Epicentral Intensity Research Articles

Seismic motion attenuation relations in Sichuan and adjacent areas

The Sichuan and adjacent areas is divided into southwest China region (SWCR) and Sichuan Basin region (SCBR) according to tectonic backgrounds and seismic damage distribution features. 96 modern destructive earthquakes in SWCR and 40 in SCBR are gathered respectively. All their magnitude parameters are checked. Based on the statistic relations between epicentral intensity and magnitude as well as relation between sensible radius and magnitude, the near and far field seismic intensity attenuation features are represented and controlled. And then the seismic intensity attenuation relations along major axis, minor axis and mean axis are established separately. The systematic deviations of surface wave magnitude between China seismograph network and U.S. seismograph network are considered in this paper. By making use of the new attenuation relations of bedrock horizontal ground acceleration response spectrum in west U.S., the attenuation relations of bedrock horizontal ground acceleration response spectrum in SWCR and SCBR are digital transformed based on the attenuation model considering acceleration saturation of distance and magnitude in near field.

Seismicity of the Bánát region

In the seismic source zone of Bánát more than 600 earthquakes are known since 1773 among them six events with magnitude of 5.0–5.7 measured on the surface magnitude scale. The macroseismic reinterpretation of the April 2, 1901 earthquake yields epicentral intensity of VII on the European Macroseismic Scale, and a focal depth value of 12 km. Based on empirical relations the maximum rupture area is estimated as 50–55 km 2 and the maximum displacement along the fault is about 16 cm in the Bánát seismic zone due to the MS = 5.7 event occurred on July 12, 1991. The average recurrence that we may expect an earthquake of M ≥ 3.4 every 1 year, an earthquake of M ≥ 4.3 every 10 years and an earthquake of M ≥ 5.3 every 100 years in the studied source zone. The probabilistic seismic hazard assessment predicts 1.3–2.1 m/sec 2 peak ground accelerations, and 6.7–7.3 maximum (theoretical) earthquake intensity values with 10% chance of exceedance for an exposure time of 100 years in the region.

The Verny, 1887, earthquake in Central Asia: Application of the INQUA scale, based on coseismic environmental effects

The INQUA scale, based on coseismic environmental effects, appears to be a very promising tool to get long-term and reliable information on seismicity. However, it has to pass through comprehensive testing procedures. Results of the INQUA scale application to earthquake intensity calibration are presented, part of the worldwide testing of the scale. As a case study, the Verny, 1887, earthquake in Central Asia has been chosen. It was a large earthquake (felt over 2,000,000 km 2) located in a region with a specific temporal and spatial organization of seismicity. Verification of magnitudes of some large past earthquakes is important for the correct understanding of regional seismotectonics and seismic hazard assessment. The work is based on the original materials collected by the expedition soon after the earthquake in the epicentral area. It is demonstrated that assessment of epicentral intensity derived from total area of secondary environmental effects is reliable. This enables evaluation of the parameters of historical earthquakes based on generalized information of observed earthquake environmental effects (EEE). The epicentral intensity I 0 is assessed to be IX-X degrees; the highest observed local intensities are coherent with I 0 assessment.

Synsedimentary deformation of Pleistocene glaciolacustrine deposits in the Albese con Cassano Area (Southern Alps, Northern Italy), and possible implications for paleoseismicity

We describe and interpret the well exposed soft-sediment deformations preserved in a Mid-Pleistocene proglacial sequence outcropping at Albese con Cassano, near Como (Southern Alps, N Italy). The observed deformations affect six distinct stratigraphic intervals within the same depositional sequence. The stratigraphy of this sequence, the geomorphic setting, and the careful geological mapping of the area clearly show that these deformations are not the result of glaciotectonics or cryoturbation, but are due to six separate events of synsedimentary liquefaction. In particular, the 3 basal deformed units include sand and gravel volcanoes that formed at the bottom of a proglacial lake. We examined several hypothesis of possible causative mechanism for the formation of these features. Taking into account all the information available on the local geology and sedimentary environment, it is possible to assess that the liquefaction features at Albese con Cassano had a coseismic origin. To our knowledge, this would be the first report of similar evidence of paleoseismicity in the Lombardia Southern Alps. Also, there is no record of historical liquefaction triggered by seismic events in an area of ca. 70 km of radius near Albese con Cassano, including the town of Como, the large metropolitan area of Milano and most of W Lombardia, that is one of the largest industrial districts in Europe. Therefore, the interpretation of the observed deformations can have critical impact for understanding the current seismicity level in the region, and mitigating the associated risk. In this paper we show that this interpretation is not a simple process. Liquefaction features must be treated with caution in order to derive suitable information for seismic hazard characterization, even if their coseismic origin has been definitely proved. It is necessary to understand the amount of seismic shaking (for instance, in terms of local macroseismic intensity) that can have produced that specific feature at that specific site, the location of the causative seismic event (epicenter and focal depth), and eventually its size (in terms of epicentral intensity and/or earthquake magnitude). In the case of Albese con Cassano, the implications in terms of seismic hazard of the observed possible earthquake paleoliquefactions can only be assessed through the definition of several scenarios, taking into account: a) different thresholds of shaking for triggering the described synsedimentary structures, and b) different seismotectonic frameworks related to the Mid-Pleistocene to Holocene evolution of the S Alps, including seismicity induced by isostatic glacial rebound. We conclude that it is worth checking these scenarios in the field with further paleoseismological research on other possible evidence of past earthquakes. There are no unequivocal sedimentological indicators of paleoseismicity, however, when carefully interpreted within the proper local seismotectonic context and compared with other earthquake-induced features, soft-sediment deformations can offer information of critical value for seismic hazard assessment.

The earthquake of Carnuntum in the fourth century a.d. – archaeological results, seismologic scenario and seismotectonic implications for the Vienna Basin fault, Austria

Excavations in the former Roman provincial capital of Pannonia Superior, Carnuntum, 40 km east of Vienna revealed damaged masonry structures from many parts of the ancient settlements. A compilation of structurally damaged buildings has formerly been given by Kandler (Acta Archaeol Acad Sci Hung, 41:313–336, 1989), who related damage to an earthquake in the middle of the fourth century a.d. This paper reviews and supplements these data, and discusses the significance of the style of damage. It is concluded that seismic damage is the only likely interpretation for the damaging mechanism. Although archaeological age dating for the individual collapsed buildings only constrains the timing of their destruction to a few decades around 350 a.d., we assume a single damaging event. In spite of the restrictions on damage assessment by the nature of the archaeological data, it is possible to give a reasonable appraisal of macroseismic intensity. The tentative seismological interpretation of damage leads to an intensity estimate of about nine of the European macroseismic scale (EMS-1998). Comparison with macroseismic data of modern earthquakes in the region, which show a rapid decrease of intensity with distance form the epicentre, indicate a near-by seismic source unless exceptionally high epicentral intensities are assumed for the fourth century event. The most likely source is an active sinistral strike-slip fault (Lassee Fault) passing about 8 km NW of the archaeological site. The fault belongs to Vienna Basin fault system with about 2 mm sinistral movement per year. The system is characterized by fault segmentation and distinct seismicity along the different segments. Moderate seismicity during the last centuries at the southern segments (e.g., Schwadorf 1927, I0=8) strongly contrasts from the Lassee fault segment with Carnuntum as the only known severe earthquake. The earthquake of Carnuntum provides evidence for the overall seismic style of deformation along this segment, which previously has not been regarded seismically active. Also, the fourth century earthquake is the strongest event known from the Vienna Basin fault so far.

Atténuation de l'intensité macrosismique pour la France métropolitaine : importance de l'intensité épicentrale

The main result of this work is to show that macroseismic intensity decay with distance strongly depends on the epicentral intensity. An attenuation law that takes this parameter into account is proposed for Metropolitan France, from the analysis of SISFRANCE macroseismic database. Such a model significantly reduces the difference between observed and theoretical intensities. A map of the attenuation variations is also set up for Metropolitan France. No major site effects are observed, but at a broad scale, young Alpine regions display a stronger attenuation than old Hercynian regions. To cite this article: P. Arroucau et al., C. R. Geoscience 338 (2006).

In Search of the 31 March 1761 Earthquake and Tsunami Source

Earthquake catalogs for the Iberian Peninsula report three strong- magnitude events in the eighteenth century: 27 December 1722, 1 November 1755, and 31 March 1761. These events have magnitudes greater than 7 and generated tsunamis that damaged the Portuguese coasts. However, their source areas are controversial because of the lack of detailed and coherent historical descriptions. The 31 March 1761 earthquake was felt in Lisbon at noon, alarming the inhabitants and throwing down ruins of the past 1 November 1755 earthquake. According to several sources the earthquake was followed by a tsunami that was observed as far as Cornwall (United Kingdom), Cork (Ireland), and Barbados (Caribbean). The Portuguese catalogs locate this event on the Horseshoe Abyssal Plain, south of Gorringe Bank, and attribute a magnitude of 7.5. The Caribbean tsunami catalog (Lander et al. , 2002) locates the event further north 37° N 10° W and estimates of its epicenter intensity as IX. In this study we present a reappraisal of the available historical reports concerning the 1761 event, a revision of the macroseismic intensities along Iberia, and the tsunami observations along the western Portuguese and Galicia coasts, England, Ireland, and the West Indies. With this dataset we use backward raytracing techniques to discuss the location of the event and its integration with one of the major tsunami generation areas in the western Portuguese margin. We conclude that the 31 March 1761 earthquake took place at 12:01 a.m. (Lisbon time). Its epicenter was located about 34.5° N 13° W and had a tsunami magnitude close to 8.5. Online material: Felt reports from the 31 March 1761 earthquake.

On a homogeneous representation of seismic history in large regions

The possibility to obtain a more complete and unbiased long-term history of seismic shakings over large territories than is explicitly reported from inhabited localities is discussed in the paper. An approach proposed for this purpose consists in complementing the spatial distribution of the macroseismic effect of earthquakes by calculated intensities at localities where information on felt shakings is absent. The calculated intensity is obtained on the basis of data on the epicentral intensity and location of epicenters provided by earthquake catalogs. This approach is applied to the analysis of the history of seismic shaking in Spain. The calculated intensities are shown to be comparable in accuracy with the ordinary practice of intensity determinations at national seismological centers.

The “exceptional” earthquake of 3 January 1117 in the Verona area (northern Italy): A critical time review and detection of two lost earthquakes (lower Germany and Tuscany)

In the seismological literature the 3 January 1117 earthquake represents an interesting case study, both for the sheer size of the area in which that event is recorded by the monastic sources of the 12th century, and for the amount of damage mentioned. The 1117 event has been added to the earthquake catalogues of up to five European countries (Italy, France, Belgium, Switzerland, the Iberian peninsula), and it is the largest historical earthquake for northern Italy. We have analyzed the monastic time system in the 12th century and, by means of a comparative analysis of the sources, have correlated the two shocks mentioned (in the night and in the afternoon of 3 January) to territorial effects, seeking to make the overall picture reported for Europe more consistent. The connection between the linguistic indications and the localization of the effects has allowed us to shed light, with a reasonable degree of approximation, upon two previously little known earthquakes, probably generated by a sequence of events. A first earthquake in lower Germany (I0 (epicentral intensity) VII–VIII MCS (Mercalli, Cancani, Sieberg), M 6.4) preceded the far more violent one in northern Italy (Verona area) by about 12–13 hours. The second event is the one reported in the literature. We have put forward new parameters for this Veronese earthquake (I0 IX MCS, M 7.0). A third earthquake is independently recorded in the northwestern area of Tuscany (Imax VII‐VIII MCS), but for the latter event the epicenter and magnitude cannot be evaluated.

The Valais earthquake of December 9, 1755

The earthquake on December 9, 1755 is one of the major events in the Valais region, having an important influence on the seismic hazard assessment of the area. The re-evaluation of the event was undertaken in the course of upgrading the Earthquake Catalog of Switzerland (ECOS). It is now based on a newly investigated and reliable database created through research in archives and libraries. Using the data made available by the historical information, we assigned site intensities according to the criteria established by the European macroseismic scale EMS 98 (Grunthal 1998). Based on the broad spectrum of the available information, we assigned minimum and maximum possible values (Imin; Imax) and determined a most probable intensity value (Iw) for each site. The maximum observed intensity, Ix, is the largest intensity for each quake. Epicentral intensity, I0, is equal to the maximum observed intensity Ix, if at least two data points are assigned an intensity of Ix. We obtained maximum Ix = I0 = VIII at Brig/VS (46.3/8.0) and moment magnitude Mw = 6.1.

Earthquakes in Switzerland and surrounding regions during 2003

This report of the Swiss Seismological Service summarizes the seismic activity in Switzerland and surrounding regions during 2003. During this period, 532 earthquakes and 118 quarry blasts were detected and located in the region under consideration. With 30 events with M L ≥ 2.5, the seismic activity in the year 2003 was slightly above the average over the last 29 years. As in previous years, most of the seismic activity was concentrated in the Valais and in Graubünden. In addition, several earthquakes occurred along the northern front of the Alps. The strongest event, with M L 4.0 and epicentral intensity V, occurred in the area of Urnerboden, on the border between the cantons Uri and Glarus. Two earthquakes with M L 3.9 occurred in the Valais near the town of Salgesch and south of the Sanetsch Pass. In Graubünden, the Sertig valley south of Davos was the site of a sequence of 51 earthquakes that included three events with magnitudes between M L 3.6 and 3.9.

Focal depths of earthquakes in the Carpathian Basin

Analysing the areal distribution of earthquakes produced in the Carpathian Basin the conclusion can be drawn that only certain parts can be considered active along fracture lines, namely those parts which separate individually moving blocks. Generally accepted working theory states that if one fracture line ever generated an M-magnitude earthquake then at any point of the same line a similar or larger tremor may happen again. However, this principle is not supported by domestic experiences. In accordance with focal depths analysis we are going to verify that earthquakes were produced within more or less consolidated layers inside subsiding basins. Our analysis is aimed to explain the possible origin of earthquakes within small depth range and to point out the practical benefit of these investigations. We present also an analysis on the possible origin of „basin tremors” not taken so far into consideration and we offer a plausible explanation. Uncertainties of focal depth (hypocenter) determinations will also be given and we define relations between the focal depth (h), the magnitude (M), and the epicentral intensity (Io). The result will be presented in tables and comparison will be given between the focal depth data determined by us and by others. Finally viewpoints will be presented to help the recognition of earthquake foci and to set earthquake hazard determination on a real basis.

The record of historic earthquakes in lake sediments of Central Switzerland

Deformation structures in lake sediments in Central Switzerland can be attributed to strong historic earthquakes. The type and spatial distribution of the deformation structures reflect the historically documented macroseismic intensities thus providing a useful calibration tool for paleoseismic investigations in prehistoric lake sediments. The Swiss historical earthquake catalogue shows four moderate to strong earthquakes with moment magnitudes of M w=5.7 to M w=6.9 and epicentral intensities of I 0=VII to I 0=IX that affected the area of Central Switzerland during the last 1000 years. These are the 1964 Alpnach, 1774 Altdorf, 1601 Unterwalden, and 1356 Basel earthquakes. In order to understand the effect of these earthquakes on lacustrine sediments, four lakes in Central Switzerland (Sarner See, Lungerer See, Baldegger See, and Seelisberg Seeli) were investigated using high-resolution seismic data and sediment cores. The sediments consist of organic- and carbonate-rich clayey to sandy silts that display fine bedding on the centimeter to millimeter scale. The sediments are dated by historic climate and environmental records, 137Cs activity, and radiocarbon ages. Deformation structures occur within distinct zones and include large-scale slumps and rockfalls, as well as small-scale features like disturbed and contorted lamination and liquefaction structures. These deformations are attributed to three of the abovementioned earthquakes. The spatial distribution of deformation structures in the different lakes clearly reflects the historical macroseismic dataset: Lake sediments are only affected if they are situated within an area that underwent groundshaking not smaller than intensity VI to VII. We estimate earthquake size by relating the epicentral distance of the farthest liquefaction structure to earthquake magnitude. This relationship is in agreement with earthquake size estimations based on the historical dataset.

Macroseismic Survey of the 2002 Molise, Italy, Earthquake and Historical Seismicity of San Giuliano di Puglia

The eastern Molise earthquake had an epicentral intensity of Io=7–8 MCS (Mercalli-Cancani-Sieberg scale) and a maximum intensity of Imax=8–9 in the village of San Giuliano di Puglia. The historical portion of this village, built on a marly limestone hill, had intensities of 6–7 MCS, whereas the most recently developed area, on a crest of marly clays, had a local intensity of I=9–10 MCS, and was almost totally destroyed. Neighboring villages were generally struck with an intensity of 6–7 MCS. In several places, the damage was due to gravity-driven phenomena affecting both the rocky and clayey substratum of the villages. The epicentral area is characterized by the lack of historical earthquakes comparable to the 2002 sequence, having suffered only the effects of distant, strong (M>6.5) events, coming either from the Apennine seismogenic belt or from the Gargano area.

Hidden behind the Ranges: How the 13 April 1558 "Sienese" Earthquake Was Put in Its Place

Determining epicentral locations and magnitudes of historical earthquakes has always been a foremost goal of historical seismology. From the 1980\'s onward such studies have produced abundant and important results in many countries and contexts, if not always entirely painlessly. Any historical seismologist knows the vexation of having to squeeze down an intricate investigation, full of brilliantly solved puzzles, into a couple of epicentral coordinates and an epicentral intensity value. More vexing still is finding a puzzle one is not able to solve and having to draw a conclusion from unsatisfactory data. Such an experience befell the writer some years ago, while working on the compilation of the Camassi and Stucchi (1997) Italian catalog, with the earthquake of 13 April 1558. Its memory rankled for a long time, until a clue of sorts came her way at a time favorable to a resumption of the quest to make sense of the previously enigmatic event. The historical investigation of the 13 April 1558 earthquake started again, from a completely new viewpoint, and about thirty previously unknown earthquake-related original documents were unearthed. These accounts are of tremendous value for understanding the 1558 earthquake, as this article will show by presenting and discussing them.

Macroseismic Surveys in Theory and Practice

Macroseismology is the part of seismology that collects and evaluates non-instrumental data on earthquakes, i.e., effects on people, objects, buildings and nature. The methods that seismologists use for collecting and evaluating the macroseismic data are often based on long (trial-and-error) experience more than on some formal procedure. Until very recently manuals or guidelines on how to do a macroseismic survey were rare and often superficial. After an earthquake is felt in some region, the data are usually collected by means of questionnaires. Field survey is an obligatory tool that complements the questionnaires in the case of a damaging earthquake. An overview of the approaches to deriving the earthquake parameters (epicentre and barycentre, epicentral intensity, magnitude, depth, source parametres) from macroseismic data, as well as a review of some existing practices is given.

Seismicity and seismic hazard mapping of northern Algeria: Map of Maximum Calculated Intensities (MCI)

An earthquake catalogue covering the period1716–2000, comprising 2430 events, has beencompiled for the region lying between3°W-9°E and 31°N-38°N. It results fromraw data of IGN, ISC, USGS and Algeriansources, enabling an input consisting oforigin time H, geographical coordinates(longitude λ and latitudeϕ) and at least one of thefollowing parameters: surface wavemagnitude Ms, body wave magnitude Mb,epicentral intensities Io. Empiricalrelations permit transformations of Mb andMs into Io. The output consists in H,λ, ϕ, Ms, Mb, Io, and focal depth h whichis fixed to 10 km. The number ofevents falls to 1458 characterised by Ms≥ 3.3 and Mb ≥ 3.6, or Io ≥III. The fixed depth is suggested by thebest documented Algerian macroseismic mapsthat also lead to an empirical intensityattenuation law. A first application ofthis catalogue allows the drawing up of anupdated Seismicity and a MaximalCalculated Intensities (MCI) Maps ofAlgeria. The MCI map is obtained by usingthe empirical attenuation law: theintensities inferred by the whole eventsconstituting the catalogue are computed atnodes of a 5×5-km grid covering the area ofstudy. The corresponding maximum value isassigned to each node. The MCI map producedthat way gives precise spatial informationin comparison with Maximum ObservedIntensities (MOI) maps obtained in previousmacroseismic studies. This document may beuseful in mapping the seismic hazard inNorthern Algeria, without attachingprobabilities to ground-motionparameters.

Network assesses earthquake potential in Italy's southern Alps

On 6 May 1976, a magnitude 6.4 earthquake struck the Friuli region of northeastern Italy near the towns of Gemona and Venzone. Although it was not as large as some previous earthquakes in Italy, its severe ground motion (up to 0.36 g) affected an area with numerous historical towns, resulting in 989 fatalities and 45,000 people left homeless. At least four other destructive earthquakes with epicentral intensity greater than or equal to IX on the Mercalli‐Cancani‐Sieberg scale have occurred in the Friuli region in the last 5 centuries (1511, 1700, 1794, and 1928) [Slejko et al., 1999].To better understand the seismic hazards of this vulnerable area, a network of continuously operating Global Positioning System (GPS) receivers—the Friuli Regional Deformation Network (FReDNet)—was installed to monitor the regional distribution of crustal deformation (Figure 1).

Re-appraisal of seismicity and seismotectonics in the north-eastern Algeria. Part I: Review of historical seismicity

As large destructive seismic events are not frequent in Algeria, anexhaustive knowledge of the historical seismicity is required to have arealistic view of seismic hazard in this part of the world. This research workpresents a critical reappraisal of seismicity in the north-eastern Algeria forseismotectonic and seismic hazard purposes. This part of work focuses onthe seismicity of pre-1900 period for the area under consideration[33°N-38°N, 4°E-9.5°E]. By going back tothe available documentary sources and evaluating and analysing the eventsin geographical, cultural and historical context, it has been possible toidentify 111 events, from 1850–1899, which are not reported in therecent Algerian catalogue. Several spurious events, reported in standardlistings, have been deleted and nine unknown events have been discovered.It is quite clear that macroseismic information derived from press reportsand published documents in Algeria, under certain conditions, is veryincomplete, even for destructive earthquakes, located in the countrysideaway from communication centres. One of the reasons for this iscensorship, noticeable during the colonisation period. Critical analysis ofnewly collected information has allowed the determination and/or theimprovement of the macroseismic parameters of each event, such aslocation, maximum epicentral intensity and magnitude to produce anearthquake catalogue as homogeneous and complete as the available data,for the zone under study. The criteria used in this research are explainedand eight historical earthquakes have been the subject of retrospectivemacroseismic field construction.The investigation of historical earthquakes is one of the most important taskin studying seismotectonic for seismic hazard evaluation purposes.

Estimation of earthquake magnitudes from epicentral intensities and other focal parameters in Central and Southern Europe

The publication of an earthquake catalogue by Kárník in 1996 (a continuation and revision of an earlier one (1969)) makes important data available covering one century of the seismic history of Central and Southern Europe. It allows us to study in detail empirical relations between the magnitude and other focal parameters. In this study well-known relations combining two or three focal parameters, M=A+BI0+C log(H), Ms=D+EI0+F log(H), ML=G+OI0+P log(H), ML=Q+RMs+Slog(H), are investigated (M, Kárník's magnitude; ML, local magnitude; Ms, surface wave magnitude; I0, epicentral intensity; H, focal depth in kilometres). The data show a considerable scatter with respect to the relations above. The relations are considered useful, if the following significance criteria are fulfilled. (1) The data sets comprise a minimum of 20 entries.(2) The partial correlation between the two most important parameters is greater than 70 per cent. (3) The parameter of least importance still influences the correlation of the others by more than 5 per cent. The partial correlation coefficients help to decide whether the data are to be rejected as insufficient for the regression analysis or to determine the level beyond which it is useful to perform a regression analysis excluding the parameter of lowest importance. Two kinds of regression are carried out: (1) standard linear regression assumes that only M or ML, respectively, are in error, while the remaining two parameters are error-free. (2) Orthogonal regression assumes that all three parameters have errors. This is the case for the data in the catalogue used here. The orthogonal regression M=−1.682 + 0.654 I0+ 1.868 log (H), with a standard deviation of ±0.284, differs considerably from Kárník's empirical relation M= 0.5 I0+ log (H) + 0.35 for shallow foci, but agrees well with the results of earlier studies by the authors for earthquakes in SE Europe. The data set M, I0, H (for H < 50 km) fails criterion (3). The orthogonal least-squares fit without log (H) has been found as follows: Ms= 0.550 I0+ 1.260, with a standard deviation of ±0.412. We observe systematic regional deviations from this relationship, which need further investigation. The correlation analysis shows that ML and Ms are weakly linked with log (H), but the correlation between ML and Ms is very high (93 per cent). Therefore, the orthogonal relation between ML and Ms without the log (H) term was chosen: ML= 0.664 + 0.893 Ms, with a standard deviation of ±0.163. The correlations between ML, I0 and log (H) do not fulfil the significance criteria. For the purpose of earthquake hazard analysis the orthogonal regression visualizes simultaneously the errors of all input data, i.e. δMLi, δMi and δ log (Hi). Our new relationships result from orthogonal regression analysis using a large high-quality data set. They should be applicable in Central and Southern Europe unless there are regional relationships available that fit the data better.