Yuzuru Ashida

Seismic traveltime tomography using Fresnel volume approach

Summary A Fresnel volume approach is applied to represent wave propagation for seismic traveltime tomography instead of rays. A Fresnel volume is defined as a set of many waves delayed after the shortest traveltime by less than half a period. It is derived by calculating traveltimes both from a source and from a receiver. Tracing rays from sources to receivers is completely avoided. This considerably reduces computational time. We solved the eikonal equation by using a finite-difference method to calculate traveltimes. The advantage of this approach is as follows; First, the frequency of wave can be introduced into analysis. Therefore, we can evaluate the resolution of seismic tomography. Next, The smoothing feature can be naturally introduced. Finally, Fresnel volumes with finite bandwidth considerably reduces the sparseness of ray distribution (data kernel). These advantages make 3-D tomography analysis possible.

Genetic Algorithm Inversion of Rayleigh Wave Dispersion from CMPCC Gathers Over a Shallow Fault Model

Lateral shear-wave velocity imaging, based on 1D surface wave inversion, is becoming routine in commercial site characterisation. A Genetic Algorithm (GA) is applied to the inversion of fundamental mode Rayleigh wave dispersion over a 3-layered, shallow, vertical-fault model. The data are calculated using a 2D finite difference method, then sorted into CMP cross-correlated (CMPCC) gathers, from which the dispersion is measured. Dispersion is relatively smooth over flat portions of the model, as well as when the spread is equally centered over the sharp lateral discontinuity. When between one and two-fifths of the spread is “overhanging” the fault, low-frequency dispersion is corrupted by wavefield scattering. Each dispersion curve is inverted using a 1D forward model, constrained to four layers, with parameters allowed to vary within liberal limits except the layer 1 shear-wave velocity. A novel variation is that the optimisation is partially directed, by including the most successful shear-wave velocity ...

Decomposed element-free Galerkin method compared with finite-difference method for elastic wave propagation

The decomposed element-free Galerkin (DEFG) method is a modified scheme to resolve shortcomings of memory use in element-free Galerkin (EFG) methods. DEFG solves elastic wave equation problems by alternately updating the stress-strain relations and the equations of motion as in the staggered-grid finite-difference (FD) method. DEFG requires at most twice the memory space, a size comparable to that used by the FD method. In addition, DEFG can adopt perfectly matched layer (PML) absorbing boundary conditions as in the FD case. To confirm that DEFG performs as well as FD, a 2D DEFG under PML boundary conditions was compared with an FD with fourth-order spatial accuracy (FD4) using an exact analytical solution of PS reflection waves. The DEFG results are as accurate as those obtained by FD4. In a comparison using Lamb’s problem with eight nodal spaces for the shortest S-wavelength, DEFG provides a remarkably accurate Rayleigh waveform over a distance of at least 50 wavelengths compared with 10 wavelengths for...

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.

Seismic imaging ahead of tunnel face with three component geophones

Summary The present paper proposes an accurate imaging technique for looking ahead of tunnel face using three-component geophones with tunnel blasting and TBM vibrations as seismic sources. Its procedure is as follows: 1) Using three-component receivers set on the tunnel walls, record the seismic signal from the reflectors ahead of the tunnel face; 2) Detect the direction of incidence of the reflected wave; and 3) By weighting according to the direction of incidence of the reflected wave, image the reflector planes using the equi-travel time plane. The proposed technique is applied to datasets collected at an actual drilling operation site, and the results agreed with the geological observation of the walls after the drilling of the tunnel.

Depth transform of offset VSP data

The present paper proposes a new algorithm for depth transform by use of the equation of equi-travel time Plane of upgoing waves obtained from offset VSP seismograms. It is derived that the equation of equi-travel time plane of waves on VSP seismograms which travel from source to receiving point through reflection point on reflector becomes the equation of the ellipse of which foci are source and receiving points. The procedure of depth transform of offset VSP data is as follows. (1) The average velocities of each layer are determined from the travel times of downgoing waves and their ray-paths from the source to receiving points. (2) The ellipses for each pair of source and receiving point are drawn using travel times of upgoing waves and the estimated average velocity. (3) Each reflector is fixed as the common tangent line to these ellipses. Judging from the model studies for the dipping layers, it was clarified that this algorithm reconstructed the structure with a good accuracy, the short calculation time and the requirement for small size of core memory.

Imaging of Refracted Waves by Convolution

Summary Refraction seismology has a long history in obtaining estimates of subsurface structures. Among the many methods developed for the refracted waves the reciprocal method is the most popular. However, the application of the reciprocal and most other methods depends initially on picking the first arrival times. In this paper, we discuss a method for imaging refraction interfaces by using a convolutional method that does not require picking first break times. This avoids both the time-consuming first break picking and the possibility of erroneous picks. We use the analogy of convolution to the summation of time delays and correlation to differences of time delays. Therefore, the reciprocal method can be performed as a convolution of the initial arrival portion of the forward and reverse profile traces and a correlation of the travel time between forward and reverse source positions. With the elimination of picking, the proposed method may be more productive than graphical procedures. However, convolutions produce more ringing than the original records, so it is necessary to apply some data processing procedures before using the proposed method. We present the theoretical background of the convolutional method and its application to synthetic and field data.

2D and 3D Simulation of Elastic Wave Propagation by Using Element Free Galerkin's Method

The element free Galerkin’s (EFG) technique is proposed for solving 2D and 3D elastic wave equation. In this paper, we compare the waveforms calculated by three methodologies; Finite Difference Method with 4th order accuracy in space (FDM4), traditional FEM and EFG. Traditional FEM and EFG are tested on two individual interpolating functions (IFUNC); 1st order (plane) IFUNC and 2nd order (curved) IFUNC. From the comparison to the exact waveforms of Lamb’s problem, the proposed algorism gives accurate waveforms. By two-dimensional implementation, FEM4 demonstrates more accurate result than traditional FEM with plane IFUNC and EFG with plane IFUNC demonstrates more accurate one than FEM4. However, by employing curved IFUNC, traditional FEM and EFG demonstrate almost same accuracy. Moreover, we expand 2D program to 3D one. On the case of 1st order (plane) interpolating function, EFG improves numerical accuracy of traditional FEM without the increase of computational memory.

True Tri-Axial Test Using Distinct Element Method

Many kinds of rock test for engineering properties have been carried out to obtain rock kinetic properties. However it is difficult to visualize inside rock specimen during laboratory tests. This studys objective is to reconstruct true tri-axial tests using Distinct Element Method (DEM). At first, tri-axial compression test is carried out to know correlations between analytical properties and rock properties obtained through compression test like cohesion and internal friction angle. Next, true tri-axial test is simulated using properties above. The result of the simulation, it was clarified that the simulation result can reconstruct a laboratory test qualitatively.

Study on Simulation Algorithm of Borehole Radar for Well Logging and its Application to Measuring Volumetric Water Content of Formation

Borehole radar becomes useful tool for high resolution probing of both deep oil reservoir and shallow subsurface. In order to improve understanding of the electromagnetic wave propagation in single hole, a pseudo-spectral time domain (PSTD) algorithm that allows us to model the full EM wavefield for rotational symmetric structure was developed. This technique is based on Finite Difference Time Domain (FDTD) method and uses fast Fourier transform (FFT) algorithm for spatial derivatives. The PSTD algorithm can reduce grid number and save computer memory for large-scale forward calculation and inversion. The simulation provides a method for processing of field data. The measured volumetric water content from borehole radar data gave good agreement with other logging curves, such as resistivity logging curve.