Shuhei Okubo

A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth

The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky’s is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincare (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

Gravity and potential changes due to shear and tensile faults in a half‐space

Analytic expressions derived from a simplified model are invaluable because they often provide deep insight into geophysical phenomena. Such is the case with potential and gravity changes. Here we present expressions of potential and gravity changes caused by faulting on a finite rectangular plane buried in a homogeneous half-space. The expressions can be used to evaluate coseismic changes in surface gravity and geoid height. Observed gravimetric data combined with our formulae thus provide constraints on the fault geometry and magnitudes of dislocation.

Global displacements caused by point dislocations in a realistic Earth model

We define dislocation Love numbers [h nm ij , l nm ij , k nm ij , l nm t , ij ] and Greens functions to describe the elastic deformation of the Earth caused by a point dislocation and study the coseismic displacements caused in a radially heterogeneous spherical Earth model. We derive spherical harmonic expressions for the shear and tensile dislocations, which can be expressed by four independent solutions : a vertical strike slip, a vertical dip slip, a tensile opening in a horizontal plane, and a tensile opening in a vertical plane. We carry out calculations with a radially heterogeneous Earth model (1066A). The results indicate that the dominating deformations appear in the near field and attenuate rapidly as the epicentral distance increases. The shallower the point source, the larger the displacements. Both the Earths curvature and vertical layering have considerable effects on the deformation fields. Especially the vertical layering can cause a 10% difference at the epicentral distance of 0.1°. As an illustration, we calculate the theoretical displacements caused by the 1964 Alaska earthquake (m w = 9.2) and compare the results with the observed vertical displacements at 10 stations. The results of the near field show that the vertical displacement can reach some meters. The far-field displacements are also significant. For example, the horizontal displacements (u ψ ) can be as large as 1 cm at the epicentral distance of 30°, 0.5 cm at about 40°, magnitudes detectable by modern instrument, such as satellite laser ranging (SLR), very long baseline interferometry (VLBI) or Global Positioning System (GPS). Globally, the displacement (u r ) caused by the earthquake is larger than 0.25 mm.

First detection of absolute gravity change caused by earthquake

Unequivocal coseismic gravity change was detected for the first time by absolute gravimetry. The measurements were done just one day before and only 7 days after a M6.1 earthquake (M6.1). The absolute gravity change was −6 microgal, significantly larger than the observational error of about 1 microgal. Of particular interest is that the observed spatial gravity variations agree remarkably well with those expected from an elastic dislocation model constructed on displacement data alone. The result strongly encourages us to perform a simultaneous inversion of both gravity and displacements to have better insight of earthquakes.

Verifying the precision of a new generation absolute gravimeter FG5—Comparison with superconducting gravimeters and detection of oceanic loading tide

We carried out a several day experiment at two sites to verify the precision of the FG5 absolute gravimeter through collocation with superconducting gravimeters. We found 2 to 4 microgal diurnal/semi-diurnal signals in the time series of absolute gravity measurements. These signals agreed well with theoretical ocean tide both in amplitude and in phase, demonstrating that the FG5s precision is better than 2 microgal. Furthermore, we found that the discrepancy between the FG5 measurements and the SG measurements is 1.3 to 1.5 microgal. These results verify that the FG5 is precise to 1 to 2 microgal.

Drain‐back process of basaltic magma in the summit conduit detected by microgravity observation at Izu‐Oshima Volcano, Japan

Basalt magma sometimes moves through volcanic conduits causing only minor deformation. In that case, we may detect magma movements directly by microgravity observations. After the 1986 eruption of Izu-Oshima volcano, we observed anomalous gravity variations localized at the summit. Based on a vertical cylindrical conduit model, we estimate the time variations of the head of magma in the summit conduit and clarify the magma drain-back process after the 1986 eruption.

Partial derivative of love numbers

We present a simple formula for the partial derivatives of Love numbers with respect to density, bulk modulus and rigidity without urging the Adams-Williamson condition in the liquid core. Partials of the second degree Love numbers are computed for model 1066 A. Love numbers prove to be either completely or virtually independent of the elastic profile within the whole core. Delta-function-like changes occur in Love numbers when we perturb the density of the top and bottom layers of the outer core.

Imaging the density profile of a volcano interior with cosmic-ray muon radiography combined with classical gravimetry

Cosmic-ray muon radiography has the potential to reveal the density structure of gigantic objects. It utilizes the strong penetration ability of high-energy muons. By measuring the number of muons that travel through a target object, the average density can be calculated along the muon path. Since muons travel in straight paths through matter, specially designed detectors can generate density maps with higher spatial resolution than those obtained with conventional geophysical methods. However, this technique has a few notable limitations in that it can only be applied to near-surface structures above the muon sensor and strongly depends on the characteristics of the local topography. This is due to the fact that almost all cosmic-ray muons arrive only from the upper hemisphere. Geological structures, e.g. volcanoes, that allow for muon detectors to be placed on a slope directly below the point of interest are thus the best candidates for this technique. The drawback of muon radiography that only the horizontally integrated density above the sensor is measured with a time resolution larger than several weeks may be partly remedied by combining its results with gravity data, as they are both sensitive to target density while complementary to each other in several aspects. An example of such a combination is presented: real-time monitoring of magma head height in a volcano conduit.

Integrated processing of muon radiography and gravity anomaly data toward the realization of high‐resolution 3‐D density structural analysis of volcanoes: Case study of Showa‐Shinzan lava dome, Usu, Japan

We have developed an integrated processing method for muon radiography and gravity anomaly data for determining the 3-D density structures of volcanoes with a higher spatial resolution than is possible by conventional gravity inversion. In the present paper, we demonstrate the performance of the proposed method by performing numerical tests using synthesized data, and we present the results obtained by applying the proposed method to a volcano, Showa-Shinzan lava dome, Hokkaido, Japan. We obtained the detailed shape of a vent beneath the dome and detected the presence of solidified dense lava near the top of the dome. The results demonstrate the advantage of a hybrid measurement based on both gravity and muon radiography for imaging small structures with sizes of a few hundreds of meters near the surface of a volcano.

Absolute gravity change associated with the March 1997 earthquake swarm in the Izu Peninsula, Japan

We carried out both absolute and relative gravity measurements in the Izu Peninsula just before and after the March 1997 earthquake swarm occurred. The measurements revealed significant absolute gravity changes, which we find to be made of three spatial components. The first one is located near Cape Kawana, and would be associated with the volcanic activity that caused the earthquake swarm. The second one would be associated with shallow and localized magma intrusion just beneath Ito. The third one may be due to a change in the deep region beneath the Kita-Izu fault system, which is considered to be a major tectonic line of this region. The gravity changes can be used to detect underground mass movement. For this purpose, we first use crustal movement observations to construct an elastic dislocation model with two tensile faults and a left lateral fault. Then we use the gravity changes to constrain the density of the material which filled the tensile faults. We find that the density is likely to be small, and that the gravity changes of the first component are reproduced well by the fault model. The smallness of the density implies that highly vesiculated magma or water would have injected into the faults.