Diffraction and conversion of elastic waves at a corrugated interface

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1415-1424 ◽  
Author(s):  
Anne Paul ◽  
Michel Campillo
Keyword(s):  
Wave Field ◽  
Boundary Integral Equations ◽  
Incidence Angle ◽  
Boundary Integral ◽  
P Wave ◽  
Plane Boundary ◽  
Small Scale ◽  
Local Geometry ◽  
P Waves ◽  
S Waves

Numerical modeling is used to investigate the effect of small‐scale irregularities of a reflecting boundary on elastic wave reflections. The scattered wave field is computed by using a discretized form of boundary integral equations and a plane‐wave decomposition of seismic wave fields. For various values of incidence angle of the P wave, we compute the distribution of diffracted energy for both P waves and S waves as a function of reflection angle. We show that corrugations with mean wavelength of the order of, or smaller than, the seismic wavelength have little effect on the reflected P wave. However, the pattern of P‐to‐S conversion is very different from that with a plane boundary. Scattered S waves appear at postcritical angles for any angle of incidence of the P wave. The amplitude of these nongeometrical shear waves decreases rapidly with decreasing amplitude of the corrugations, or when the mean wavelength of the corrugations becomes larger than the dominant seismic wavelength. The local geometry of the irregularities has a negligible effect on the scattered S waves. By analogy with perturbation theory, we propose interpreting the postcritically scattered S waves as the contribution to the shear wave field of converted inhomogeneous P waves diffracted along the boundary.

Numerical simulation of azimuthal acoustic logging in a borehole penetrating a rock formation boundary

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D283-D291 ◽  
Author(s):  
Peng Liu ◽  
Wenxiao Qiao ◽  
Xiaohua Che ◽  
Xiaodong Ju ◽  
Junqiang Lu ◽  
...  
Keyword(s):  
Domain Model ◽  
P Wave ◽  
S Wave ◽  
Angle Variation ◽  
P Waves ◽  
Acoustic Logging ◽  
S Waves ◽  
Rock Formation ◽  
Logging Tool ◽  
Difference Time

We have developed a new 3D acoustic logging tool (3DAC). To examine the azimuthal resolution of 3DAC, we have evaluated a 3D finite-difference time-domain model to simulate a case in which the borehole penetrated a rock formation boundary when the tool worked at the azimuthal-transmitting-azimuthal-receiving mode. The results indicated that there were two types of P-waves with different slowness in waveforms: the P-wave of the harder rock (P1) and the P-wave of the softer rock (P2). The P1-wave can be observed in each azimuthal receiver, but the P2-wave appears only in the azimuthal receivers toward the softer rock. When these two types of rock are both fast formations, two types of S-waves also exist, and they have better azimuthal sensitivity compared with P-waves. The S-wave of the harder rock (S1) appears only in receivers toward the harder rock, and the S-wave of the softer rock (S2) appears only in receivers toward the softer rock. A model was simulated in which the boundary between shale and sand penetrated the borehole but not the borehole axis. The P-wave of shale and the S-wave of sand are azimuthally sensitive to the azimuth angle variation of two formations. In addition, waveforms obtained from 3DAC working at the monopole-transmitting-azimuthal-receiving mode indicate that the corresponding P-waves and S-waves are azimuthally sensitive, too. Finally, we have developed a field example of 3DAC to support our simulation results: The azimuthal variation of the P-wave slowness was observed and can thus be used to reflect the azimuthal heterogeneity of formations.

Shallow near-surface effects

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. T221-T231 ◽  
Author(s):  
Christine E. Krohn ◽  
Thomas J. Murray
Keyword(s):  
Time Delay ◽  
Velocity Gradient ◽  
P Wave ◽  
Unconsolidated Sediments ◽  
P Waves ◽  
Large Computer ◽  
Near Surface ◽  
S Waves ◽  
High Attenuation ◽  
Pulse Broadening

The top 6 m of the near surface has a surprisingly large effect on the behavior of P- and S-waves. For unconsolidated sediments, the P-wave velocity gradient and attenuation can be quite large. Computer modeling should include these properties to accurately reproduce seismic effects of the near surface. We have used reverse VSP data and computer simulations to demonstrate the following effects for upgoing P-waves. Near the surface, we have observed a large time delay, indicating low velocity ([Formula: see text]), and considerable pulse broadening, indicating high attenuation ([Formula: see text]). Consequently, shallowly buried geophones have greater high-frequency bandwidth compared with surface geophones. In addition, there is a large velocity gradient in the shallow near surface (factor of 10 in 5 m), resulting in the rotation of P-waves to the vertical with progressively smaller amplitudes recorded on horizontal phones. Finally, we have found little indication of a reflection or ghost from the surface, although downgoing reflections have been observed from interfaces within the near surface. In comparison, the following have been observed for upgoing S-waves: There is a small increase in the time delay or pulse broadening near the surface, indicating a smaller velocity gradient and less change in attenuation. In addition, the surface reflection coefficient is nearly one with a prominent surface ghost.

scholarly journals MORE ABOUT THE WILSONIAN ANALYSIS ON THE PIONLESS NEFT

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3191-3225 ◽  
Author(s):  
KOJI HARADA ◽  
HIROFUMI KUBO ◽  
ATSUSHI NINOMIYA
Keyword(s):  
Fixed Points ◽  
Scattering Amplitude ◽  
Flow Equation ◽  
Effective Field ◽  
P Wave ◽  
P Waves ◽  
S Waves ◽  
Partial Waves ◽  
The One ◽  
Power Divergence

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective field theory in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of [Formula: see text] in the S waves, and, on the other hand, (2) we consider the RG flows in higher partial waves (P and D waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two "fixed lines" and a "fixed surface" which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the S waves, but there are two relevant directions in the P waves at the nontrivial fixed points and three in the D waves. We explain the physical meaning of the P-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern and Richardson, and possible implementation of power divergence subtraction in higher partial waves.

Imaging beneath a high‐velocity layer using converted waves

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1444-1452 ◽  
Author(s):  
Guy W. Purnell
Keyword(s):  
High Velocity ◽  
Energy Partitioning ◽  
P Wave ◽  
Converted Wave ◽  
P Waves ◽  
Lower Velocity ◽  
S Waves ◽  
High Velocity Layer ◽  
The Waves ◽  
Velocity Layer

High‐velocity layers (HVLs) often hinder seismic imaging of deeper reflectors using conventional techniques. A major factor is often the unusual energy partitioning of waves incident at an HVL boundary from lower‐velocity material. Using elastic physical modeling, I demonstrate that one effect of this factor is to limit the range of dips beneath an HVL that can be imaged using unconverted P‐wave arrivals. At the same time, however, partitioning may also result in P‐waves outside the HVL coupling efficiently with S‐waves inside. By exploiting some of the waves that convert upon transmission into and/or out of the physical‐model HVL, I am able to image a much broader range of underlying dips. This is accomplished by acoustic migration tailored (via the migration velocities used) for selected families of converted‐wave arrivals.

Dipping structure under Dourbes, Belgium, determined by receiver function modeling and inversion

1995 ◽  
Vol 85 (1) ◽  
pp. 254-268 ◽  
Author(s):  
Jie Zhang ◽  
Charles A. Langston
Keyword(s):  
Receiver Function ◽  
Receiver Functions ◽  
P Wave ◽  
P Waves ◽  
S Waves ◽  
The North ◽  
Shear Wave Velocities ◽  
Geophysical Surveys ◽  
Vector Rotation ◽  
Anomalous Particle

Abstract Teleseismic broadband P and S waves recorded at the NARS station NE06 (Dourbes, Belgium) are shown to exhibit strong anomalous particle motion not attributable to instrument miscalibration or malfunction. Azimuthally varying radial and tangential components have been observed on 38 recordings after vector rotation of horizontal P waves into the ray direction. The tangenital P waves attain amplitudes comparable to the radial components from the east with negative polarity and west with positive polarity, but tend to be zero in the north and south, suggesting major discontinuities in the crust dipping southward. The SH wave from the east contains a large SPmP phase, an S-to-P conversion at the free surface and then reflected back to the surface from the Moho. The polarity of this SPmP phase presents further evidence for a southward-dipping Moho. We employ ray theory for three-dimensionally dipping interfaces to compute the P-wave response. Linear inverse theory with smoothness constraints is applied to the simultaneous inversions of P-wave receiver functions for four different backazimuths. Through the progressive change of interface strike and dip and the inversion of layer shear-wave velocities, a dipping crustal model that is consistent with both the observed waveforms and results of previous local geophysical surveys has been determined. The results suggest a large velocity contrast in the shallow structure near the surface, another major interface at a depth of 12 km with dip of 10°, and a seismically transparent unit below the interface. The interface at a depth of 12 km reportedly emerges at the Midi fault 50 km north of the station NE06.

A MERMAID Miscellany: Seismoacoustic Signals beyond the P Wave

2021 ◽  
Author(s):  
Joel D. Simon ◽  
Frederik J. Simons ◽  
Jessica C. E. Irving
Keyword(s):  
Acoustic Pressure ◽  
Outer Core ◽  
French Polynesia ◽  
P Wave ◽  
P Waves ◽  
S Waves ◽  
Detection And Identification ◽  
The Pacific ◽  
Wave Tomography ◽  
Marine Areas

Abstract Mobile Earthquake Recorder in Marine Areas by Independent Divers (MERMAID) is a passively drifting oceanic diving float that transmits acoustic pressure records from global earthquakes within hours or days of their rupture. The onboard algorithm used for the detection and identification of signals from the hydrophone prioritizes the recovery of ∼1 Hz teleseismic P waves, which are useful for seismic imaging of Earth’s mantle. Two years into a mission that launched 50 MERMAIDs to map 3D mantle wavespeed anomalies with high resolution under the Pacific in French Polynesia, it is clear that the data returned contain much information beyond the first-arriving seismic P phases. These include acoustic conversions from S waves, surface waves, T waves, and inner- and outer-core phases, generated by earthquakes heard across the globe—and sounds from otherwise unidentified events occurring in remote and uninstrumented parts of the world’s oceans. Our growing database of automatically accumulating ∼240 s long-triggered segments contains a treasure trove for geophysicists interested in seismology beyond P-wave tomography. Furthermore, equipped with two-way communication capabilities, MERMAID can entertain requests to deliver data from its 1 yr buffer. In this article, we highlight the data classes and categories in MERMAID’s “extended-utility” catalog.

scholarly journals METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

2021 ◽  
Author(s):  
Assiyat Dadayeva ◽  
Lyudmila Alexeyeva
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Plane Boundary ◽  
Unknown Boundary ◽  
Singular Boundary

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

scholarly journals Comparison of recent S-wave indicating methods

2018 ◽  
Vol 29 ◽  
pp. 00019
Author(s):  
Katarzyna Hubicka ◽  
Jakub Sokolowski
Keyword(s):  
Real Data ◽  
The Body ◽  
Body Waves ◽  
Identification Accuracy ◽  
P Wave ◽  
S Wave ◽  
P Waves ◽  
S Waves ◽  
Mode Decomposition ◽  
Wave Arrival

Seismic event consists of surface waves and body waves. Due to the fact that the body waves are faster (P-waves) and more energetic (S-waves) in literature the problem of their analysis is taken more often. The most universal information that is received from the recorded wave is its moment of arrival. When this information is obtained from at least four seismometers in different locations, the epicentre of the particular event can be estimated [1]. Since the recorded body waves may overlap in signal, the problem of wave onset moment is considered more often for faster P-wave than S-wave. This however does not mean that the issue of S-wave arrival time is not taken at all. As the process of manual picking is time-consuming, methods of automatic detection are recommended (these however may be less accurate). In this paper four recently developed methods estimating S-wave arrival are compared: the method operating on empirical mode decomposition and Teager-Kaiser operator [2], the modification of STA/LTA algorithm [3], the method using a nearest neighbour-based approach [4] and the algorithm operating on characteristic of signals’ second moments. The methods will be also compared to wellknown algorithm based on the autoregressive model [5]. The algorithms will be tested in terms of their S-wave arrival identification accuracy on real data originating from International Research Institutions for Seismology (IRIS) database.

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