Large earthquake doublets and fault plane heterogeneity in the northern Solomon Islands subduction zone

In the Solomon Islands and New Britain subduction zones, the largest earthquakes commonly occur as pairs with small separation in time, space and magnitude. This doublet behavior has been attributed to a pattern of fault plane heterogeneity consisting of closely spaced asperities such that the failure of one asperity triggers slip in adjacent asperities. We analyzed body waves of the January 31, 1974,M _w =7.3, February 1, 1974,M _w =7.4, July 20, 1975 (1437)M _w =7.6 and July 20, 1975 (1945),M _w =7.3 doublet events using an iterative, multiple station inversion technique to determine the spatio-temporal distribution of seismic moment release associated with these events. Although the 1974 doublet has smaller body wave moments than the 1975 events, their source histories are more complicated, lasting over 40 seconds and consisting of several subevents located near the epicentral regions. The second 1975 event is well modeled by a simple point source initiating at a depth of 15 km and rupturing an approximate 20 km region about the epicenter. The source history of the first 1975 event reveals a westerly propagating rupture, extending about 50 km from its hypocenter at a depth of 25 km. The asperities of the 1975 events are of comparable size and do not overlap one another, consistent with the asperity triggering hypothesis. The relatively large source areas and small seismic moments of the 1974 doublet events indicate failure of weaker portions of the fault plane in their epicentral regions. Variations in the roughness of the bathymetry of the subducting plate, accompanying subduction of the Woodlark Rise, may be responsible for changes in the mechanical properties of the plate interface.To understand how variations in fault plane coupling and strength affect the interplate seismicity pattern, we relocated 85 underthrusting earthquakes in the northern Solomon Islands Are since 1964. Relatively few smaller magnitude underthrusting events overlap the Solomon Islands doublet asperity regions, where fault coupling and strength are inferred to be the greatest. However, these asperity regions have been the sites of several previous earthquakes withM _s 7.0. The source regions of the 1974 doublet events, which we infer to be mechanically weak, contain many smaller magnitude events but have not generated any otherM _s 7.0 earthquakes in the historic past. The central portion of the northern Solomon Islands Arc between the two largest doublet events in 1971 (studied in detail bySchwartz et al., 1989a) and 1975 contains the greatest number of smaller magnitude underthrusting earthquakes. The location of this small region sandwiched between two strongly coupled portions of the plate interface suggest that it may be the site of the next large northern Solomon Islands earthquake. However, this region has experienced no known earthquakes withM _s 7.0 and may represent a relatively aseismic portion of the subduction zone.     

Motion of particles in turbulent flow: Hyperbolicity,strange attractors and dynamic stochasticity of a system

¶rt;naa, m ma um uu maunuu m am muu ¶rt;uauu um. nua a mau ammama a, n¶rt; mnu ma u u au uu u¶rt;mu.     

Source parameters of some large earthquakes in the eastern Mediterranean region based on an itertive maximum entropy technique

TeleseismicP-waves of some large earthquakes that occurred in the eastern Mediterranean region have been analysed by using an iterative maximum entropy technique in order to obtain the independent spectral parameters, the long-period spectral level ₀ and the corner frequencyf ₀ of the far-field displacement spectra.Based on these parameters, the seismic source parameters seismic momentM ₀, source dimensionr, fault lengthl, average displacement u, shear stress drop , radiated energyE _s and apparent stressn are calculated for the considered earthquakes by using Brune's and Madariaga's models.The striking feature of the source parameters obtained in this study is the low stress drop value which varies between 5 and 15 bars. If Madariaga's model had been used, higher stress drop values would have been obtained.The low stress drop earthquakes in the eastern Mediterranean region might be interpreted either by the possible presence of low strength material near the source or by the partial stress drop model.     

Source characteristics of the 1992 Nicaragua tsunami earthquake inferred from teleseismic body waves

We analyzed the broadband body waves of the 1992 Nicaragua earthquake to determine the nature of rupture. The rupture propagation was represented by the distribution of point sources with moment-rate functions at 9 grid points with uniform spacing of 20 km along the fault strike. The moment-rate functions were then parameterized, and the parameters were determined with the least squares method with some constraints. The centroid times of the individual moment-rate functions indicate slow and smooth rupture propagation at a velocity of 1.5 km/s toward NW and 1.0 km/s toward SE. Including a small initial break which precedes the main rupture by about 10 s, we obtained a total source duration of 110 s. The total seismic moment isM _o =3.4×10²⁰ Nm, which is consistent with the value determined from long-period surface waves,M _o =3.7×10²⁰ Nm. The average rise time of dislocation is determined to be 10 s. The major moment release occurred along a fault length of 160 km. With the assumption of a fault widthW=50 km, we obtained the dislocationD=1.3 m. From andD the dislocation velocity isD=D/0.1 m/s, significantly smaller than the typical value for ordinary earthquakes. The stress drop =1.1 MPa is also less than the typical value for subduction zone earthquakes by a factor of 2–3. On the other hand, the apparent stress defined by 2E _s /M _o , where andE _s are respectively the rigidity and the seismic wave energy, is 0.037 MPa, more than an order of magnitude smaller than . The Nicaragua tsunami earthquake is characterized by the following three properties: 1) slow rupture propagation; 2) smooth rupture; 3) slow dislocation motion.     

Some comparisons between mining-induced and laboratory earthquakes

Although laboratory stick-slip friction experiments have long been regarded as analogs to natural crustal earthquakes, the potential use of laboratory results for understanding the earthquake source mechanism has not been fully exploited because of essential difficulties in relating seismographic data to measurements made in the controlled laboratory environment. Mining-induced earthquakes, however, provide a means of calibrating the seismic data in terms of laboratory results because, in contrast to natural earthquakes, the causative forces as well as the hypocentral conditions are known. A comparison of stick-slip friction events in a large granite sample with mining-induced earthquakes in South Africa and Canada indicates both similarities and differences between the two phenomena. The physics of unstable fault slip appears to be largely the same for both types of events. For example, both laboratory and mining-induced earthquakes have very low seismic efficiencies where _a is the apparent stress and is the average stress acting on the fault plane to cause slip; nearly all of the energy released by faulting is consumed in overcoming friction. In more detail, the mining-induced earthquakes differ from the laboratory events in the behavior of as a function of seismic momentM ₀. Whereas for the laboratory events 0.06 independent ofM ₀, depends quite strongly onM ₀ for each set of induced earthquakes, with 0.06 serving, apparently, as an upper bound. It seems most likely that this observed scaling difference is due to variations in slip distribution over the fault plane. In the laboratory, a stick-slip event entails homogeneous slip over a fault of fixed area. For each set of induced earthquakes, the fault area appears to be approximately fixed but the slip is inhomogeneous due presumably to barriers (zones of no slip) distributed over the fault plane; at constant , larger events correspond to larger _a as a consequence of fewer barriers to slip. If the inequality _a / 0.06 has general validity, then measurements of _a =µE _a /M ₀, where is the modulus of rigidity andE _a is the seismically-radiated energy, can be used to infer the absolute level of deviatoric stress at the hypocenter.     

Turbidometric estimations in Mexico city using the Volz sun photometer

Summary Measuring, with the aid of two filters, the instantaneous intensity of the solar radiation in two wave lengths ( _B = 0.44 , _R = 0.64 ) by means of a sun photometer designed byVolz, we carried out determinations of the decadic turbidity coefficientB (=0.5 ) and the wave length exponent of the haze extinction for Mexico City. Observations were made for almost two and a half years (1960 to 1962 period). A seasonal size distribution in both parameters was found. Although the data thus obtained are provenient of a contaminated atmosphere, comparison of our data is made with those found for higher latitudes ofÅngström, Schüepp andVolz. The height of the homogeneous haze layerH _D was calculated showing pronounced variations for a given wind direction. The maximum and minimum values ofB enable us to get, by the first approximation, the aerosol size distribution ofJunge for our latitudes. However, for exceptional very clear days having maximum actinometric intensity of the solar radiation the sensitivity of the microamperimeter in theVolz sun photometer fails.     

Die Seismizität der Türkei

Summary Using the fromulae given byGutenberg andRichter, the writer has computed the magnitude and energy of 1804 earthquakes which occurred in Turkey during the period 1850–1960. For drawing the Isenerget, the formula =log₁₀ S has been used in accordance with the definitions given byToperczer andTrapp, whereS=e _i/F·p represents the energy in erg/m² h corresponding to the surface element of 0.5° Lat. x 0.5° Long. Also the relationship between the seismicity and the tectonics of Turkey has been studied by drawing the maps of the epicenters, the focus-depths and the frequences of the earthquakes with various intensities.     

A study of rupture length vs. moment for synthetic earthquakes

From the events synthesized from the one-dimensional dynamical mass-spring model proposed byBurridge andKnopoff (1967), the relation between rupture length and earthquake momentM is studied for various model parameters. The earthquake moment is defined to be the total displacement of a connected set of mass elements which slide during an event. A parameter stiffness ratios is defined as the ratio of the spring constant between the two mass elements to that between one mass element and the moving plate. The velocity-dependent friction law (including weakening and hardening processes) is taken to control the sliding of a mass element. The distribution of the breaking strengths over the system is considered to be a fractal function. The cases for severals values and different velocity-dependent friction laws with different decreasing ratesr _w of the frictional force with sliding velocity are studied numerically. The weakening process of the frictional force from the static one to the dynamic one obviously affects theM– relation. Meanwhile, a rapid weakening process rather than a slow weakening process can result in aM– relation, which is comparable to the observed one. Although an increase in thes value can yield an increase in the upper bound of the value and the number of events with largeM and values, the scaling of theM– relation is not affected by the change of thes value. For the cases in this study, the theoretical –M relations for small events withM<1 are almost in the form: M ^1/2, while those for large events withM>1 have a scaling exponent less than but close to 1. In addition, the fractal dimension, the friction drop ratio and the roughness of the distribution of the breaking strengths over the fault surface are the minor parameters influencing the –M relation. A comparison between the theoreticalM– relation and the observed one for strike-slip earthquakes shows that for large events the theoreticalM– relation is quite consistent with the observed one, while for small events there is a one-order difference in the two relations. For the one-dimensional model, the decreasing rate of the dynamic frictional force with velocity is the main factor in affecting the characteristic value of the earthquake moment, at which the scaling of theM– relation changes.     

Magnitude estimation of Koyna-Warna earthquakes, India

The paper presents the current state of magnitude estimation for Koyna earthquakes exceeding magnitude 3.0. We estimate coda duration magnitude from analogue seismograms recorded on the short period vertical (SPZ) seismometer at Hyderabad seismic observatory HYB and determine moment magnitude using very broad-band (VBB) data from the Geoscope station (HYB)and short period digital data from the local seismic network of NationalGeophysical Research Institute (NGRI) around the Koyna and Warna reservoirs.Firstly, the seismograms of 97 Koyna earthquakes exceeding magnitude 4.0 havebeen used to establish a new empirical coda duration magnitude scale which includes the higher order terms of log₁₀, where is the coda length in seconds. Four background noise levels (1, 2, 6 and 10 mm) areconsidered to estimate the coda duration. We found that the duration magnitudes for 1 mm background level are more stable than those for 2, 6 and 10 mm. The new coda duration magnitude (M_dnew) scale, for 1 mmlevel, is:M_dnew = –0.594 + 2.04 log₁₀ – 0.0435 (log₁₀)²The estimated M_dnew are compatible with the reported M_S values of the NGRI observatory and the m_b values of the United States Geological Survey (USGS). These magnitudes can be obtained within the standard deviation of ± 0.26 units of M_S (NGRI). A new relatively homogeneous catalog for Koyna earthquakes of M_dnew 4.0 is obtained. The momentmagnitudes for 34 Koyna-Warna events of M_dnew ranging from 3.0 to 5.4 have been estimated using two techniques. The first utilizes amplitudes of band-pass filtered (between 15 and 30 sec) velocity traces of moderate Koyna-Warna earthquakes of M_W} 4.4 to 5.4, we abbreviate the magnitude using M_A. The second is based on the S-wave spectrum of short period seismograms of local earthquakes (M_W < 3.8). Moment magnitudes estimated by spectral analysis mainly depend on the estimation of event's long-period spectral level and appears to saturate for moderate Koyna-Warnaearthquakes (M_W > 3.8). We recommend the use of both techniques whenever possible. The estimated moment magnitudes and M_dnew show an almost linear relationship with a standard deviation of ± 0.05.     

Seismic risk of circum-Pacific earthquakes: II. Extreme values using Gumbel's third distribution and the relationship with strain energy release

In a previous paper (Makropoulos andBurton, 1983) the seismic risk of the circum-Pacific belt was examined using a whole process technique reduced to three representative parameters related to the physical release of strain energy, these are:M ₁, the annual modal magnitude determined using the Gutenberg-Richter relationship;M ₂, the magnitude equivalent to the total strain energy release rate per annum, andM ₃, the upper bound magnitude equivalent to the maximum strain energy release in a region.The risk analysis is extended here using the part process statistical model of Gumbel's IIIrd asymptotic distribution of extreme values. The circum-Pacific is chosen being a complete earthquake data set, and the stability postulate on which asymptotic distributions of extremes are deduced to give similar results to those obtained from whole process or exact distributions of extremes is successfully checked. Additionally, when Gumbel III asymptotic distribution curve fitting is compared with Gumbel I using reduced chi-squared it is seen to be preferable in all cases and it also allows extensions to an upper-bounded range of magnitude occurrences. Examining the regional seismicity generates several seismic risk results, for example, the annual mode for all regions is greater thanm(1)=7.0, with the maximum being in the Japan, Kurile, Kamchatka region atm(1)=7.6. Overall, the most hazardous areas are situated in this northwestern region and also diagonally opposite in the southeastern circum-Pacific. Relationships are established between the Gumbel III parameters and quantitiesm ₁(1),X ₂ and , quantities notionally similar toM ₁,M ₂ andM ₃ although is shown to be systematically larger thanM; thereby giving a physical link through strain energy release to seismic risk statistics. Inall regions of the circum-Pacific similar results are obtained forM ₁,M ₂ andM ₃ and the notionally corresponding statistical quantitiesm ₁(1),X ₂ and , demonstrating that the relationships obtained are valid over a wide range of seismotectonic enviroments.     

The Local Magnitude Scale in the Korean Peninsula

A formula to determine the local magnitude (M_L) following Richters original definition was empirically derived for the Korean Peninsula. A total of 1,644 digital seismograms from 142 Korean earthquakes that occurred from 1997 to 2000 were corrected for instrument response and convolved with the nominal Wood-Anderson torsion seismograph response to be appropriate for the original definition of M_L. Then, the zero-to-peak amplitude was measured in millimeters on the synthetic Wood-Anderson seismogram. Multiple regression analysis was conducted to determine distance and station correction terms for the measured peak amplitudes. The best-fit solution for M_L yielded the following formula for the Korean Peninsula:where A() and S denote the peak amplitude on the synthetic Wood-Anderson seismogram at distance and the station correction term, respectively. Note that the second term, distance correction, was adjusted with Richters M_L, taking into consideration attenuation differences between the Korean Peninsula and southern California, where Richter originally introduced M_L. On average, the magnitudes determined in this study are nearly the same as those determined by the Korea Institute of Geoscience and Mineral Resources (KIGAM), but are larger than those of the Korea Meteorological Administration (KMA) by as much as 0.36.     

(ϖμ/ϖT) P of the lower mantle

We estimate (/T) _P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T) _P | by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV _S / lnV _P ) _P =1.8–2, which directly relates (/T) _P with (K _S /T) _P . An average (K _S /T) _P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK _S profile of PREM along several possible adiabats. Both (K _S /T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T) _P vs. (K _S /T) _P curves, which intersect at a composition similar to pyrolite with (/T) _P =–0.02 to –0.035 and (K _S /T) _P =–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV _S ) _P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV _S / lnV _P ) _P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV _S ) _P and ( / lnV _S ) _P are free parameters arbitrarily adjusted to fit the tomography and geoid data.     

Multifractal measures,especially for the geophysicist

This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD _q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD _q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).     

Radioactivity and geochemistry of granulites and some related rocks from the saxonian granulite complex

Summary The distribution of radioactive(Th, U, K), major and selected trace(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) elements of granulites from the Saxonian Granulite Complex was studied. Similarly to the South Bohemian granulites, the Saxonian granulites can be divided according to the contents of their major and trace elements into two main groups, groupA containing mostly acid and subacid granulites (K ₂ O>2.5%, SiO ₂ >68%), and groupB containing mostly intermediate and basic granulites (K ₂ O<2.5%, SiO ₂ <68%). Statistically significant differences between groupsA andB were found for all major oxides and several trace elements(Rb, V, Cr, Ni). The Saxonian granulites follow the same calc-alkaline trend as the South Bohemian, granulitesA being placed mostly in the rhyolite field and granulitesB mostly in the dacite, andesite and basalt fields of this trend. The investigated granulites are characterized by a considerable scatter ofTh andU contents accompanied by very variableTh/U ratios; theTh andU concentrations of granulitesA are substantially lower than is usual for rocks of corresponding acidity.

---

¶rt;a an¶rt;u a¶rt;uamu(Th, U, K) u ua ¶rt;u(Rb, Sr, Ba, Y, Zr, V, Cr, Ni) m aum n¶rt;a aaum na. naa, m u¶rt;aum n uu aam n aaum u ¶rt;u am aua, u u uu. aum n u uu ma a¶rt;um ¶rt; ¶rt;nn; nnA nua¶rt;ama a au¶rt; u au¶rt;aum (K ₂ O>2,5%, Si O ₂ >68%), nnB ¶rt;u u aum (K ₂ O<2,5%, SiO ₂ <68%). ¶rt; muunnau mm mamumuu m au ¶rt; a u u ¶rt; m ¶rt;u m(Rb, V, Cr, Ni). auaum n¶rt;¶rt;m um- m¶rt; a u -uaum;aumA a¶rt;ma a uum n, uaumB a a ¶rt;aum, a¶rt;um u aam n m m¶rt;a. ¶rt;aum — u unnA — aamum uu ¶rt;au da¶rt;uamu mTh uU.

     

Mechanics of seismic instabilities induced by the recovery of hydrocarbons

We review earthquake distributions associated with hydrocarbon fields in the context of pore pressure diffusion models, poroelastic stress transfer and isostasy theory. These three mechanisms trigger or induce seismic instabilities at both local scale (D5 km) and at regional scale (D20 km). The modeled changes in stress are small (1 MPa), whatever the tectonic setting. Each mechanism corresponds to different production processes. (1) Local hydraulic fracturing due to fluid injection induces seismic-slip on cracks (M _L3) within the injected reservoir through decreasing the effective stress. (2) Pure fluid withdrawal causes pore pressure to decrease within the reservoir. It triggers adjustments of the geological structure to perturbations related to the reservoir response to depletion. Poroelastic mechanisms transfer this stress change from the reservoir to the surrounding levels whereM _L5 seismic instabilities occur either above or below the reservoir. (3) Massive hydrocarbon recovery induces crustal readjustments due to the removal of load from the upper crust. It can induce larger earthquakes (M _L6) at greater distance from the hydrocarbon fields than the two other mechanisms.Due to the mechanical properties of the shallow rock matrices involved, seismic slip triggered either by mechanism (1) or (2), is a second-order process of the main elastoplastic deformation. for a minimum of 80% of commercially productive basins, most of the local deformation is reported as aseismic, i.e., there is no evidence forM _L3 earthquakes. Nevertheless, the induced stresses vary as a function of time in a manner that depends on the hydraulic diffusivity (i.e., permeability) of the reservoir and surrounding rocks. Because small earthquakes (M _L3) indicate changes in stress and pore pressure, monitoring of seismicity is a means of assessingin situ reservoir behavior.The less constrained seismic response to hydrocarbon recovery is the possible connection between local fluid manipulations, triggered earthquakes and major regional earthquakes. Positive feedback mechanisms suggest that the region of seismic hazard changes is much larger than the area where hydrocarbons are extracted. These observations and models testify that fluid movement and pore pressure changes (increase or decrease) play important roles in the mechanics of earthquakes and in the triggering of natural earthquakes.     

Sur l'influence de la loi de répartition des densités à l'intérieur de la Terre dans les variations luni-solaires de la gravité en un point

Résumé Les observations des variations luni-solaires de la gravité en divers points du globe ne donnent pas des valuers très concordantes pour le facteur lié au module de rigidité de la Terre. On démontre ici que la répartition croissante des densités vers le centre de la Terre a pour conséquence d'amplifier encore les effets dus à l'élasticité. En adoptant la répartition deBullen, on aurait =1+0.244h>1, (h étant le premier nombre deLove). En outre une relation simple lie les facteurs et (déviations de la verticale). La valuer deh déduite de telles observations ne peut conduire directement à une valeur significative du module de rigidité du globe car il faut encore tenir compte des variations de la période et de l'amplitude du mouvement chandlérien du pôle.

---

Summary Observations of luni-solar variations of gravity at various points of the Earth do not give values in agreement for the factor bound to the Earth's modulus of rigidity. It is shown here that the law of increasing of density toward the center of the Earth emphasizes the effect of elasticity: following the law ofBullen, we should have =1+0.244h>1, (h is the firstLove's number). Further, there is a simple relation between the factors and (deviations of the vertical). The value ofh deduced from such observations could not give directly a significative value of the modulus of rigidity because we must take into account the variations of period and amplitude of the chandlerian motion of the pole.

---

Riassunto Le osservazioni delle variazioni luni-solari della gravità in diversi punti della Terra non dànno valori concordanti per il fattore legato al modulo di rigidità del Globo. Si dimostra che la ripartizione crescente della densità verso il centro della Terra ha per conseguenza di amplificare ancora gli effetti dell'elasticità; adottando la legge diBullen, abbiamo =1+0.244h>1, (h essendo il primo numero diLove). Inoltre, una semplice relazione lega i fattori e (deviazioni della verticale). Il valore dih dedotto da tali osservazioni non può condurre ad un valore significativo del modulo di rigidità del Globo poiché bisogna considerare anche le variazioni del periodo e dell'ampiezza del moto polare diChandler.

     

Macroseismic observations of earthquake in Yugoslavia (April 15, 1979, 06h21m gmt), on the territory of Czechoslovakia

an¶rt;u am mu 15- an 1979. a auu a mumuu auu.     

La risoluzione dell'equazione di Laplace nel campo esterno a uno sferoide

Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q ₁,Q ₃, ....Q _2s–1 tali che la sommatoria delleQ _2i–1/^2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.

---

Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q ₁,Q ₃ ....Q _2s–1 in such a way as to make the summatory of theQ _2i–1/^2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.

     

Re-visiting large historical earthquakes in the Colombian Eastern Cordillera

A re-assessment of the historic seismicity of the central sector of the Colombian Eastern Cordillera (EC) is made by revision of bibliographic sources, by calibration with modern instrumental earthquakes, and by interpretations in terms of current knowledge of the tectonics and seismicity of the region. Throughout the process we have derived an equation to estimate M_w for shallow crustal earthquakes in Colombia using the length of isoseismal VIII, L_VIII:

On the propagation of finite Love Waves

Summary The problem of the propagation of finite Love Waves in a heterogeneous elastic half space lying over a homogeneous elastic half space, using the quasilinear stress-strain relation due toS. Ferhst [4] is considered in detail. The variations of the parameter in the layer assumed to be of the form 1= 0e ^z, 0e ^z where is a constant andz is distance measured from the surface into the layer.