The Italian historical earthquake record is among the richest worldwide; as such it allows for the development of advanced techniques for retrieving quantitative information by calibration with recent earthquakes. Building on a pilot elaboration of northern Italian earthquakes, we developed a procedure for determining the hypocentral depth of all Italian earthquakes from macroseismic intensity data alone. In a second step the procedure calculates their magnitude, taking into account the inferred depth.

Hypocentral depth exhibits substantial variability countrywide but has so far received little attention: pre-instrumental earthquakes were routinely “flattened” at the upper-crustal level (

We gathered a learning set of 42 earthquakes documented by reliable instrumental data and by numerous macroseismic intensity observations. We observe (1) that within 50 km from the epicenter the ground motion attenuation rate is primarily controlled by hypocentral depth and largely independent of magnitude, (2) that within this distance the fluctuations in crustal attenuation properties are negligible countrywide, and (3) that knowing both the depth and the expected epicentral intensity makes it possible to estimate a reliable magnitude.

In addition to earthquake magnitude, the severity of seismic ground shaking at any given site is primarily controlled by its geometric spreading; by elastic and anelastic attenuation of the upper-crustal rocks; and by hypocentral distance, i.e., the combination of horizontal distance from the epicenter and earthquake depth. Other parameters controlling the ground shaking include the earthquake radiation pattern; the rupture directivity, if any; and the inevitable site amplification effects.

When dealing with damaging instrumental earthquakes, the magnitude, depth, and focal mechanism – which in its turn determines the radiation pattern – are generally known, and even the rupture directivity may be at least hypothesized if the recording network is dense enough. Things change drastically when dealing with historical earthquakes. For the vast majority of these events the severity of shaking is expressed by the macroseismic intensity reported at a number of sites, a proxy for a set of accelerometric records

Nevertheless, given the limited length of the available instrumental record, historical earthquakes are the primary source of information for the assessment of seismic hazard, at any scale and with any approach. Historical catalogues are especially relevant for assessing seismic hazard in Italy (e.g.,

Italy affords a unique opportunity to explore what type of information can be realistically derived from intensity data. In the early 1990s, macroseismic intensity data started being organized into

Starting at the end of the 1990s and following the inception of analytical historical catalogues, different workers developed computer algorithms for calculating the earthquake location, its magnitude, and even the presumed rupture orientation and length, for many well-documented pre-instrumental earthquakes (e.g.,

Unlike instrumental data, which offer a variety of relevant independent observations (arrival times, amplitudes, phase delays), historical earthquake data are essentially

Aside from the inevitable uncertainties that may arise from such a limited and often poorly distributed dataset, the mono-variable nature of the data inevitably leads to the existence of a trade-off among magnitude and depth because a deeper earthquake will generate less shaking and may thus simply appear as a smaller event. In most cases the magnitude has been estimated without considering the depth or by fixing it in advance. Other methods were based on a joint inversion of intensity data to obtain magnitude and depth

At least in Italy, the limited consideration of the depth variability of damaging crustal earthquakes (in this work we are not concerned with subduction zone events) has often been explained with the inherent difficulty in evaluating the depth of historical earthquakes, motivated by an allegedly large variability in the propagation characteristics of the upper crust

Building on the findings of

First we extend the experimental method put forward by these investigators to the whole Italian territory and to the whole pre-1984 earthquake catalogue (CPTI15 v2.0, the Parametric Catalogue of Italian Earthquakes,

We then develop a scheme for objectively ranking the quality of an intensity dataset and hence for selecting only earthquakes that are suitable for calculating a reliable source depth.

Similarly to what was done by

Finally, from the data from the learning set we derive a multiple regression equation relating expected epicentral intensity to magnitude and hypocentral depth so as to estimate also the magnitude of pre-instrumental earthquakes.

Notice that the approach we adopted in this work was specifically designed for analyzing also higher-magnitude earthquakes (

the awareness that their causative fault cannot be assumed to be a point source;

the awareness that they are often characterized by sizable directivity effects; and

empirical relationships (e.g.,

In the process we aim to (a) use our learning set to evaluate the properties of wave propagation (within 50 km of the epicenter) in the crust versus the variability in source depth, exploring the trade-off between these two parameters in different tectonic settings, and (b) discuss the potential implications of these developments for the estimation of seismic hazard. The inferred distribution of earthquake depth may have important seismotectonic implications, but these are beyond the scope of this work and will be discussed in a further, dedicated paper.

The Italian Peninsula is located along the complex Africa–Europe convergent plate boundary. Due to this complexity, the causative sources of Italian earthquakes exhibit highly variable kinematics and geometrical parameters, as shown by focal mechanisms

Normal faulting dominates along the hinge of the Apennines chain and in the Calabrian Arc.

Thrust and reverse faulting are widespread along the external fronts of the southern Alps and of the northern and central Apennines, in the northern and southern Tyrrhenian domain, and in the Sicilian–Maghrebian Chain.

Strike-slip faulting is found in northeastern Italy, in the most external portions of the central and southern Apennines, and in the corresponding foreland areas (Fig.

Location of the 42 earthquakes of the learning set used in this work and regional-scale tectonic information from the DISS database

In addition, an active slab related to the subduction of the Ionian lithosphere exists below the Calabrian Arc: the slab is bounded by tear faults along its edges

The active faults and seismogenic sources identified so far in the Italian region belong both to extensional or compressional fault systems that formed during the presently active stress regime (

The inherited faults have been interpreted either as Mesozoic extensional structures characterizing the African northern passive margin and separating fossil paleogeographic domains (e.g.,

Finally, further evidence of the seismotectonic complexity of the Italian region is supplied by the control exerted by the inherited structural and paleogeographic grain of the African paleomargin, which resulted in the segmentation and differential retreat of independent panels of the “foreland monocline”, i.e., of the subducting Adriatic, Ionian, and Pelagian lithosphere

As a result of this framework, Italian earthquakes exhibit an unusually broad depth range, mainly as a function of their faulting mechanism and of their location in the upper or lower plate (e.g.,

very shallow in the active volcanic areas of the peri-Tyrrhenian margin and of Sicily (

shallow (

shallow–intermediate (

deep (up to 600 km depth) in the subduction system below the Calabrian Arc

The earthquakes generated by the new faults and by the inherited faults are often geographically overlapped, as seen in the Po Plain

We updated and extended the method proposed in

We adopt a distance binning method, and we use only well-located instrumental earthquakes (see Sect.

A further issue concerns the treatment of intensity data as integers or real numbers. When estimating macroseismic intensity, all potential diagnostic effects are jointly evaluated to assess which degree of the scale best matches those effects. Typically, however, the effects may belong to contiguous degrees: this circumstance results from multiple reasons, including the geological nature of the outcropping lithology near building foundations; differences in the vulnerability of adjacent buildings; or – for the lowest shaking levels – differences in the perception of seismic vibration depending on the number of stories comprising the building, on whether the observer is still or is moving, and so on

In the following step we plot the instrumental depth of the earthquakes used as a learning set versus the steepness of the attenuation curve. By fitting these values we obtain a logarithmic function that is then used for the last step, that is, to infer the depth of the non-instrumental earthquakes of our analyzed set.

Notice that the radius of our ring-shaped moving windows is now calculated from the instrumental earthquake epicenter rather than based on the distance from the epicenter of the innermost MDP within the first 10 km, as proposed by

Workflow of the moving-window procedure.

Full learning set used for this work. Event no. 1 to no. 20 occurred in northern Italy and were already used in the pilot work by

To compose our learning set (Table

The use of web-based data was fundamental to accomplishing our goals because these data were almost always the only observations available, especially for deeper earthquakes (

The events comprising the learning set were further selected based on the following criteria:

Pre-2007 earthquakes must have

Post-2007 earthquakes must have

The earthquake depth must not have been fixed a priori by INGV's National Seismic Network.

Only for pre-2012 earthquakes, the event must not be an aftershock occurring within a week of the mainshock or a foreshock that occurred less than 24 h before the mainshock.

All earthquakes with

The earthquake must be documented by at least 100 MDPs, at least 60 of which must fall within the first 55 km from the epicenter.

The MDPs falling at a 10–55 km distance from the epicenter must be distributed in an azimuthal range

The attenuation steepness must be calculated based on six or more averaged points; thus at least 6 of the 10 rings must contain suitable MDPs.

The standard error of the estimated attenuation steepness must be

All 42 earthquakes listed in Table

Notice that selection criteria 1–4 had already been adopted by

Criterion no. 5 was added due to the recurring lack of data in the epicentral areas of the main aftershocks of the 2016–2017 central Italy sequence, due to the widespread evacuations following the

Criterion no. 6 was added after various experimental tests, in order to achieve more reliable and stable estimates of the attenuation.

Criteria no. 7 and no. 8 were introduced to discard earthquakes located offshore or near the coastline, whose epicentral location generally exhibits greater uncertainty.

Criterion no. 9 was adopted to retain only earthquakes for which we could calculate a reliable attenuation steepness.

We analyzed separately two data subsets, respectively, comprising only earthquakes located in northern Italy and earthquakes located in the rest of the Italian Peninsula. We made this choice because the dataset used in

Due to the intervening minor updates in our methodology – and specifically in the calculation of the starting point of our moving window, which implies a slightly different steepness for the first 50 km of the attenuation curve (mean:

Attenuation curves obtained for the northern Italian earthquakes in the learning set (Table

Attenuation curves obtained for the central and southern Italian earthquakes in the learning set (Table

As discussed earlier, in both datasets, which together form our new learning set, we observed a distinct break in steepness at an epicentral distance of about 50 km (see Figs.

For all the earthquakes in the learning set we then plotted the steepness (

Depth versus attenuation steepness for the 42 earthquakes used as a learning set. Blue and red symbols indicate the northern Italian and the central and southern Italian datasets, respectively: the corresponding best-fitting logarithmic functions are shown in blue (Eq.

The coefficients of each function fall within the 95 % confidence interval of the other function, suggesting that our method does not detect any statistically significant change in the attenuation of macroseismic intensity between the two domains, at least over the first 50 km of epicentral distance. This finding also suggests that an approach based on averaging the intensity values distributed over circular search areas has the ability to smooth out most of the inevitable azimuthal differences in crustal propagation properties.

We decided to calculate a new logarithmic function using all 42 earthquakes in the learning set so as to obtain a law that may be used over the whole Italian region (green line in Fig.

The regression

The steepness of the first 50 km of the attenuation curves calculated for the earthquakes of our learning set (Figs.

Attenuation curves obtained for two groups of earthquakes featuring a similar hypocentral depth but a different magnitude:

The invariance of the attenuation steepness with magnitude for events in the learning set is a key point as it makes our approach suitable for analyzing historical earthquakes even if their size is not well constrained. Instead, other methodologies

We analyzed the possibility of reproducing the empirical trend of Fig.

We then used two different conversion equations

Figure

Attenuation curves and steepness simulated with different intensity or ground motion models for a

The reliability of the steepness of the first 50 km of the attenuation curve depends on the quality and spatial distribution of the available MDPs and on the accuracy of the epicentral locations. Italian macroseismic data are systematically stored in the DBMI v4.0 database

To test our procedure we investigated the minimum number of MDPs of the macroseismic field that are needed to obtain an estimate of the attenuation steepness. To this end we intentionally and randomly depleted the macroseismic field of the 20 May 2012

The linear fit of the attenuation trend was calculated 1000 times for each depletion step so as to evaluate the steepness variability through its standard deviation.

Figure

Application of the depletion test to the macroseismic field of the 20 May 2012 earthquake (Figs.

Our depletion test shows that we may obtain an acceptable attenuation steepness even for historical earthquakes for which at least 30 MDPs are available, provided that they are homogeneously distributed for each distance window. Moreover we calculated the depth reliability by estimating the depths corresponding to the confidence bands of Eq. (

While the inferred hypocentral depth is independent of magnitude and can be obtained simply based on the steepness of the line that best fits the first 50 km of the attenuation curve, the estimation of the magnitude itself affects the

We devised a two-step procedure where depth is estimated first (step 1) and then

Equation (

Magnitude as a function of the natural logarithm of depth and expected intensity at the epicenter

For

Deriving magnitude using only well-studied earthquakes with their expected epicentral intensities provides a better estimate of

The method summarized by Eqs. (

In conclusion, starting from our empirical observations of the independence of the attenuation steepness from magnitude, we were able to mitigate the trade-off between magnitude and depth when estimating both these parameters from macroseismic data.

It is hard to estimate macroseismic intensities for individual earthquakes occurring close in time and space (multiple events, strong aftershocks, etc.; e.g.,

To quantify the effect of multiple events on the determination of earthquake depth, we analyzed the 29 May 2012

A similar case of contamination could be that of two earthquakes that occurred 7 months apart in two distinct but relatively close areas of the northern Apennines: the 10 November 1918

Our approach works well if the size of the seismic source is negligible relative to the epicentral distances, but it may not be immediately applicable to estimate the attenuation of the macroseismic intensity for a high-magnitude earthquake

We used the empirical relationships proposed by

Then we applied to this group of higher-magnitude earthquakes a procedure that we call “variable moving windows”. More specifically, we used as the first search area a circular window of radius

The comparison of the attenuation steepness calculated using the

In conclusion, using an extended source approach for the largest earthquakes has a minimal influence on the steepness. Conversely, the effect on the

Finally, we recalculated the magnitude of these 21 earthquakes using Eq. (

Since ours is a two-step method and magnitude is calculated after estimating depth, we provided the estimate of the error associated with the magnitude of the earthquakes in the analyzed set, based on the confidence limits of depth, by applying Eq. (

As a countercheck we used our method to calculate the depth first (Eq.

Correlation between the

We then compared the macroseismic magnitudes calculated through our method with those calculated through the Boxer method

Comparison of

Finally, the reliability of the

We applied our methodology to the pre-1984 earthquakes of the DBMI15 v2.0 catalogue

We first selected the earthquakes to be analyzed: they must meet all criteria listed in Sect.

Estimated depth calculated using our approach (color-coded) for the 206 earthquakes in the analyzed set, shown with symbol size scaled with the magnitude calculated in this work. The areas with different patterns indicate active tectonic domains that exist in the Italian Peninsula and surrounding areas (same as Fig.

In Sect.

We wish to stress once again that the reliability of the magnitude and depth determinations shown in Fig.

Once the depth of the 206 selected earthquakes is known, we can estimate their magnitude using Eq. (

Before comparing the

Figure

Correlation between the

The calculated

It is important to be aware that the calculation of

The

In this study we present a two-step procedure for deriving the depth and magnitude of Italian pre-instrumental earthquakes from official, publicly accessible macroseismic intensity datasets: the traditional macroseismic historical dataset supplied by DBMI15 and the new web-based macroseismic HSIT dataset. The main merit of the proposed methodology is its objectivity and ease of application.

Web-based macroseismic platforms allow for a large number of data to be collected through crowdsourcing; they are often the only available source of information concerning the effects of low–medium-magnitude earthquakes and of the far-field effects of larger events. In fact, HSIT data were critical to perform this work because – especially for deeper earthquakes (

We proved that the initial 50 km of the attenuation curve contains all the elements needed to retrieve not only the depth but also the magnitude of any given earthquake. The methodology was tested on Italian earthquakes, but we maintain that it can be extended to other countries, following the necessary calibrations.

The first step of our procedure involves the calculation of earthquake depth (Eq.

The second step involves estimating the magnitude through an empirical law obtained from a regression function that relates the expected epicentral intensity to the depth and magnitude of the 42 earthquakes comprising our learning set (Eq.

Our approach allowed us to verify that the inferred depth is consistent with the presumed earthquake-causative tectonic structures and is essential to obtain a well-calibrated magnitude value. We contend that the new methodology may be crucial for mitigating the trade-off between earthquake depth and magnitude; this is a pre-condition for calculating reliable depth estimates – and hence reliable magnitudes – for earthquakes of the pre-instrumental era.

In Italy the historical record is still the main pillar of any seismic-hazard analysis conducted at any scale and using any approach. We maintain that the revised framework discussed in this work may ultimately serve for exploiting more systematically the enormous potential of historical earthquake data and ultimately for providing inherently more reliable input data for seismic-hazard assessment.

Code cannot be shared at this stage.

This work used only published or public domain datasets:

The supplement related to this article is available online at:

PS conceived the work and wrote the initial draft of the paper. PB, PT, PV, and GV contributed to delineating the structure of the paper. PB, PV, and GV provided information on the seismotectonic background, along with the associated interpretations. PS and RV analyzed the macroseismic data, and RV implemented the algorithms in the R language. PT tested the method through the use of synthetic data. VDR statistically evaluated the effects of using finite seismic sources. PS and GV did most of the writing. All authors discussed the results and contributed to the final version of the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Franco Mele, Mario Locati, Graziano Ferrari, Livio Sirovich, and Franco Pettenati for suggestions and for providing valuable insight during the early stages of this work.

This research has been supported by the Dipartimento della Protezione Civile, Presidenza del Consiglio dei Ministri (INGV DPC, 2019–2021 agreement; All. A, WP 7).

This paper was edited by Filippos Vallianatos and reviewed by three anonymous referees.