, August 1998)

Abstract
We present a method that uses macroseismic intensity data to assess the location, physical dimensions and orientation of the source of large historical earthquakes. Intensity data contain a great deal of information that can be used to constrain the essential characteristics of the seismic source. In particular, both the seismological theory and its practice suggest that the orientation of the source of significant earthquakes is reflected in the elongation of the associated damage pattern. A plausible and easily manageable way of describing a seismic source is by representing it as an oriented ñrectangleî, the length and width of which are obtained from moment magnitude through empirical relationships. This rectangle is meant to represent either the actual surface projection of the seismogenic fault or, at least, the projection of the portion of the Earth crust where a given seismic source is likely to be located.

The systematic application of this method to all the M>5.5 earthquakes that occurred in the central and southern Apennines (Italy) in the past four centuries returned encouraging results that compare well with existing instrumental, direct geological and geodynamic evidence. The method is quite stable for different choices of the algorithm parameters and provides elongation directions which in most cases can be shown to be statistically significant. In particular, the resulting pattern of source orientations is rather homogeneous, showing a consistent Apennines-parallel trend that agrees well with the NE-SW extension style of deformation active in the central and southern portions of the Italian peninsula.

Introduction
Modern seismic hazard techniques are increasingly focusing on assigning the most severe historical earthquakes to the relevant seismogenic sources. This effort aims at supplying more faithful predictions of ground shaking than those obtained from conventional seismotectonic analyses, both for the near-field and for the more populated areas away from the main tectonic belts, through the calculation of reliable earthquake scenarios for each well constrained source. Localizing destructive historical seismicity onto a discrete number of tectonic sources and developing segmentation models involves a systematic examination of the location, geometry, size, and possibly recurrence properties of the largest possible number of individual seismogenic faults. Unfortunately, modern seismology tends to treat all these parameters separately, often reflecting the variable level of certainty with which they can be investigated. For example, several methods allow the estimation of the earthquake focal mechanism from instrumental data, but this can be done only for earthquakes that occurred during the past half century or so. Similarly, most of the available instrumental estimates of seismic moment for damaging earthquakes refer to events that occurred after the deployment of standardized global networks (such as the WWSSN, established in the early ï60s). The uncertainty in the location of many sources is often as large as that of earthquakes located with a regional network, unless the event fortuitously occurred within a local network. This uncertainty is even larger for historical earthquakes not associated with obvious and known tectonic features. At any rate, the location of a damaging earthquake is usually treated separately from its magnitude or its relations with the local tectonics, that is, by separate investigators using widely different data. Exceptions may be represented by the few earthquakes investigated through observations of coseismic strain (geodetic data) in addition to seismometric data, but this circumstance is limited to very few earthquakes of this century. Finally, the characterization of a seismic source rests on the possibility of uncovering purely geological evidence for previous events, or paleoearthquakes, or at least geological evidence for the rate of associated tectonic strain; an exercise that is possible only for a limited number of major sources, usually a small fraction of all those that hold a potential for damaging earthquakes.

Defining a set of seismogenic sources through a standardized criterion is therefore not an easy assignment. As Reiter [1990] puts it ñDefining and understanding seismotectonic sources is often the major part of a seismic hazard analysis and requires knowledge of the regional and local geology, seismicity and tectonicsî. Perhaps due to the difficulties in identifying individual large sources, either by recourse to geological data alone or through a combination of historical and geological evidence, most national seismic hazard plans still rely almost exclusively on catalogues of historical seismicity with very little support from field and instrumental data (e.g. Muir-Wood [1993]). This condition is further stressed by the circumstance that in many countries the amount of available knowledge on historical seismicity is often considered sufficient to supply a satisfactory representation of the earthquake potential.

Although we certainly agree that historical catalogues supply a reasonable first-cut representation of regional seismicity, we want to use Italy as an example to demonstrate that the information contained in homogeneously collected intensity observations can be used to quantify the essential parameters of the seismic source, therefore providing a more valuable contribution to the assessment of seismic hazard than commonly assumed. In particular, we want to propose a strategy through which seismogenic sources documented solely by historical information can be described by the same set of physical parameters normally used to describe sources for which modern instrumental observations are available. The ultimate goal of this strategy is to complement and strengthen with historical information the usually limited instrumental or surface faulting evidence forming the current earthquake distribution and recurrence models.

Our approach is similar to that taken by Johnston [1996] for quantifying the seismic moment of some large pre-instrumental earthquakes in stable continental regions, but somewhat more ambitious. In this paper we process intensity data (1) to estimate the earthquake location, expressed as the center of the distribution of damage; (2) to assess the earthquake seismic moment, expressed in terms of moment-magnitude obtained from the overall extent of the damage pattern; and (3) to make inferences about the physical dimensions and (4) orientation of the causative fault, respectively using empirical relationships and using an original algorithm described later on in this paper. The estimated parameters are then calibrated using earthquakes for which both intensity and modern instrumental data are available. Finally, each earthquake source is conceptually and graphically delineated by a rectangle representative of the fault at depth.

Our ultimate goal is to learn about as many as possible potential or proven sources of damaging earthquakes of an extended region. After a first catalogue of historical sources has been obtained, additional and often perfectly unknown seismogenic faults can be inferred from the analysis of the spatial relations between adjacent sources, or between them and other smaller (non-damaging) historical or instrumental earthquakes, or by recourse to more focused geological observations. In the process we would also test the extent of overlap between adjacent sources, that is, the regularity of the seismic release in space. Proving or disproving a stringent regularity would obviously have important implications for the assessment of regional seismic hazard.

In this paper we summarize the full approach describing in better detail the part of it that deals with the assessment of the fault orientation. We use the central and southern Apennines of Italy as a test area for the stability and appropriateness of the proposed method.

Previous efforts
Estimating fault parameters from Mercalli intensity (ñmacroseismicî) data has been the object of numerous investigations during the past twenty years and represents one of the most challenging developments of modern seismic hazard assessment. Probably the first attempt to derive quantitative information on the earthquake source from macroseismic data can be traced back to Shebalin [1973], who proposed to estimate the dimension and the orientation of a seismogenic fault from the ellipticity of the highest degree isoseismals. This study, however, analyzed the shape of hand-drawn isoseismals of a limited number of selected earthquakes, and therefore its conclusions are still essentially qualitative.

Starting with the contribution of Ohta and Satoh [1980], several attempts have been made at modeling macroseismic intensities generated by sources of known geometry with various techniques. Among them are the kinematic function KF [Chiaruttini and Siro, 1981], the generation of synthetic seismograms by normal mode summation [Panza and Cuscito, 1982; Suhadolc et al., 1988; Pierri et al., 1993] or by ray-tracing [Zahradn'k, 1989]. Some of these investigators have subsequently tried to infer the focal parameters of historical earthquakes from intensity data (e.g., Chiaruttini and Siro [1991]; Sirovich [1996]), but so far the results of these attempts have not been extensively tested against instrumental data, partly due to the fact that good quality and homogeneously collected intensity data have not been largely available in revised catalogs until 1995.

Notwithstanding possible rapid developments of these techniques in the near future, we believe that at present most of them are not reliable enough for widespread application. In the absence of a physical model explaining the spatial pattern of intensity data (in particular, of a function for converting ground displacement, velocity and acceleration into felt intensity), macroseismic data alone have not been able to constrain efficiently parameters of the seismogenic source which do not have a straightforward correspondence with the observed intensity, such as the fault dip and the sense of slip (fault rake). On the contrary, the strike of the seismic source (that is, the azimuth of the seismogenic fault) is somehow related to the distribution of the earthquake effects. In the past, the fault azimuth was commonly inferred by means of a visual inspection of hand- drawn isoseismals (e.g., in Shebalin [1973] and subsequent Shebalin-type approaches). This procedure obviously introduces a strong amount of arbitrariness, since the person in charge of drawing the isoseismals may somehow convey in the artwork his or her own preconceptions about the location and geometry of the seismogenic fault, often forcing the data to say more than they really show. More recently other workers have produced ñobjectiveî isoseismals through automatic computer contouring (e.g., De Rubeis et al. [1992]), but also in this case all possible inferences can only be visual, and therefore subjective and almost impossible to test statistically.

A visual analysis of isoseismal lines may indeed be helpful for identifying survey blunders or anomalous intensity poits resulting from site effects. However, the statistical analysis of individual observed intensity values must be preferred when the goal of the analysis is to derive global quantitative estimates of the main source parameters. This is now a viable option in Italy, following the recent publication of two large and comprehensive databases of macroseismic data by Boschi et al. [1995, 1997] (ñCatalogue of Strong Italian Earthquakes from 461 B.C. to 1990î, hereinafter referred to as CFTI, containing over 31,000 data relative to 460 earthquakes) and Monachesi and Stucchi [1997] (ñDOM 4.1 Catalogueî, containing over 37,000 data relative to 950 earthquakes). Unlike traditional catalogues, which for each earthquake usually report only synthetic information on the origin time, location and magnitude, these new compilations also include the list of the localities for which the Mercalli intensity was re-evaluated with homogeneous and standardized criteria.

Modeling approach
Our analysis is based exclusively on the latest version of the CFTI [Boschi et al., 1997] as this compilation specifically focuses on earthquakes that are large enough to grant a seismologically plausible basis to the approach described in this paper. We focused on the central and southern Apennines (a portion of the Italian territory between 40.0Á and 43.2Á latitude North, 12.8Á and 17.0Á longitude East). for this is the most seismically active region of the whole Italian peninsula and is characterized by a relatively well defined and uniform tectonic pattern. Although we realize that a systematic comparison between the results obtained from the CFTI and the DOM 4.1 would be of interest for many readers, we feel that a similar analysis would require a thorough examination and comparison of the criteria used in the compilation of the two databases which goes beyond the scope of this paper. This systematic comparison and an extension of our approach to the whole of Italy will be the object of a future effort. We take this opportunity to observe that any future effort in this area of research will benefit from the availability of a joint CFTI/DOM 4.1 database currently in preparation (as of September 1998).

Due to the peculiar characteristics of the historical information available in Italy, all the intensities of this database are referred to the definitions of the MCS scale [Sieberg, 1932] rather than to the more recent EMS scale [GrÄnthal, 1993] or to the Modified Mercalli scale (MM) [Wood and Neumann, 1931], which is most commonly used in North America.

For the region of our interest the CFTI catalogue lists 41 large earthquakes, for a total of over 7,500 intensity data points (see Table 1 ). When this paper was in the final stage of preparation, we decided to include in our analysis the felt reports gathered during a preliminary survey of the effects of the 26 September 1997, Colfiorito, central Italy earthquakes [WGMSCE, 1997], as it allows for an interesting a posteriori test of our approach.

Our strategy involves five steps ( Figure 1 ):

Step 1 - Locating the source

We first compute the epicenter of each of the 42 earthquakes from macroseismic data alone. The epicenter is found through an averaging technique described by Gasperini and Ferrari [1995, 1997] and already utilized in the second release of the CFTI. This technique is briefly summarized in Appendix 1 . This epicenter is then used as the origin of the reference system for locating the extended source and for analyzing the azimuthal distribution of felt intensities to determine the source strike.

Step 2 - Assessing the earthquake seismic moment

The distribution of felt intensities of each earthquake is then used to infer the earthquake seismic moment M0 and the corresponding moment magnitude M using an algorithm described by Gasperini and Ferrari [1997]. Similarly to the earthquake location problem, this algorithm has already been used in the second release of the CFTI. This algorithm is briefly described in Appendix 2 .

Step 3 - Assessing the source dimensions (length and width)

The seismic moment of each individual earthquake is then used to infer the physical dimensions of the relevant source under the hypotheses set forth above (earthquake is characteristic and representative of maximum source potential). We used Wells and CoppersmithÍs [1994] empirical relationships to calculate the full rupture length and width of the seismogenic source. Although most of the best studied strong Italian earthquakes exhibit pure normal faulting, reverse and strike-slip faulting earthquakes are expected to take place particularly along the Adriatic margin. For this reason we used the relationships that were derived by these investigators as an average of ñAllî possible faulting styles:

Log10(RLD) = 0.59(±0.02) * M -2.44(±0.11)

Log10(RW) = 0.32(±0.02) * M -1.01(±0.10)

where RLD and RW are the subsurface rupture length and the down- dip rupture width, respectively, and M is the moment magnitude.

Step 4 - Assessing the source orientation (azimuth)

Once the source has been located and its physical dimensions evaluated, this step involves assessing its true orientation. This is accomplished by a new algorithm described in detail in the following section.

Step 5 - Representing the source

The seismic source is finally drawn as a rectangle centered on the macroseismic epicenter. The rectangle represents either the actual surface projection of the causative fault or, at least, the surface projection of the portion of the Earth crust within which the fault is more likely to be located. Since Italian faults tend to be predominantly dip-slip, as a first approximation the width of the rectangle delineating each source is plotted as if it represented the projection of a fault dipping 45ž in an unspecified direction perpendicular to the fault strike (see Figure 2a ).

The assessment of the orientation of the seismogenic source
Our reasoning starts from the common observations that the direction of maximum elongation of the highest degree isoseismals is controlled by the geometry of the seismogenic structure and that the highest degree isoseismals tend to approximate the projection of the fault upon the Earth surface ( Figure 2a ). We assume that these observations are the perceptible expression of a physical link between the source at depth and the pattern of ground shaking at the surface. Under this assumption, if all the sites where the largest intensities were observed are considered as the end-points of vectors belonging to a polar coordinate system centered on the macroseismic epicenter, the azimuth of each individual vector is likely to be close to the true strike of the fault; the larger the distance from the epicenter, the higher the probability ( Figure 2b ). Hence, the strike of the fault may be inferred by computing the ñcircular meanî of the azimuth of these sites. Since the geometry of the surface projection of the fault is symmetrical with respect to the epicenter (that is, two orientations at 180ž to one another are equivalent), the azimuth is represented by an angle ranging from 0ž to 180ž. We calculate this orientation by (1) doubling the azimuth of each site with respect to the epicenter, (2) calculating the circular mean of these angles, and (3) halving the resulting circular mean.

Similar to any other analysis of angular data, the reliability of the circular mean rests upon the uniformity in the distribution of the data themselves. Since the angular location and the dispersion are not independent variables, a uniform distribution has no significant central value and any further statistical analysis is therefore generally meaningless. A number of statistical tests are available to analyze the uniformity of a circular distribution. Among them the Kuiper test proved preferable for small datasets, while the Rayleigh test proved most powerful where the distribution of the parent population is Von Mises-type [Rock, 1988]. The mathematical details of the procedure for calculating the circular mean, the associated standard deviation and the significance levels of the distribution uniformity tests are described in Appendix 3 .

Before running the algorithm with real data we must select an appropriate lower threshold for the macroseismic intensity of the data points to be included in the averaging process. Ideally, the dataset of each earthquake source should include only the localities where the observed intensity is largest. In real applications, however, such maximum effects often occur at a limited number of scattered sites as a result of local amplifications induced by the near- surface geology, of particular characteristics of the local buildings, of focusing of the seismic energy or constructive interference of wave- trains from different portions of the source. Under such circumstances the highest intensities of a given earthquake may represent outliers in the data distribution, in which case the source is more correctly represented by the pattern of sites that experienced an intensity one or even two degrees lower than the maximum observed. This apparent dualism is well established in modern earthquake catalogues, which usually separate the epicentral intensity I0 from the maximum observed intensity Imax (e.g., Boschi et al. [1997]).

A rational criterion to choose the intensity threshold is to select a value such that the average epicentral distance of sites having a larger intensity is comparable to the fault size. As we have seen in Step 3, we can use Wells and CoppersmithÍs [1994] empirical relationships to calculate an approximate source length as a function of M. We can then pick the intensity threshold that gives the best equivalence between half of the fault length and the average distance of the data points from the epicenter. Nevertheless, our experience shows that the plain application of these criteria may lead to retain data points having an intensity more than two or three degrees lower than the maximum intensity. This condition may be (1) the effect of the presence of strong intensity amplification effects, (2) the result of incompleteness of the macroseismic field and hence of mislocation of the true epicenter (e.g., when this occurs offshore or close to the shoreline), or (3) the result of overestimation of the earthquake magnitude. We therefore decided to establish a lower bound for the intensity threshold to prevent the inclusion of intensities data which are too low to be representative of the source orientation. Based on our experience with the dataset analyzed in this paper, we set this lower bound at one degree below the maximum intensity plus uncertainty (for example, for an Imax equal X we allow the intensity threshold to reach intensity VIII-IX). This is also the maximum value normally attained by the difference between the epicentral intensity I0 and the maximum intensity Imax.

An additional important issue is the choice of an appropriate distance weighting scheme. Under the assumptions mentioned above and for any given intensity, the farther a certain site, the higher the probability that the azimuth of that site approximates the strike of the fault. We assume that this probability is proportional to some function of the distance, normalized by the average epicentral distance of all data points having the same intensity. This function should be somehow related to the attenuation of the intensity with distance. A simple relation, which proved to fit well the attenuation of earthquake intensity for the Italian territory was proposed by Berardi et al. [1993]. This relation, termed CRAM (Cubic Root Attenuation Model), is given by the following expression

®I= a + b D1/3
where ®I=I0-I is the difference between the epicentral intensity and the intensity observed at a given site, and D is this siteÍs distance from the epicenter. A least squares fit over all the sites having an assigned intensity in our database returned a=-0.46 and b=0.93 (the corresponding coefficient of variation is R2=0.52). We can then invert the CRAM relation to estimate the average normalizing distance for each intensity and use the cubic root of the normalized distance as a weight assigned to each of the data used to estimate the fault azimuth.

To evaluate the overall reliability of Step 4 of our modeling approach we performed a stability analysis by comparing the results of different weighting schemes. Reasonable choices for this test include:

[a] no distance weighting (all data are assigned the same weight);

[b] cubic root of distance weighting (see above);

[c] distance weighting (weight is proportional to the normalized distance of the point from the epicenter).

Similarly, we tested different lower bounds for the intensity thresholds according to the following schemes:

[d] zero degree lower bound (which implies that only data points where maximum intensity is observed are used);

[e] one degree lower bound (see discussion above);

[f] no lower bound (all available data could be used).

Notice that in both cases we are essentially comparing the results of our preferred or ñcentralî schemes, indicated by [b] and [e] and already described in the text, with those obtained using two extreme scenarios.

Finally, we need to define the minimum size earthquake for which the method can be used with confidence. This step is crucial since the analysis of earthquake sources comparable in size with the average distance between the sites used to estimate the azimuth could return meaningless results because of the low ñresolving powerî of the data distribution itself. Based on the average spacing of historical settlements in Italy, we assume this minimum fault length to be somewhere between 5 and 10 km, which corresponds to a moment magnitude of 5.3 and 5.8 respectively [Wells and Coppersmith, 1994]. We therefore decided to analyze only earthquakes for which M> 5.5. Good candidates must also be characterized by at least 5 data, which is the minimum figure for which the statistical tests hold rigorously. This condition applies to 27 out of 42 earthquakes of magnitude 5.5. and above reported by the CFTI for the region of interest (see column NAz in Table 1 ). To maximize the use of available data, however, we tentatively extended the application of the algorithm also to 9 additional events for which at least 3 data points are made available by the selection criteria.

Modeling Results
Figure 3 shows the full modeling procedure applied to the 23 July 1930, Irpinia (southern Italy) earthquake (see also Figure 1 and discussion on modeling strategy in previous section). For this earthquake there exists an instrumental estimate of MS=6.6 [Margottini et al., 1993]. The macroseismic dataset includes 511 localities with MCS intensities in the range II to X. The epicenter (panel [a]) is computed by averaging the coordinates of the 3 sites where the maximum intensity (X) was observed (see Appendix 1 ). The moment magnitude (M=6.7: panel [b]), that was computed with the mixed epicentral intensity-isoseismal radii method (see Appendix 2 ), is slightly larger than the instrumental estimate. The source azimuth (N108ÁW: panel [c]) was determined using 16 intensity data in the range VIII-IX to X. The length and width of the inferred source (32.6 and 13.6 km, respectively: panel [d]) are computed from Wells and Coppersmith's [1994] relationships; to account for the presumable dipping geometry of the fault, however, we plotted the source width as the surface projection of a 45Á-dipping plane (multiply the width by the cosine of 45Á).

A similar procedure was followed for all the 42 M>5.5 central and southern Apennines earthquakes that we selected to test our approach. Figure 4 and 5 show the location, extent and orientation of the inferred sources. These earthquakes occurred between 1600 AD and present, and are shown by rectangles constructed using exclusively historical information following the five steps of our modeling scheme. We wish to recall that such rectangles comprise a synthetic representation of the source that is coherent with standard schematizations based on instrumental or field evidence. Figure 4 shows the results obtained using different distance weighting schemes, while Figure 5 shows the effect of different choices of different lower bounds for the intensity threshold. Under the relatively strict requisites of our preferred schemes ([b] and [e]), for 6 out of 42 earthquake sources we could calculate only the location and size but not the azimuth (all of them have M <6.0), and for this reason they are shown with circles in which the diameter is the estimated fault length (except for three solutions obtained with the more tolerant scheme [f], for which a rectangle is shown).

For many sources the estimated azimuth does not differ much for different distance weighting schemes (see Figure 4 ). The most evident discrepancy concerns the large 1627a, Gargano earthquake, which appears to vary from a trend almost parallel to the Apennines (from about N60ÁW for the [a] and [b] schemes to about N30ÁE for the [c] scheme). Less pronounced differences (within 10Á) can be observed for some of the largest earthquakes such as the 1980, Irpinia, the 1915, Avezzano, the 1732, Valle Ufita, and the 1703a, Norcia. In general, the algorithm seems quite stable for different weighting schemes; in particular, in almost all cases the [b] scheme returns a result that is intermediate with respect to the other two, and for this reason we decided to regard it as our best choice.

Choosing different lower bounds for the intensity thresholds (see Figure 5 ) also does not appear to return drastically different results. The solutions obtained using the [e] and [f] schemes are almost coincident for most of the earthquakes. The only significant difference concerns the 1703a, Norcia earthquake and three relatively small (M<6.0.) earthquakes (1762, 1786 and 1851b), for which the azimuth can only be computed using the [f] scheme. On the contrary, larger deviations exist between the [d] scheme and the other two; the largest of them again concerns the 1627a, Gargano earthquake, the source of which varies in orientation by nearly 90Á from one scheme to another. For two other large earthquakes (1688, Sannio and 1980, Irpinia) the deviation ranges between 10Á and 20Á. It should also be noted that in 21 cases (versus 6 for scheme [e] and 3 for scheme [f]) the azimuth cannot be computed with the more demanding scheme [d] due to insufficient number of data points (less than 3). In contrast, the algorithm is rather stable with respect to the other two schemes. This suggests that the choice of using only data having the same intensity as the epicentral intensity (scheme [d]) is too restrictive and represents an unjustified limitation of the applicability of the algorithm. We therefore decided to assume the [e] scheme, which is also more plausible from the point of view of the physics of the problem, as the most reasonable and reliable choice.

Our preferred solutions are shown by white rectangles enclosed by a solid line in Figure 5 and are listed in Table 1 along with our estimated macroseismic epicenter and moment magnitude M. For each earthquake Table 1 also reports the significance level (s.l.) obtained from the Rayleigh and Kuiper distribution uniformity tests (see Appendix 3 ). In most cases the Kuiper test allows the H0 hypothesis that the data distribution is uniform to be rejected at least at s.l.<0.05, and therefore the source orientation can be estimated with confidence. For 11 earthquakes the significance level is larger than 0.05 and the H0 hypothesis cannot be confidently rejected. We could tentatively reject the H0 hypothesis for 4 of these 11 earthquakes where s.l.<0.10, whereas for the remaining 7 events the results must be considered with caution. The reason why we do not simply discard these results is because for most of these events the test statistics are not rigorous as the source azimuth was computed using less than five intensity data. In turn, the Rayleigh test does not allow the uniformity hypothesis to be rejected for about half of the computed azimuths (it can be rejected tentatively at s.l.<0.10 for 5 of them). At least some of these failures, however, could be ascribed to significant departures from a Von Mises-type distribution (which is not established for our data) more than to actual uniformity in the distribution of the data. At any rate, for both tests most of the failures concern moderate-sized events (M<6.0), hence smaller sources for which the azimuth is more difficult to estimate.

Comparing the inferred sources with instrumental and geologic evidence
As most of the 42 analyzed earthquakes occurred in the pre- instrumental era, very few extended fault models and focal plane solutions are available for a direct comparison with our intensity- derived sources. In this respect we wish to recall that, due to the peculiar characteristics of Italian tectonics, and particularly to the youthfulness of the present stress regime (see for example Pantosti et al. [1993]), very few of the major Italian historical earthquakes have been positively associated with a well-identified active tectonic feature. The CMT database (published in Dziewonski et al. [1981] and subsequent quarterly papers on Phys. Earth Plan. Inter.) supplies data for the four most recent earthquakes (1979, Valnerina; 1980, Irpinia; 1984, Val Comino; 1997, Colfiorito). For the 1962, Irpinia earthquake, a reasonably reliable focal mechanism computed using P-wave polarities is given by Westaway [1987]. Direct surface faulting evidence was documented for the 1915, Avezzano and for the 1980, Irpinia earthquakes, both of which were modeled also by inversion of coseismic elevation changes (see discussion below).

Table 2 shows a summary of the comparison between these instrumentally or geologically derived azimuths and the results of our intensity-based computations. In general the agreement is quite satisfactory. In particular for the 1980, Irpinia earthquake our estimate is very close (within 10Á) to the orientation of both of the CMT nodal planes and of the geologically inferred fault. For the 1979, Valnerina earthquake our solution is almost coincident with one of the two nodal planes, but unfortunately no geological or seismological evidence is available to date to decide which is the actual rupture plane. For the 1915, Avezzano earthquake the maximum difference is 13Á. For the remaining two earthquakes (1962, Irpinia and 1984, Val Comino) our result lies almost in the middle of the two instrumental solutions, with differences in the order of 20Á-30Á. Also for these two events no conclusive evidence exists to date as to which of the two nodal planes is the actual rupture plane.

For three especially well documented earthquakes we decided to extend the comparison to the full definition of the seismogenic source. Figures 6a , 6b and 6c summarize the results of a comparison of evidence available respectively for the 1915 Avezzano, 1980 Irpinia, and 1997 Colfiorito earthquakes versus the estimates derived in this paper. The following discussion focuses on the most evident discrepancies that come out of this exercise. For the source parameters that are fit satisfactorily the reader may refer directly to the information shown in Figure 6a , 6b and 6c .

1915 Avezzano

The 1915, Avezzano (central Italy) is the second deadliest earthquake of Italian history ( Figure 6a ). The concentration of population in the depression of the former Fucino Lake, which had been reclaimed in the 1860Ís and soon after re-utilized for extensive agricultural development and for new settlements, and the widespread amplifications of the ground motion induced by the particular configuration of the area, conspired in turning this earthquake into an immense catastrophe. Perhaps for this reason in current catalogues this earthquake is characterized by a large number of localities which were assigned intensity XI (see Figure 6a ). This circumstance has driven the inferred M up to 6.9, which implies a nearly 40 km-long causative fault. The geodetic model proposed by Ward and Valensise [1989] implies a M 6.6, but this is a minimum figure as it is based on the portion of the fault that could be resolved by observations of coseismic strain. In view of this limitation and given the extent of the observed surface ruptures, we may conclude that the true M of the 1915 earthquake was between 6.7 and 6.8.

Part of the misfit in the orientation of the fault could be accounted for by the northwestward propagation of the coseismic rupture [Berardi et al., 1995] and by the lack of settlements to the north and south of the epicenter.

1980 Irpinia

Our intensity-based source for the 1980, Irpinia earthquake ( Figure 6b ) is quite surprising for it fits the real seismic source nearly to perfection except for its location, which is shifted to the northwest by about 8 km. Indeed the macroseismic solution could not capture the intrinsic complexity of the earthquake rupture, that was characterized by at least three discrete subevents occurring within a 40 s time span, but it somehow responded to the northwestward propagation of the rupture (e.g., Bernard and Zollo [1989]), which caused an asymmetry in the distribution of the highest reported intensities with respect to the location of the seismogenic source.

1997 Colfiorito

The Colfiorito earthquakes ( Figure 6c ) make an especially interesting case as they occurred immediately after the modeling procedure and its parameters had been firmly established based on the experience gained from the rest of our dataset. The analysis uses the results of a preliminary survey of the earthquake [WGMSCE, 1997] completed on 2 October, that is, a week after the mainshocks, because the damage pattern was soon after worsened by a series of strong aftershocks (M>5), which effectively extended the region that ruptured during the sequence.

The main limitation of our macroseismic solution is represented by its inadequacy to account for multiple ruptures occurring closely spaced in time. Unlike the case of 1980, when the moment release was dominated by the first mainshock subevent, the two mainshocks of the Colfiorito sequence were comparable in size and are presumed to have ruptured in opposite directions, generating a pattern of cumulative damage that does not fully reflect the actual energy release. We believe that, had the two shocks occurred separated in time by a few years, our approach would have retrieved the correct extent of each individual source.

Tectonic constraints and implications
Although this work was not expressly intended to contribute to the understanding of recent Italian geodynamics, we feel that a discussion of our modeling results in the framework of the general seismotectonic context of this region may supply an independent means of assessing the ability of the algorithm to evaluate the true location, extent and orientation of major seismogenic sources. At the same time, some of our results may support on a more quantitative basis some of the current ideas concerning the Apennines seismicity.

A general conclusion from a simple visual inspection of Figure 5 is that the main earthquake sources of this region align along the crest of the Apennines within a <50 km-wide corridor, suggesting the existence of a relatively simple yet extremely continuous seismogenic belt. This intriguing circumstance was first pointed out exactly 150 years ago by Perrey [1848] based on a qualitative examination of intensity data, and has later become the basis for the development of modern earthquake recurrence models for the region (e.g., Valensise et al. [1993]). Notable exceptions are represented by the 1627, 1646, 1731, 1881, 1943, 1948 earthquakes, which following Frepoli and Amato [1997a, 1997b] could be interpreted as the manifestation of the existence of an active compressive belt rather well separated from the main active extensional belt straddling the crest of the Apennines.

A subsequent observation is that there appears to be limited overlap between adjacent sources. This condition supports the earlier assumption that our dataset of 42 large historical earthquakes is representative of as many individual sources belonging to a segmented belt. In conjunction with additional tectonic and instrumental evidence, this circumstance may form the basis for a systematic search of potential gaps in historical seismic release throughout the investigated region.

The combination of a mildly heterogeneous tectonic regime, some scatter in the input data and some instability in the processing algorithm could indeed be reflected in a tendency for the investigated sources to exhibit a rather scattered orientation. Quite surprisingly, no such tendency appears from the results shown in Figure 5 ; on the contrary, most of the sources seem to align in a rather orderly fashion along the trend of the Apennines. In particular, while the main sources of the southern Apennines all trend between N40ÁW and N60ÁW, the sources inferred for the two largest shocks of the 1703 sequence (1703a and 1703b in Figure 5 ) seem to testify a known transition from the N70ÁW-trending northern Abrutii tectonic structures to the decidedly more north- south trend of the Umbria-Marche Apennines (see for example Cello et al. [1997]). The only significant departures from the general trend concern smaller-size, less constrained earthquakes such as the 1639, 1646, 1853, 1873, 1881, 1904, 1933, 1948. Following the interpretation proposed by Valensise et al. [1993], at least some of these earthquakes (particularly those closer to the axis of the Apennines) might reflect the activity of known transverse tectonic lineaments (that is, perpendicular to the main trend of the Apennines) which are known to predate the onset of the present stress regime.

Overall, our modeling results are compatible with the general notion that the central and southern portions of peninsular Italy are actively extending in a direction perpendicular to the local strike of the Apennines. This circumstance has been qualitatively known for some time based on conventional geological evidence (e.g., Scandone [1983]), but it has been recently demonstrated to hold also for present-day tectonics by Valensise et al. [1993] and Amato and Montone [1997], respectively based on the analysis of the largest historical earthquakes comprising the central and southern Apennines segmented seismogenic belt and on a careful examination of direct indicators of the modern stress field (earthquake focal mechanisms and borehole breakout data). The uniformity of the trend delineated by our intensity-based sources and its consistency with the information supplied by several independent lines of evidence represent an implicit validation of the approach itself.

Conclusions
We developed a scheme for estimating the location, physical dimensions and orientation of seismogenic sources associated with large historical earthquakes for which no instrumental or field data are available. Our fundamental goal was to maximize the amount of information that can be extracted from historical seismicity observations supplied by modern catalogues, and organize it in a way that is fully compatible with the information made available by modern seismological networks, by geodetic observations of coseismic strain or by direct observations of surface faulting. The approach relies on the working hypothesis that each analyzed historical earthquake represents the maximum-size event that can be generated by its respective source. If proven, this hypothesis allows each earthquake to be regarded as an individual characteristic source that can be used to construct a fault segmentation model, or integrate an existing one.

We tested our approach using Mercalli intensity felt reports taken from the ñCatalogue of Strong Italian Earthquakes from 461 B.C. to 1990î electronic database [Boschi et al., 1997] for 41 events that occurred in central and southern Italy between the year 1600 and 1984 and for the 26 September 1997, Colfiorito (central Italy) events.

The approach turns the intensities reported for a given earthquake into a three-dimensional extended source of specified size, location and orientation, ready to be used for deterministic modeling of ground motion or for any other calculation of seismic hazard. The procedure is quite stable for different choices of the algorithm parameters and, in most cases, provides a result which is statistically significant against the hypothesis of uniform distribution of the data. The computer code used for the calculations was written in Fortran and will be available upon request.

The resulting pattern of source orientations for the central and southern Apennines is rather homogeneous and fully compatible with the prevailing style of local tectonic deformation of the area, which shows extension consistently trending perpendicular to the axis of this section of the Italian peninsula. Our results agree fairly well with instrumental or surface faulting evidence available for a limited number of large earthquakes, with typical inaccuracies in the order of 5-10 km for the source location, 0.2-0.3 moment magnitude units for the source size, and 10Á-15Á for the source orientation.

A significant limitation of the approach is represented by its inability to filter out possible distortions of the macroseismic field associated with source directivity or extreme source complexity. This characteristic, however, could eventually be turned to our advantage for exploring the dynamic properties of the source if independent information on the rupture timing and propagation direction becomes available. Nevertheless, the examination of the information available for modern earthquakes shows that in several cases the inaccuracy of our intensity-based estimates is comparable with the uncertainties in instrumental determinations.

In spite of this limitation, the overall arrangement of the inferred sources suggests only minimal overlap between adjacent sources and highlights "missing" source areas that may be incorporated in current fault segmentation models and should become the locus of more focused investigations in the future.

Acknowledgments

Many of the concepts in this paper benefited from discussions with D. Albarello, G. Ferrari and W. Marzocchi. We acknowledge thoughtful and encouraging contributions by A. Johnston and by an anonymous reviewer. This work was partially supported by the Italian Ministry for the University, Scientific Research and Technology (MURST).

Appendix 1
Calculation of the Macroseismic Epicenter
While the definition of instrumental epicenter is well established in seismological literature (e.g. Richter [1958]), the definition of macroseismic epicenter is still the matter of debate (see for example Cecic et al. [1996]). A natural definition is ñthe barycenter of the region of largest earthquakes effectsî, and it is widely accepted that at least for damaging earthquakes (M>5.5) and due to the details of the rupture history of the earthquake causative fault, this point may not correspond to the instrumental epicenter. The above definition is the core of the algorithm developed by Gasperini and Ferrari [1995, 1997] for the systematic relocation of the earthquakes reported in the CFTI [Boschi et al., 1995, 1997]. The main objective of this algorithm is to constrain within prescribed bounds the influence of various sources of uncertainty (e.g., local site amplifications, wrong location of historical sites, biased intensity assignments) over the final determination. This is accomplished by recourse to a robust central tendency estimator.

The algorithm operates through five steps:

1) The data are subdivided into classes of intensity; data in between classes are assigned to the lower intensity class (e.g., an intensity VII-VIII is assigned to class VII);

2) Localities that reported the maximum observed intensity (Imax) are set aside for subsequent calculations;

3) If the maximum observed intensity falls in between full values (e.g., IX-X), the localities that experienced the lower full value are selected in addition to all those where Imax was reported (e.g., all intensity IX-X plus all intensity IX data);

4) If the number of selected localities is less than 3 the dataset is extended to include data from the lower intensity classes up to Imax minus one degree;

5) The epicentral coordinates are calculated as the 25% trimmed average, that is, the average of all values included in the interval between the first and third interquartiles, of the coordinates of all selected localities.

All arbitrary parameters of the algorithm, such as the minimum number of data to be included, the minimum intensity threshold and the central tendency estimator, were selected by Gasperini and Ferrari [1995, 1997] based on a stability analysis.

Unfortunately the uncertainty associated with the algorithm cannot be estimated a priori nor a posteriori, but only assessed in terms of internal consistency of the full procedure. For this purpose, the sum of square residuals between the coordinates of the selected localities and the coordinates of the inferred epicenter are calculated for every earthquake. This parameter cannot be directly used as an estimate of the uncertainty in the location because it also reflects the size of the mezoseismal area, however, it may be used as a parameter controlling the reliability of the estimate: for example, a large value may implicitly indicate the existence of highly anomalous intensity points or the incompleteness of data distribution (e.g., when the epicenter falls offshore or in a sparsely populated area).

Appendix 2
Calculation of the equivalent moment magnitude
As in the case of epicenter calculation, there is no established consensus on how to derive an objective estimate of the earthquake size from intensity data alone. In the absence of a simple physical link between magnitude and intensity data, the only reasonable criterion to assess the validity of an empirical relationship is through statistics. Tinti et al. [1987] summarized three main approaches to this problem: 1) magnitude as a function of the epicentral intensity I0 only; 2) magnitude as a function of the isoseismal area or of the ñfelt areaî FA (i.e., the area where the earthquake was actually ñfeltî by people); 3) mixed methods combining I0 and FA.

Epicentral Intensity method. Due to the limited number of intensity data normally available for smaller or older earthquakes, until recently the most commonly used procedure involved fitting magnitude estimates of recent earthquakes to their epicentral intensity by a least squares regression, and then using the regression parameters to infer the magnitude of pre-instrumental events. The empirical relationships obtained from these types of analyses are normally characterized by an enormous dispersion due to the inherent uncertainty of the intensity parameter and by the uncertainty on the ipocentral depth. Since for the same size earthquake the deeper the source, the smaller the effects at the Earth surface, the magnitude of slightly deeper earthquakes is systematically underestimated by these methods, while that of shallower earthquakes is overestimated.

Isoseismals and Felt Area method. The area or average radius of individual isoseismals, or of the Felt Area, is indeed a much better estimator of the earthquake magnitude than a single intensity value [Toppozada, 1975]. Using this type of data, which reflect a combination of many spatially distributed observations, the irregularities of the intensity field due to source directivity, to the anisotropy of the seismic attenuation, or to site effects, are averaged out and hence strongly reduced. Even with this method, however, the source depth may play a significant role because it controls rather strongly the decay of intensity with distance.

Mixed method. This approach was first proposed by Galanopulos [1961] based on the observation that the two previous criteria are affected in opposite directions by the unknown depth of the source. Sibol et al. [1987] applied a variation of this method to compute the magnitude of historical earthquakes in the United States. The mixed method is certainly preferable when spatially distributed intensity data are available. The data supplied by the CFTI [Boschi et al., 1995, 1997] form an opportunity to test this technique for most of the strong Italian earthquakes of the past four centuries. The algorithm, originally developed by Gasperini and Ferrari [1995, 1997], attempts to compute an ñequivalent magnitudeî, that is, an estimate compatible with those that can be derived rigorously only by the usual instrumental procedure. We used the functional relationship derived by Sibol et al. [1987], modified to use not only FA data but also the area of individual available isoseimals.

The algorithm operates through six steps:

1) the macroseismic epicenter is computed for each earthquake (see Appendix 1 );

2) the epicentral intensity I0 is assumed to be equal to the observed Imax if at least two data with that intensity value are present; otherwise I0 is set to the second highest observed intensity value (with a lower bound represented by Imax minus one degree);

3) for each earthquake the distance between the macroseismic epicenter and each of the sites for which intensity is available is computed. This dataset is then used to derive the average distance RI for each intensity value (using the median as central tendency estimator);

4) using the instrumental magnitudes of Italian earthquakes revised by Margottini et al [1993], a bi-varied weighted regression law of the type proposed by Sibol et al. [1987] is fitted over the dataset of instrumental events for each intensity level:

M=a + b I02 + c log2(AI)
where AI is the area of a circle of radius RI. Intensity levels for which RI was computed with less than four data and the maximum intensity reported for each earthquake are not included in the computation. The weight assigned to each observation takes into account the uncertainity associated with the instrumental magnitude, the level of knowledge of each individual earthquake [Guidoboni, 1995], and the number of observations used to compute the average distances;

5) through the regression parameter computed in the previous step (one regression for each isoseismal intensity), the magnitude and corresponding uncertainty is computed for all the other earthquakes of the database and for each intensity level for which the average distance can be evaluated;

6) the equivalent moment magnitude M is computed for each earthquake as the weigthted average of the values estimated using the RI obtained for different intensity levels. The weight of each estimate is taken as the inverse of the squared error, and the uncertainty of the resulting magnitude is given by the inverse of the square root of the sum of weights. The actual values of the regression coefficients and the parameters of the goodness of fit for each regression are given in Gasperini and Ferrari [1997]. In most cases the coefficient of variation R2 is larger than 80%.

Finally, a regression analysis is performed to evaluate the correspondence between macroseismic and instrumental magnitudes, using the dataset of 75 earthquakes that were used for tuning the initial empirical regression. The coefficient of variation R2 is 74% and the mean square residual equal 0.28 magnitude units. The same analysis performed over a reduced dataset of 14 earthquakes for which a reliable direct measure of seismic moment is available yields R2 =91% and mean square residual equal 0.17 magnitude units.

Appendix 3
Calculation of the circular mean, of the associated standard deviation,

and of the significance level of the uniformity tests

The circular mean Q of a set of angles qi is determined by the vector sum of the N individual unitary vectors representing the sites:
Q = cos-1 (C/R)=sin-1 (S/R)
where
C=ácosqi/N
S=ásinqi/N
R=(C2+S2)1/2
R is called ñmean resultant lengthî and represents a dispersionª­°³·º½ÃÅÉÑÔÙÚ¶ÆÎâãäðö÷ùúûýþÿõÄÊÁ¢£Û´Ï¤¬©»ÇÂШø¡± ÓÒ«µ¦áüռȹ¸²ÀËçåÌ€®‚éƒæèíêëìÜ„ ñîïͅׯôòó† Þ§ˆ‡‰‹ŠŒ¾àØØØŽ‘“’”•Ý–˜—™› šÖ¿œžŸàßØ index of the site distribution. R varies in the interval 0-1. As the number of observations increases, the central limit theorem applied to circular data leads to a Von Mises-type distribution (somewhat similar to the Gauss normal distribution for the linear case). The parameter that corresponds to the standard deviation of the linear case is the concentration k, the definition of which involves a maximum likelihood estimation. However, an approximation to the first two significant figures was given by Cheeney [1983]:
for R<0.65, k=R/6(12+6R2 +5R4);
for RÒ0.65, k=1/[2(1-R)-(1-R)2 -(1- R)3]
The Kuiper test is the circular analogue of the linear ñone sampleî Kolmogorov-Smirnov test. It is based on the the maximum deviation of the data distribution from a uniform distribution which is given by:
VN=pos(Ui-i/N)-neg(Ui- i/N)+1/N
where Ui =qi/360 for each of the available angular measurements qi (which are ordered by increasing azimuth), and the ñposî and ñnegî functions are respectively the maximum positive and negative values of the argument obtained by varying i between 1 and N. For 5ÓN<17 the critical value VC can be found on published statistical tables Cheeney [1983], while for N>8 they can also be calculated by the formula
V*N=VC(N1/2+0.155+0.24/N1/2)
where the critical valuesV*N=1.620, 1.747, 1.862 and 2.001 correspond respectively to the 0.1, 0.05, 0.025, and 0.01 significance levels (i.e. the probability that the H0: hypothesis of a uniform distribution of circular data is true against the H1: hypothesis of non- uniform distribution) [Mardia, 1972].

The Rayleigh test is the standard parametric test for a Von Mises- type distribution. This test is simply based on the mean resultant length R of a group of data. For N>4 the critical value for R can be found in Davis [1986]. As an alternative, the probability of rejection of the null H0: hypothesis of a random distribution, for a value kÒ2NR2 , can be computed as follows [Mardia, 1972]:

p=e-k[1+(2k-k2)/4N-(24k-132k2+76k3- 9k4)/288N2]
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Table 1
List of M>5.5 earthquakes of the central and southern Apennines
Date Lat Lon Me Locality NTot NAz Azimuth Rayleigh Kuiper
7/30/1627a 41.74 15.34 6.7 Gargano 65 22 111 ± 37 <0.10 <0.01
7/30/1627b 41.69 15.38 5.8 San Severo 1 - - - -
8/ 7/1627c 41.76 15.33 5.9 Gargano 5 3 111 ± 44 uniform uniform
9/ 6/1627d 41.60 15.36 5.8 Gargano 2 - - - -
10/15/1639 42.65 13.25 6.0 Monti della Laga 15 10 062 ± 20 <0.01 <0.05
5/31/1646 41.87 15.94 6.1 Gargano 18 5 062 ±156 uniform uniform
7/23/1654 41.63 13.68 6.1 Sorano-Marsica 44 16 110 ± 47 uniform <0.01
6/ 5/1688 41.28 14.56 6.6 Sannio 26 17 118 ± 14 <0.01 <0.01
9/ 8/1694 40.88 15.34 6.8 Irpinia 294 31 121 ± 12 <0.01 <0.01
3/14/1702 41.12 14.99 6.3 Beneventano 37 4 107 ±189 uniform uniform
1/14/1703a 42.68 13.12 6.7 Norcia 196 33 165 ± 30 <0.05 <0.01
1/16/1703b 42.62 13.10 6.0 Roio Piano 22 10 117 ±146 uniform <0.05
2/ 2/1703c 42.46 13.21 6.6 Aquilan o 70 7 114 ± 28 <0.05 <0.05
11/ 3/1706 42.08 14.08 6.6 Maiella 99 7 136 ± 18 <0.01 <0.01
5/12/1730 42.74 13.12 6.3 Appennino umbro 22 10 004 ± 59 uniform <0.01
3/20/1731 41.27 15.76 6.5 Foggiano 50 5 120 ± 35 <0.10 <0.10
11/29/1732 41.08 15.06 6.5 Valle Ufita 168 4 092 ± 96 uniform uniform
10/ 6/1762 42.31 13.59 5.6 Aquilano 6 - - - -
7/31/1786 42.32 13.37 5.6 San Demetrio 7 - - - -
3/18/1796 40.75 13.91 5.7 Casamicciola Terme 1 - - - -
7/26/1805 41.50 14.47 6.5 Molise 223 8 124 ± 27 <0.05 <0.05
2/ 1/1826 40.52 15.73 5.8 Basilicata 18 4 162 ± 44 uniform <0.10
11/20/1836 40.14 15.78 6.3 Basilicata merid. 17 6 151 ± 34 <0.10 <0.10
8/14/1851a 40.96 15.67 6.3 Basilicata 102 6 161 ± 33 <0.10 <0.05
8/14/1851b 40.99 15.65 5.6 Melfi 10 - - - -
4/ 9/1853 40.82 15.22 5.9 Irpinia 47 6 005 ± 40 uniform <0.05
12/16/1857 40.35 15.84 6.9 Basilicata 337 18 127 ± 11 <0.01 <0.01
3/12/1873 43.09 13.24 6.0 Polverina 196 3 080 ± 09 <0.01 uniform
9/10/1881 42.23 14.28 5.6 Lanciano 29 4 037 ± 17 <0.01 <0.05
7/28/1883 40.74 13.89 5.7 Casamicciola Terme 27 8 092 ± 77 uniform <0.05
2/24/1904 42.10 13.32 5.6 Marsica 22 7 086 ± 48 uniform uniform
6/ 7/1910 40.90 15.42 5.8 Irpinia 376 4 126 ± 16 <0.01 <0.10
1/13/1915 41.99 13.65 6.9 Avezzano 860 25 122 ± 16 <0.01 <0.01
7/23/1930 41.05 15.36 6.7 Irpinia 511 16 108 ± 11 <0.01 <0.01
9/26/1933 42.05 14.19 6.0 Maiella 326 3 025 ± 05 <0.01 <0.05
10/ 3/1943 42.91 13.65 5.9 Offida 131 16 149 ± 22 <0.01 <0.01
8/18/1948 41.58 15.75 5.7 Zapponeta 59 9 010 ± 31 <0.05 <0.01
8/21/1962 41.14 14.97 6.2 Irpinia 214 11 160 ± 28 <0.05 <0.01
9/19/1979 42.71 13.07 5.8 Valnerina 691 30 156 ± 24 <0.01 <0.01
11/23/1980 40.84 15.28 6.9 Irpinia 1319 15 126 ± 25 <0.01 <0.01
5/ 7/1984 41.67 14.06 5.9 Val Comino 913 3 152 ± 34 <0.10 uniform
9/26/1997 43.02 12.87 5.8 Colfiorito 182 19 145 ± 10 <0.01 <0.01

Table 1. The table lists 41 M>5.5 earthquakes of the central and southern Apennines taken from the CFTI Catalogue [Boschi et al., 1997], and the 1997 Colfiorito earthquake. Me is the ñequivalent magnitudeî computed analyzing the distribution of Mercalli intensity data [Gasperini and Ferrari, 1995; 1997], that we assume to represent the moment magnitude M. NTot and NAz are total number of data available for the given earthquake and number of data used for computing the source azimuth, respectively. The reported azimuths are those obtained using our preferred choice for distance weighting and lower bound for the intensity threshold (see text) and correspond to the orientations of the solid white rectangles in Figure 5 . The table lists also the standard deviation of the computed azimuths (under the assumption of Von Mises-type distribution) and the significance levels of the Rayleigh and Kuiper tests (ñuniformî means that the test returns a significance level higher than 0.10 and therefore the hypothesis H0 of uniformity of the data distribution cannot be rejected: see Appendix 3 for details).

Table 2

Comparison between published and intensity-based source azimuths

Date Locality Azi muth(s) Reference




01/15/1915 Avezzano ~130Á Serva et al. [1986]


135Á Ward andValensise [1989]


122Á This study




08/21/1962 Irpinia 130Á or 6Á Westaway [1987]


160Á This study




09/19/1979 Valnerina 3Á or 161Á CMT


156Á This study




11/23/1980 Irpinia 135Á or 123Á CMT


125Á…135Á Pantosti and Valensise [1990]


126Á This study




05/07/1984 Val Comino 174Á or 132Á CMT


152Á This study




09/26/1997 Colfiorito 155Á or 140Á Quick CMT


145Á This study

Table 2. Source azimuths computed in this paper are compared with the corresponding seismological, geological or geodetic estimates for six of the largest earthquakes that occurred in the study region during this century. Azimuths are derived from strikes of focal mechanism nodal planes by reducing them to the 0Á- 180Á range. Notice that available published literature suggests that all of these earthquakes were characterized by predominantly normal faulting.

Figures

figure 1

Figure 1. Block diagram showing the various steps of our analysis.

figure 2

Figure 2. Geometry of the problem. Panel a) fault plane, its surface projection, and isoseismals. Panel b) vector representation of Mercalli intensity data points with respect to the macroseismic epicenter (i.e., the mid point of the data distribution).

figure 3

Figure 3. Example of the application of the procedure (see text) to the 23 July 1930, Irpinia earthquake. Determination of the macroseismic epicenter (a), of the macroseismic moment magnitude (b), of the source azimuth (c), and final representation of the inferred source (d).

figure 4

Figure 4. M>5.5 earthquakes in the central and southern Apennines from the year 1600 to 1997, with rectangles representing the surface projection of the inferred seismogenic sources. The source azimuths are computed as described in the text. The larger side of the rectangle represents the fault length computed as function of the moment magnitude M using Wells and CoppersmithÍs [1994] relationships; the smaller side represents the surface projection of the fault width assuming a dip angle of 45Á. The figure shows the solutions obtained for different distance weighting schemes (see text and legend in figure). The rectangles drawn with solid lines represent our best guess and were obtained using the [b] scheme (cubic root weighting). Notice that [a] and [c] scheme solutions may not appear if identical to the corresponding [b] solution. A circle having the diameter equal to the fault length replaces the rectangle for all sources for which the azimuth could not be computed due to insufficient number of data points (less than 3).

figure 5

Figure 5. Same as Figure 4 except for the rectangles (seismogenic sources), which are obtained using the [b] weighting scheme (cubic root weighting: see text and Figure 4) and varying the lower bound for the intensity threshold according to three different schemes (see text and legend in figure). The rectangles drawn with solid lines represent our best guess and were obtained using the [e] scheme (one degree lower bound). Notice that [d] and [f] scheme solutions may not appear if identical to the corresponding [e] solution.

figure 6a

figure 6b

figure 6c

Figure 6. Visual comparison of source parameters obtained in this paper with published estimates from seismological, geological and geodetic data for three selected large earthquakes of the study region (see also Table 2): a) Avezzano earthquake of 13 January 1915, b) Irpinia earthquake of 23 November 1980, and c) Colfiorito earthquakes of 26 September 1997. In all three cases the solid box represents our best guess of the source dimension, size and location obtained from macroseimic data alone (same as in Figures 4, 5). The dashed box delineates a solution available in current literature (from geological and geodetic data for the 1915 earthquake [Serva et al., 1986; Ward and Valensise, 1989]; from seismological, geological and geodetic data for the 1980 earthquake [Westaway and Jackson, 1984;Bernard and Zollo, 1989; Pantosti and Valensise, 1990]; from seismological data for the 1997 earthquake [Amato et al., 1998; Ekstrûm et al., 1998]). Intensity data from Boschi et al. [1997] (1915, 1980 earthquakes) and from WGMSCE [1997] (1997 earthquake). Discontinuous red lines indicate fault scarps from Serva et al. [1986] and from Pantosti and Valensise [1990], respectively for the 1915 and 1980 earthquakes (no unambiguous surface faulting was reported for the 1997 earthquake). The instrumental epicenters of the 1915 and 1980 earthquakes were calculated by Basili and Valensise [1986] and Giardini et al. [1996], respectively. The epicenters of the two mainshocks of the 1997 Colfiorito earthquake sequence were taken from the Monthly Bulletin of the Istituto Nazionale di Geofisica. The symbol M indicates moment magnitude.