Junichi Takekawa

A mesh-free method with arbitrary-order accuracy for acoustic wave propagation

In the present study, we applied a novel mesh-free method to solve acoustic wave equation. Although the conventional finite difference methods determine the coefficients of its operator based on the regular grid alignment, the mesh-free method is not restricted to regular arrangements of calculation points. We derive the mesh-free approach using the multivariable Taylor expansion. The methodology can use arbitrary-order accuracy scheme in space by expanding the influence domain which controls the number of neighboring calculation points. The unique point of the method is that the approach calculates the approximation of derivatives using the differences of spatial variables without parameters as e.g. the weighting functions, basis functions. Dispersion analysis using a plane wave reveals that the choice of the higher-order scheme improves the dispersion property of the method although the scheme for the irregular distribution of the calculation points is more dispersive than that of the regular alignment. In numerical experiments, a model of irregular distribution of the calculation points reproduces acoustic wave propagation in a homogeneous medium same as that of a regular lattice. In an inhomogeneous model which includes low velocity anomalies, partially fine arrangement improves the effectiveness of computational cost without suffering from accuracy reduction. Our result indicates that the method would provide accurate and efficient solutions for acoustic wave propagation using adaptive distribution of the calculation points. A mesh free method with arbitrary-order accuracy has been developed.Dispersion analyses showed that sufficient number of nodes provide better results.The method can treat numerical models with high velocity contrast in a simple manner.

A Hamiltonian Particle Method with a Staggered Particle Technique for Simulating Seismic Wave Propagation

We present a Hamiltonian particle method (HPM) with a staggered particle technique for simulating seismic wave propagation. In the conventional HPM, physical variables, such as particle displacement and stress, are defined at the center, i.e., at the same position, of each particle. As most seismic simulations using finite difference methods (FDM) are practiced with staggered grid techniques, we know the staggered alignment of space variables could improve the numerical accuracy. In the present study, we hypothesized that staggered technique could improve the numerical accuracy also in the HPM and tested the hypothesis. First, we conducted a plane wave analysis for the HPM with the staggered particles in order to verify the validity of our strategy. The comparison of grid dispersion in our strategy with that in the conventional one suggests that the accuracy would be improved dramatically by use of the staggered technique. It is also observed that the dispersion of waves is dependent on the propagation direction due to the difference in the average spacing of the neighboring two particles for the same parameters, as is usually observed in FDM with a rotated staggered grid. Next, we compared the results from the conventional Lamb’s problem using our HPM with those from an analytical approach in order to demonstrate the effectiveness of the staggered particle technique. Our results showed better agreement with the analytical solutions than those from HPM without the staggered particles. We conclude that the staggered particle technique would be a method to improve the calculation accuracy in the simulation of seismic wave propagation.

Self-potential Inversion for the Estimation of Permeability Structure

ABSTRACT The self-potential (SP) method is one geophysical method useful for estimating properties of groundwater flow. The effect of a permeability anomaly on a SP profile has been discussed in the literature, but neither the feasibility of using SP measurements to estimate the permeability structure nor the resolution of the inversion results of an SP profile have been given much attention. In this study, we developed a two-dimensional inversion code for the estimation of permeability structure. We applied this inversion to a synthetic SP profile on the ground surface affected by the permeability structure to evaluate the resolution of the SP inversion. Four models, which include a permeability anomaly located in the center of a slope, are used for the evaluation of the inversion performance. A priori data, including the distribution of the streaming current coefficient, electrical conductivity and flux volume at the discharge and recharge, are input to the inversion. A horizontal zone with high permeab...

A random layer-stripping method for seismic reflectivity inversion

Reflection coefficients and arrival times, together with seismic velocities, are significantly important for possible evaluation of reservoir properties in exploration seismology. Reflectivity inversion is one of the robust inverse techniques used to estimate layer properties by minimising misfit error between seismic data and model. On the other hand, the layer-stripping method produces subsurface images via a top-down procedure so that a given layer is modelled after all the upper layers have been inverted. In this paper, we have combined these two methods to develop a new random layer-stripping scheme which first determines the reflectivity series via a random-search algorithm and then estimates P-wave velocities. The first step can be viewed as a variant of sparse spiking deconvolution, and the second step is accomplished by considering empirical relations between density and P-wave velocity. The method has been successfully applied to Marmousi synthetic data to examine dipping reflectors and velocity gradients, and it has been found to be quite reliable for analysing complex structures. A comparison with minimum entropy deconvolution showed that our inversion algorithm gives better results in detecting the amplitudes and arrival times of seismic reflection events.

Numerical simulation using a Hamiltonian particle method for effective elastic properties in cracked media

We apply a Hamiltonian particle method, one of the particle methods, to simulate seismic wave propagation in a cracked medium. In the particle method, traction free boundaries can be readily implemented and the spatial resolution can be chosen in an arbitrary manner. Utilisation of the method enables us to simulate seismic wave propagation in a cracked medium and to estimate effective elastic properties derived from the wave phenomena. These features of the particle method bring some advantages of numerical efficiencies (e.g. calculation time, computational memory) and the reduction of time for pre-processing. We describe first our strategy for the introduction of free surfaces inside a rock mass, i.e. cracks, and to refine the spatial resolution in an efficient way. We then model a 2D cracked medium which contains randomly distributed, randomly oriented, rectilinear, dry and non-intersecting cracks, and simulate the seismic wave propagation of P- and SV-plane waves through the region. We change the crack density in the cracked region and determine the effective velocity in the region. Our results show good agreement with the modified self-consistent theory, one of the effective medium theories. Finally, we investigate the influence of the ratio of crack length to particle spacing on the calculated effective velocities. The effective velocity obtained becomes almost constant when the ratio of crack length to particle spacing is more than ~20. Based on this result, we propose to use more than 20 particles per crack length.

Application of Marine Controlled-source Electromagnetic Sounding to Submarine Massive Sulphides Explorations

In conventional marine CSEM methods, we need a survey vessel that tows a long cable to which both an EM transmitter and receivers are attached. Therefore, it is difficult to survey shallow sub-seafloor structure below the seafloor of complex topography around submarine massive sulphides (SMS) because of the risk of cable-tangling. In this research, we propose a new marine CSEM method to solve this problem using two autonomous underwater vehicles (AUV). Using this method, it is possible to keep a low height of diving AUVs from the seafloor, so we can carry out the exploration of SMS effectively. We discussed the possibility of new CSEM method employing the 2.5-D FEM program. From numerical results, it is possible to detect the rough existent area of SMS and the rough thickness of SMS.

Development of hydraulic low frequency marine seismic vibrator

We have fabricated an underwater vibratory seismic source with the scale of 60-70 %, to the real design for towed marine seismic vibrator (MSV) using hydraulic servo system. Several evaluation tests were conducted in the sea using the downsized MSV at a depth of about 250m in water. The performance of the downsized MSV was tested for maximum sound level, frequency characteristic, horizontal directivity, and vertical directivity of the sound field generated from the downsized MSV in Suruga Bay about 100 km away from Tokyo. The sound source level and the frequency characteristic were equal to or higher than the estimated specification between 3Hz and 300Hz. The intensities of the generated sound fields observed at vertical and horizontal directions were equivalent to each other, which indicate that the generated sound field could be regarded almost omnidirectional. A trial seismic survey using a short streamer was also conducted and a shot gather was acquired with several different conditions in sweep frequency bands and in sweep lengths. The results showed that the downsized MSV could perform well to be deployed as a marine seismic source in shallow water surveys and that MSV would be a versatile source as one of alternatives to the existing impulsive seismic sources in practice such as airguns, waterguns, boomers, etc.

Coupled Simulation of Seismic Wave Propagation and Failure Phenomena by Use of an MPS Method

The failure of brittle materials, for example glasses and rock masses, is commonly observed to be discontinuous. It is, however, difficult to simulate these phenomena by use of conventional numerical simulation methods, for example the finite difference method or the finite element method, because of the presence of computational grids or elements artificially introduced before the simulation. It is, therefore, important for research on such discontinuous failures in science and engineering to analyze the phenomena seamlessly. This study deals with the coupled simulation of elastic wave propagation and failure phenomena by use of a moving particle semi-implicit (MPS) method. It is simple to model the objects of analysis because no grid or lattice structure is necessary. In addition, lack of a grid or lattice structure makes it simple to simulate large deformations and failure phenomena at the same time. We first compare analytical and MPS solutions by use of Lamb’s problem with different offset distances, material properties, and source frequencies. Our results show that analytical and numerical seismograms are in good agreement with each other for 20 particles in a minimum wavelength. Finally, we focus our attention on the Hopkinson effect as an example of failure induced by elastic wave propagation. In the application of the MPS, the algorithm is basically the same as in the previous calculation except for the introduction of a failure criterion. The failure criterion applied in this study is that particle connectivity must be disconnected when the distance between the particles exceeds a failure threshold. We applied the developed algorithm to a suspended specimen that was modeled as a long bar consisting of thousands of particles. A compressional wave in the bar is generated by an abrupt pressure change on one edge. The compressional wave propagates along the interior of the specimen and is visualized clearly. At the other end of the bar, the spalling of the bar is reproduced numerically, and a broken piece of the bar is formed and falls away from the main body of the bar. Consequently, these results show that the MPS method effectively reproduces wave propagation and failure phenomena at the same time.

ESTIMATION OF PERMEABILITY STRUCTURE WITH SELF POTENTIAL INVERSION

Self-potential (SP) method is one of geophysical methods expected useful to estimate the property of groundwater flow. The effect of permeability anomaly on SP profile has sometimes been discussed, but neither the feasibility of SP measurement to estimate the permeability structure nor the resolution of inversion result of SP profile has been well considered. In this study, we developed a twodimensional inversion code for the estimation of permeability structure from synthetic SP profile on the surface of predefined permeability structure to evaluate the resolution of our SP inversion. Four models including the permeability anomalies located in the center of slope model are used for the evaluation of the performance of our inversion. A priori data of the distribution of streaming current coefficient, electrical conductivity and the flux volume at the discharge and recharge are given to our inversion. The horizontal zone with high permeability and the vertical zone with low permeability can be reconstructed with our inversion properly. However, the horizontal low permeable and the vertical high permeable zone cannot be imaged clearly. The regional groundwater flow pattern around the permeability anomaly has the great effect on the SP pattern on the surface. As our conclusion, the consideration of flow pattern around the permeability anomaly and effect on the SP profile are necessary for the accurate inversion of SP data.

Numerical studies on stress field monitoring using Coda-Q

Summary In this study, we attempt to obtain state parameters of a subsurface medium from stochastic parameter Q. We employ a 2-D finite different method (FDM) and a 2-D boundary integral equation method (BIEM). Using them, we simulate scattering of a 2-D model to see if we can obtain two major state parameters, i.e., the magnitude of the differential stress and the orientation of the principal stress loaded in the underground from the variation of coda-Q. FDM is useful for the description of the change in the macro-scale anisotropic parameters induced by the stress field in the model. On the other hand, BIEM is useful for the description of the change in the micro-scale parameters such as the orientation of each crack in the model. We revealed that the coda-Q has the relationship with the loaded stress. The result of FDM indicates that the magnitude of the stress could be estimated from the variation of the coda-Q. Since the coda-Q shows the behavior depending on the orientation of the loaded stress, it also turned out that the stress orientation could be estimated as well. This tendency is derived from the occurrence of the velocity anisotropy in the elastic wave propagation due to the stress loading. The results from BIEM indicate that that behavior of the coda-Q variation has a different tendency from that from FDM. Although the orientation of each crack, which reflects the stress history of the medium, is aligned to specific direction and influences the behavior of the coda-Q, the tendency in the variation of coda-Q value is perceived similar to that in FDM. In conclusion, our results show the possibility that the loaded stress could be estimated if we obtain the change of the coda-Q varying with the loaded stresses. It means that non-stochastic physical-state properties could be obtained from stochastic-parameter and will lead to more clear deterministic model essential for engineering application of wave theories.