Wave Generations from Line Sources within the Ground.

AKEUCHI, Hitoshi; Kobayashi, Naota

doi:10.4294/jpe1952.3.7

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1, we shall denote the density and rigidity in the superficial and the lower thickness of the superficial layer is H, and the wave origin is at (x=y=0, z=D to be positive real. The integral in (2.14) is of the similar type as that we had in a previous paper (TAKEUCHI, H. and KOBAYASHI, N.: 1955). Thus following the way in that paper, we shall transform (2.14) into The points E and D will be made far away from A in the following analysis.…”

mentioning

confidence: 87%

Wave Generations in a Superficial Layer Resting on a Semi-infinite Lower Layer.

Takeuchi

Kobayashi

1956

J,Phys,Earth

Self Cite

View full text Add to dashboard Cite

Wave generations from a line source of SH type in a superficial layer resting on a lower layer are studied.The movement at a point is shown to be composed of pulses, each representing a disturbance arriving at the theoretical time for one of the reflected and refracted waves.When we superpose these component waves, we get, at points far away from the wave origin, the theoretical movement which is very similar to that predicted by the normal mode solution.The reflected and refracted waves are shown to appear at the respective critical distances.Thus we can make clear how the transition from the aperiodic motion near the origin to the complicated oscillatory motion far away from the origin takes place. The most significant result obtained is that the amplitude of the reflected wave is very large at the respective critical distance given by (3.12).Examples which have some connections with this result are given in the last section.

show abstract

mentioning

confidence: 87%

Wave Generations in a Superficial Layer Resting on a Semi-infinite Lower Layer.

Takeuchi

Kobayashi

1956

J,Phys,Earth

Self Cite

View full text Add to dashboard Cite

show abstract

“…Using the mathematically simpler line rather than point source, Nakano (1925) and Lapwood (1949) have given qualitative asymptotic solutions of this problem. Garvin (1956) and Gilbert (1956) have obtained the exact closed form solution for the same problem utilizing 58-2 the method of Cagniard, whereas Takeuchi & Kobayashi (1955) have obtained exactly the same result by means of the Fourier integral. For a point source, numerically incomplete solutions have since been given by Pinney (1954) and Pekeris (19553).…”

Section: Introductionmentioning

confidence: 94%

Propagation of elastic wave motion from an impulsive source along a fluid/solid interface

Roever¹,

Vining²,

Strick³

1959

Phil. Trans. R. Soc. Lond. A

View full text Add to dashboard Cite

Parts I and II of this report compare the experimentally observed pressure response for the impulse excited fluid/solid interface problem with that derived from a corresponding theoretical investigation. In the experiment a pressure wave is generated in the system by a spark and detected with a small barium titanate probe. The output of the probe is displayed on an oscilloscope and photographed. Two cases are investigated: one where the transverse wave velocity is lower than the longitudinal wave velocity of the fluid and the other where the transverse wave velocity is higher. Both of these observed responses are shown to agree even as to details of wave-form, with exact computations made for a delta-excited line source. This comparison is justified by making an approximate calculation for the decaying point source and showing that at these distances it does not differ appreciably from the delta-excited line source. In the case of low transverse wave velocity one finds, besides critically refracted P , direct, and reflected waves, a Stoneley type of interface wave. Although the emphasis in recent years has been towards minimizing the importance of Stoneley waves, the evidence here is that a Stoneley wave can be the largest contributor to a response curve. In the case of high transverse wave velocity the critically refracted P wave is smaller, and the Stoneley wave, though it tends to maintain a rather constant amplitude, becomes compressed in time and arrives very soon after the reflexion. Between the critically refracted P wave and the direct arrivals one finds both experimentally and theoretically a pressure build-up preceding the arrival time that might be expected for a critically refracted transverse wave. In part III this pressure build-up is investigated and found to consist of the superposition of three arrivals. The most prominent of these is a pseudo-Rayleigh wave. The others are the critically refracted transverse wave and the build-up to the later arriving Stoneley wave. Detailed investigation of the pseudo-Rayleigh wave shows it to have the velocity of a true Rayleigh wave which is independent of the existence of the fluid. Furthermore, it has the same retrograde particle motion as the true Rayleigh wave. However, it is radiating into the fluid as it progresses and therefore has many of the properties of a critically refracted arrival when measurements are made in the fluid. Mathematically it differs from the true Rayleigh wave in that its origin is not from a pole on the real axis of the plane of the variable of integration, but rather from a pole which lies on a lower Riemann sheet in the complex plane. In the high transverse wave velocity case this pole is not too far removed from the real axis and the imaginary part of the pole location might be interpreted as a decay factor. The real part, however, yields only approximately the velocity of the pseudo-Rayleigh wave, for the actual velocity as pointed out above is precisely that of the true Rayleigh wave velocity. The migration of this complex pole explains why such a pseudo-Rayleigh wave was not observed in parts I and II in the low transverse velocity case. The problem under discussion is intimately related to the classic work of Horace Lamb On the propagation of tremors over the surface of an elastic solid. One need make only a minor re-interpretation of the source function in order to compare directly the wave-forms (excluding of course the Stoneley wave contribution). Finally, a method is suggested for obtaining the solid rigidity of bottom sediments in watercovered areas from in situ measurements of the pseudo-Rayleigh wave and/or Stoneley wave velocities and arrival times

show abstract

Interpretation of source functions of circum-Pacific earthquakes obtained from long-period Rayleigh waves

Aki¹

1960

J. Geophys. Res.

View full text Add to dashboard Cite

The source functions of 53 shocks of the circum‐Pacific belt were obtained by a method of equalization applied to Rayleigh waves in the period range of 35 sec to 150 sec recorded at the Seismological Laboratory, Pasadena. The source function was interpreted in terms of the direction of forces at the source. The interpretation was checked by additional information concerning the earthquake as well as by an error analysis. The horizontal forces deduced from the source function showed a systematic geographic distribution, which favors Benioff's hypothesis on the circum‐Pacific tectonics. The vertical forces are found to be mostly directed upward on the oceanic side.

show abstract

Wave Generations from Line Sources within the Ground.

Cited by 3 publications

References 0 publications

Wave Generations in a Superficial Layer Resting on a Semi-infinite Lower Layer.

Wave Generations in a Superficial Layer Resting on a Semi-infinite Lower Layer.

Propagation of elastic wave motion from an impulsive source along a fluid/solid interface

Interpretation of source functions of circum-Pacific earthquakes obtained from long-period Rayleigh waves

Contact Info

Product

Resources

About