Yukio Hagiwara

Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain

Abstract Probability of a large-scale earthquake occurrence is estimated from crustal strain geodetically detected over an earthquake area. The Weibull distribution function, which is widely applied to quality-control research, is made use of in this paper in the probabilistic treatments of crustal strain. Using the table of ultimate strain presented by Rikitake (1974), a Weibull model representing a statistical distribution of crustal-rupture occurrence time is determined on the assumption that the crust is strained with a constant speed. In the case of the South Kanto District, the associated probability-density function has a maximum at about 84 years after the time when the strain energy accumulation starts.

A new formula for evaluating the truncation error coefficient

In this paper, a new formula for evaluating the truncation coefficientQn is derived from recurrence relations of Legendre polynomials. The present formula has been conveniently processed by an electronic computer, providing the value ofQn up to a degreen=49 which are exactly equal to those of Paul (1973).

Truncation error formulas for the geoidal height and the deflection of the vertical

A general formula giving Molodenskii coefficientsQn of the truncation errors for the geoidal height is introduced in this paper. A relation betweenQn andqn, Cook’s truncation function, is also obtained. Cook (1951) has treated the truncation errors for the deflection of the vertical in the Vening Meinesz integration. Molodenskii et al. (1962) have also derived the truncation error formulas for the deflection of the vertical. It is proved in this paper that these two formulas are equivalent.

A stochastic model of earthquake occurrence and the accompanying horizontal land deformation

Abstract A large-scale earthquake is believed to be associated with a release of strain energy accumulated in the crust, probably by the motion of upper-mantle lithosphere. Such an earthquake mechanism is well simulated by a belt-conveyer model proposed by Utsu (1972). The probability of earthquake occurrence can be estimated on the assumption that the motion of a slider on the belt-conveyer is mathematically formulated as a Markov process. In the probabilistic expressions, the results of Mogis (1962) rock-fracture experiments are applied to the hazard-rate function of earthquake occurrence. The hazard-rate function has two coefficients, A and B, to be determined by the experiments. It is concluded that, when B is small, a number of small-scale earthquakes occur in the early time after the accumulation of crustal strain energy starts, but that the accumulated strain energy changes catastrophically into a single large-scale earthquake, when B is large.

Probability of earthquake occurrence estimated from results of rock fracture experiments

The hazard rate, the number of fracture occurrences per unit time, which has been obtained from laboratory experiments of rock fracture, is obtained for the earths crust by analysing the statistical distribution of geodetically-observed ultimate strain. The associated hazard function has two coefficients, A and B, to be determined. Comparison of the coefficients obtained by the results of rock-fracture experiments with the geodetically determined ones discloses that B is independent of the size-effect. It is therefore concluded that, if A is estimated from the statistics of the geodetically observed ultimate strain and B is obtained from fracture experiments of rock forming a local part of the crust, the probability of a local large-scale earthquake occurrence can be estimated.

Gravity Changes in the Izu Peninsula, Japan

Precise gravity surveys have been repeated at 36 stations in the Izu Peninsula since December 1974. We have found a gravity decrease occurred concurrently with a dome-like uplift centering at Hiekawa Pass. The ratio of the gravity change to the elevation change is approximately equal to a free-air rate. A possible cause of the uplift can be presumed as, say, an earthquake-triggered volcanic gas pressure increase. At a benchmark located nearby a Sacks-Evertson borehole volume-strainmeter station, we found an interesting fact that a gravity change is proportional to a volumetirc strain change with a rate of 1.4 × 10−6/μgal. This fact may suggest that the gravity increase is probably induced by a density increase due to a postseismic crustal compression started immediately after the 1978 Izu-Oshima Kinkai earthquake of M7.0.

Geodesy in Japan

T. Inoh was the first who completed a nation-wide map of Japan, in the beginning of the 19th century. He determined geodetic positions by distance and angle measurements and by astronomical observations.When Japan entered into its modern era, about 100 years ago, the Military Land Survey was established and has conducted geodetic work in Japan ever since until the end of World War II. A German surveying system belonging to Helmerts school was adopted. The Ministry of Education organized later the Geodetic Commission which promoted the geodetic activities in cooperation with the Military Land Survey.Comparison between the first and second nation-wide triangulation results obtained by the Geographical Survey Institute (GSI), the successor of the Military Land Survey, brought out marked horizontal land-deformations associated with a large earthquake. Repetitions of levelling survey also make it clear that vertical land-movements, well consistent with tide-gauge observation data, take place in association with earthquakes. The extensive subsidence in the Northeast Japan may be explained by assuming a sinking lithosphere, as is argued by the theory of plate tectonics. On the other hand, most local movements are closely correlated to pre-, co- and post-seismic land-deformations.The nation-wide gravity survey carried out by the GSI disclosed a complicated gravity distribution in Japan. Ship-borne gravimeters have now been extensively working at sea. One of the recent highlights of gravimetric work is the detection of secular gravity changes which are in accordance with the secular changes of levelling data.A portable absolute-gravity measuring instrument was constructed by the Earthquake Research Institute although it is still in a testing stage. Much advance has been made in the astrogeodetic observation devices since 1950s.