Visualizing effects of anisotropy on seismic moments and their potency-tensor isotropic equivalent

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. C85-C97 ◽  
Author(s):  
Nepomuk Boitz ◽  
Anton Reshetnikov ◽  
Serge A. Shapiro
Keyword(s):  
Radiation Pattern ◽  
Elastic Anisotropy ◽  
Moment Tensor ◽  
Matrix Multiplication ◽  
Tensor Decomposition ◽  
P Wave ◽  
Propagation Path ◽  
Tectonic Deformation ◽  
Radiation Patterns ◽  
Rock Anisotropy

Radiation patterns of earthquakes contain important information on tectonic strain responsible for seismic events. However, elastic anisotropy may significantly impact these patterns. We systematically investigate and visualize the effect of anisotropy on the radiation patterns of microseismic events. For visualization, we use a vertical-transverse-isotropic (VTI) medium. We distinguish between two different effects: the anisotropy in the source and the anisotropy on the propagation path. Source anisotropy mathematically comes from the matrix multiplication of the anisotropic stiffness tensor with the source strain expressed by the potency tensor. We analyze this effect using the corresponding radiation pattern and the moment tensor decomposition. Propagation anisotropy mathematically comes from the deviation between the polarization and the propagation direction of a quasi P-wave in an anisotropic medium. We investigate both effects separately by either assuming the source to be anisotropic and the propagation to be isotropic or vice versa. We find that both effects have a significant impact on the radiation pattern of a pure-slip source. Finally, we develop an alternative visualization of source mechanisms by plotting beach balls proportional to their potency tensors. For this, we multiply the potency tensor with an isotropic elasticity tensor having the equivalent shear modulus [Formula: see text] and [Formula: see text]. In this way, we visualize the tectonic deformation in the source, independently of the rock anisotropy.

Model-based radiation pattern correction for interferometric redatuming in 4D seismic

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. Q25-Q35 ◽  
Author(s):  
Yang Zhao ◽  
Weichang Li
Keyword(s):  
Image Quality ◽  
Radiation Pattern ◽  
Matched Filter ◽  
Time Lapse ◽  
Wave Mode ◽  
P Wave ◽  
Radiation Patterns ◽  
Near Surface ◽  
Model Based ◽  
Isotropic Radiation

Interferometric virtual source (VS) redatuming converts surface-triggered source records into the equivalent records as if they originated from buried receiver locations by crosscorrelating downgoing waves with the corresponding upgoing waves. The theory suggests that when the receivers are surrounded by an enclosing boundary of sources, then the VS has an isotropic radiation pattern and yields an accurate response. The resultant records should determine improvement in the seismic repeatability and image quality compared with non-VS. However, in the presence of a complex near surface, an intricate shallow structure and highly variable weathering layers can severely distort the raypath, such that it produces uneven angle coverage to the buried VS. In addition, near-surface reverberations, surface multiples, and other mode-converted waves may leak into the time-gated early arrivals and further corrupt the direct wavefields. The above-mentioned issues can result in distorted radiation patterns and contaminated responses of the VS. We address these issues explicitly by spatially filtering the potentially contaminated direct wavefields using a zero-phase matched filter, such that the filtered wavefield is consistent with a model-based ideal direct P-wavefield observed at common receiver locations. This ideal reference response is computed from a homogeneous approximation to the local near-surface overburden on top of each VS. The phases of the original direct arrivals are preserved. Components associated with the reverberations and other noises can be effectively suppressed as their spatial radiation patterns deviate from that of the ideal single P-wave mode. Toward an isotropic radiation pattern by the iterative matched filter, we reduce the unbalanced illumination arising from imperfect source coverage and near-surface complexity. Compared with previous methods, the new VS approach provides significantly improved image quality and repeatability based on a pilot field of 13 time-lapse surveys, which solved a significant repeatability problem across a 17 month survey gap.

The effect of an initial hypocentral stress upon the radiation patterns of P and S waves

1972 ◽  
Vol 62 (5) ◽  
pp. 1173-1182 ◽  
Author(s):  
F. A. Dahlen
Keyword(s):  
Radiation Pattern ◽  
Fault Plane ◽  
Deviatoric Stress ◽  
P Wave ◽  
Stress Deviator ◽  
Radiation Patterns ◽  
Fault Plane Solutions ◽  
S Waves ◽  
Quadrupole Component ◽  
Sufficient Magnitude

Abstract The effect of an initial hypocentral deviatoric stress upon the radiation patterns of radiated P and S waves is explicitly described for the case of an infinitesimal, nonpropagating seismic dislocation. A nonzero hypocentral stress deviator produces two small changes in the familiar quadrupole radiation pattern; it gives rise to a small additional explosion-like component, and it acts to skew slightly the quadrupole component relative to the fault plane and auxiliary plane. The latter phenomenon is not of sufficient magnitude to give rise to any serious uncertainties in the interpretation of fault-plane solutions; in fact, both phenomena are so small that they will be exceedingly difficult ever to detect. The recent measurements of P-wave amplitudes on the focal sphere by Randall and Knopoff (1970) cannot be explained by these results.

scholarly journals Body‐wave radiation patterns and AVO in transversely isotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1409-1425 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Reflection Coefficient ◽  
Radiation Pattern ◽  
Transversely Isotropic ◽  
P Wave ◽  
Wave Radiation ◽  
Reflection Coefficients ◽  
Radiation Patterns ◽  
Avo Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

scholarly journals A Planar Reconfigurable Radiation Pattern Dipole Antenna with Reflectors and Directors for Wireless Communication Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Imen Ben Trad ◽  
Jean Marie Floc’h ◽  
Hatem Rmili ◽  
M’hamed Drissi ◽  
Fethi Choubani
Keyword(s):  
Wireless Communication ◽  
Radiation Pattern ◽  
Dipole Antenna ◽  
Radiation Patterns ◽  
Pin Diodes ◽  
Dual Beam

A planar printed dipole antenna with reflectors and directors, able to steer its radiation pattern in different directions, is proposed for telecommunication applications. Starting from a dual-beam printed dipole antenna achieved by combining two elementary dipoles back to back, and by loading four PIN diodes, three modes of reconfigurable radiation patterns are achieved at the frequency 2.56 GHz thanks to switches states. A prototype of the structure was realized and characterized; an efficiency of 75% is obtained. Simulation and measured results of the results are presented and discussed.

A teleseismic body-wave analysis of the May 1980 Mammoth Lakes, California, earthquakes

1983 ◽  
Vol 73 (2) ◽  
pp. 419-434
Author(s):  
Jeffery S. Barker ◽  
Charles A. Langston
Keyword(s):  
Body Wave ◽  
Moment Tensor ◽  
Normal Fault ◽  
Strike Slip ◽  
Body Waves ◽  
P Wave ◽  
Moment Tensors ◽  
Double Couple ◽  
The Moment ◽  
Mammoth Lakes

abstract Teleseismic P-wave first motions for the M ≧ 6 earthquakes near Mammoth Lakes, California, are inconsistent with the vertical strike-slip mechanisms determined from local and regional P-wave first motions. Combining these data sets allows three possible mechanisms: a north-striking, east-dipping strike-slip fault; a NE-striking oblique fault; and a NNW-striking normal fault. Inversion of long-period teleseismic P and SH waves for the events of 25 May 1980 (1633 UTC) and 27 May 1980 (1450 UTC) yields moment tensors with large non-double-couple components. The moment tensor for the first event may be decomposed into a major double couple with strike = 18°, dip = 61°, and rake = −15°, and a minor double couple with strike = 303°, dip = 43°, and rake = 224°. A similar decomposition for the last event yields strike = 25°, dip = 65°, rake = −6°, and strike = 312°, dip = 37°, and rake = 232°. Although the inversions were performed on only a few teleseismic body waves, the radiation patterns of the moment tensors are consistent with most of the P-wave first motion polarities at local, regional, and teleseismic distances. The stress axes inferred from the moment tensors are consistent with N65°E extension determined by geodetic measurements by Savage et al. (1981). Seismic moments computed from the moment tensors are 1.87 × 1025 dyne-cm for the 25 May 1980 (1633 UTC) event and 1.03 × 1025 dyne-cm for the 27 May 1980 (1450 UTC) event. The non-double-couple aspect of the moment tensors and the inability to obtain a convergent solution for the 25 May 1980 (1944 UTC) event may indicate that the assumptions of a point source and plane-layered structure implicit in the moment tensor inversion are not entirely valid for the Mammoth Lakes earthquakes.

Measurements of Rayleigh-wave phase velocities in Nevada: Implications for explosion sources and the Massachusetts Mountain earthquake

1982 ◽  
Vol 72 (4) ◽  
pp. 1329-1349
Author(s):  
H. J. Patton
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Moment Tensor ◽  
Test Site ◽  
P Wave ◽  
Stress Axis ◽  
Phase Velocities ◽  
Wave Phase ◽  
Single Station ◽  
Source Phase

abstract Single-station measurements of Rayleigh-wave phase velocity are obtained for paths between the Nevada Test Site and the Livermore broadband regional stations. Nuclear underground explosions detonated in Yucca Valley were the sources of the Rayleigh waves. The source phase φs required by the single-station method is calculated for an explosion source by assuming a spherically symmetric point source with step-function time dependence. The phase velocities are used to analyze the Rayleigh waves of the Massachusetts Mountain earthquake of 5 August 1971. Measured values of source phase for this earthquake are consistent with the focal mechanism determined from P-wave first-motion data (Fischer et al., 1972). A moment-tensor inversion of the Rayleigh-wave spectra for a 3-km-deep source gives a horizontal, least-compressive stress axis oriented N63°W and a seismic moment of 5.5 × 1022 dyne-cm. The general agreement between the results of the P-wave study of Fischer et al. (1972) and this study supports the measurements of phase velocities and, in turn, the explosion source model used to calculate φs.

Effects of centroid location on determination of earthquake mechanisms using long-period surface waves

1990 ◽  
Vol 80 (5) ◽  
pp. 1205-1231
Author(s):  
Jiajun Zhang ◽  
Thorne Lay
Keyword(s):  
Surface Wave ◽  
Rayleigh Waves ◽  
Body Wave ◽  
Moment Tensor ◽  
Source Location ◽  
P Wave ◽  
Nodal Plane ◽  
Wave Source ◽  
Long Period

Abstract Determination of shallow earthquake source mechanisms by inversion of long-period (150 to 300 sec) Rayleigh waves requires epicentral locations with greater accuracy than that provided by routine source locations of the National Earthquake Information Center (NEIC) and International Seismological Centre (ISC). The effects of epicentral mislocation on such inversions are examined using synthetic calculations as well as actual data for three large Mexican earthquakes. For Rayleigh waves of 150-sec period, an epicentral mislocation of 30 km introduces observed source spectra phase errors of 0.6 radian for stations at opposing azimuths along the source mislocation vector. This is larger than the 0.5-radian azimuthal variation of the phase spectra at the same period for a thrust fault with 15° dip and 24-km depth. The typical landward mislocation of routinely determined epicenters of shallow subduction zone earthquakes causes source moment tensor inversions of long-period Rayleigh waves to predict larger fault dip than indicated by teleseismic P-wave first-motion data. For dip-slip earthquakes, inversions of long-period Rayleigh waves that use an erroneous source location in the down-dip or along-strike directions of a nodal plane, overestimate the strike, dip, and slip of that nodal plane. Inversions of strike-slip earthquakes that utilize an erroneous location along the strike of a nodal plane overestimate the slip of that nodal plane, causing the second nodal plane to dip incorrectly in the direction opposite to the mislocation vector. The effects of epicentral mislocation for earthquakes with 45° dip-slip fault mechanisms are more severe than for events with other fault mechanisms. Existing earth model propagation corrections do not appear to be sufficiently accurate to routinely determine the optimal surface-wave source location without constraints from body-wave information, unless extensive direct path (R1) data are available or empirical path calibrations are performed. However, independent surface-wave and body-wave solutions can be remarkably consistent when the effects of epicentral mislocation are accounted for. This will allow simultaneous unconstrained body-wave and surface-wave inversions to be performed despite the well known difficulties of extracting the complete moment tensor of shallow sources from fundamental modes.

Polar radiation patterns of P and SV waves in a multi-layered medium

1973 ◽  
Vol 63 (2) ◽  
pp. 529-547
Author(s):  
Tien-Chang Lee ◽  
Ta-Liang Teng
Keyword(s):  
Displacement Field ◽  
Layered Medium ◽  
Focal Depth ◽  
Focal Mechanisms ◽  
P Wave ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Double Couple ◽  
Spatial Coordinates ◽  
P And Sv Waves

abstract The displacement field in a multi-layered medium due to incident plane P or SV waves is formulated in terms of Haskell's layer matrices. Based on the reciprocity theorem, the far-field polar radiation patterns of single force, double force, single couple, double couple, and dilatation in a multi-layered medium can be obtained from the displacement field and its first derivatives with respect to the spatial coordinates. Numerical results for models of one layer overlying a half-space indicate that (1) the radiation patterns are sensitive to the variation of focal depth, (2) the layering has a more pronounced effect on SV-wave radiation patterns than on P-wave radiation patterns, (3) the radiation patterns become simpler as the wavelength increases, (4) polarity may reverse abruptly somewhere beyond the critical angle in SV-wave radiation patterns, (5) radiation may be discontinuous across interfaces for some assumed focal mechanisms applied slightly above and below the interfaces, and (6) no clearcut distinction among the various radiation patterns can be used to single out one type of the assumed focal mechanisms from the rest.

Source parameter determination of local earthquakes in Korea using moment tensor inversion of single station data

1999 ◽  
Vol 89 (4) ◽  
pp. 1077-1082 ◽  
Author(s):  
So Gu Kim ◽  
Nadeja Kraeva
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Moment Tensor Inversion ◽  
P Wave ◽  
Parameter Determination ◽  
Reverse Fault ◽  
3D Tomography ◽  
Single Station ◽  
Slip Event

Abstract The purpose of this investigation is to determine source parameters such as focal mechanism, seismic moment, moment magnitude, and source depth from recent small earthquakes in the Korcan Peninsula using broadband records of three-component single station. It is very important and worthwhile to use a three-component single station in Korea because for most Korean earthquakes it is not possible to read enough first motions of P-wave arrivals because of the poor coverage of the seismic network and the small size (ML 5.0 or less) of the events. Furthermore the recent installation of the very broadband seismic stations in Korea and use of a 3D tomography technique can enhance moment tensor inversion to determine the source parameters of small earthquakes (ML 5.0 or less) that occur at near-regional distances (Δ ≤ 500 km). The focal solution for the Youngwol earthquake of 13 December 1996 is found to be a right-lateral strike slip event with a NE strike, and the Kyongju earthquake of 25 June 1997 is found to be an oblique reverse fault with a slight component of left-lateral slip in the SE direction.

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