A comparison of Heelan and exact solutions for seismic radiation from a short cylindrical charge

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. E33-E41 ◽  
Author(s):  
Dane Peter Blair
Keyword(s):  
Seismic Waves ◽  
Blast Hole ◽  
Field Approximation ◽  
Source Model ◽  
P Wave ◽  
Cylindrical Charge ◽  
Numerical Comparison ◽  
Far Field ◽  
Full Field ◽  
Direct Pressure

A numerical comparison is made between the Heelan approximation and an exact (full-field) solution for the radiation of seismic waves at a distance [Formula: see text], produced by a short cylindrical charge in a dry borehole of radius [Formula: see text]. The explosive source model is based on direct pressure measurements within the blast hole, and its spectral output classified by a mean frequency [Formula: see text]. To generalize comparisons, this source model is incorporated within a scale-independent treatment of the Heelan and full-field solutions. If [Formula: see text] is the material P-wave velocity, then a mean dimensionless source frequency may be defined by [Formula: see text]. For sufficiently large [Formula: see text], the Heelan solution is a valid far-field approximation only, provided [Formula: see text]. However, for the present radiation model, the far-field condition is given by [Formula: see text] (approximately), which implies that the Heelan solution is never valid if [Formula: see text], irrespective of [Formula: see text]. If [Formula: see text], the Heelan solution significantly overestimates the true seismic motion, irrespective of [Formula: see text].

Far-field pulse shapes from circular sources with variable rupture velocities

1997 ◽  
Vol 87 (5) ◽  
pp. 1288-1296
Author(s):  
Nicholas Deichmann
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Total Duration ◽  
Source Model ◽  
P Wave ◽  
Far Field ◽  
Rupture Velocity ◽  
P Waves ◽  
S Waves ◽  
Rate Functions

Abstract Recently, Sato (1994) developed a simple earthquake source model of a circular rupture expanding outward from the center of a fault with constant stress drop. In contrast to previous models, the rupture velocity is allowed to vary over the duration of faulting. This model is used to synthesize apparent moment-rate functions for a three-stage source process: first, the rupture starts out with a gradually increasing velocity, then, it continues to expand uniformly until, finally, it slows to a gradual stop. Synthetic velocity seismograms are obtained from a convolution of the apparent moment-rate functions with a causal Q-operator and an appropriate instrument response. Comparisons with an example of an earthquake signal show that, in the context of the proposed model, the observed emergent P-wave onset, which is not compatible with a constant rupture velocity, can be explained by a gradually accelerating rupture front. Systematic departures from the generally expected scaling relationship between seismic moment and rupture duration are often interpreted as evidence for a dependence of stress drop on seismic moment. However, the trade-off between stress drop and rupture velocity inherent in all kinematic source models implies that such deviations can just as well be attributed to systematic variations of rupture velocity. Whereas, in general, the total duration of the far-field displacement pulse is shorter for P waves than for S waves, the model predicts that the rise time, τ1/2, of the displacement pulse should be longer for P waves than for S waves. This feature could constitute a critical test of the model and also provide a constraint on the rupture velocity.

Implications of a composite source model and seismic-wave attenuation for the observed simplicity of small earthquakes and reported duration of earthquake initiation phase

1998 ◽  
Vol 88 (5) ◽  
pp. 1171-1181
Author(s):  
S. K. Singh ◽  
M. Ordaz ◽  
T. Mikumo ◽  
J. Pacheco ◽  
C. Valdés ◽  
...  
Keyword(s):  
Seismic Waves ◽  
Wave Attenuation ◽  
Source Model ◽  
P Wave ◽  
Bright Spot ◽  
Power Law Distribution ◽  
P Waves ◽  
Velocity Amplitude ◽  
Initiation Phase ◽  
Composite Source Model

Abstract An examination of P waves recorded on near-source, velocity seismograms generally shows that most small earthquakes (Mw < 2 to 3) are simple. On the other hand, larger earthquakes (Mw ≧ 4) are most often complex. The simplicity of the seismograms of Mw < 2 to 3 events may reflect the simplicity of the source (and, hence, may imply that smaller and larger earthquakes are not self-similar) or may be a consequence of attenuation of seismic waves. To test whether the attenuation is the cause, we generated synthetic P-wave seismograms from a composite circular source model in which subevent rupture areas are assumed to follow a power-law distribution. The rupture of an event is assumed to initiate at a random point on the fault and to propagate with a uniform speed. As the rupture front reaches the center of a subevent patch (all of which are circular), a P pulse is radiated that is calculated from the kinematic source model of Sato and Hirasawa (1973). Synthetic P-wave seismograms, which are all complex, are then convolved with an attenuation operator for different values of t*. The results show that the observed simplicity of small events (Mw < 2 to 3) may be entirely explained by attenuation if t* ≧ 0.02 sec. The composite source model predicts that the average time delay between the initiation of the rupture and the rupture of the largest patch, τ, scales as M01/3, such that log τ = (1/3) log M0 − 8.462. This relation is very similar to that reported by Umeda et al. (1996) between M0 and the observed time difference between the initiation of the rupture and the rupture of the “bright spot.” It roughly agrees with the relation between M0 and the duration of the initiation phase reported by Ellsworth and Beroza (1995) and Beroza and Ellsworth (1996). The relation also fits surprisingly well the data on duration of slow initial phase, tsip, and M0, reported by Iio (1995). One possible explanation of this agreement may be that the composite source model, which is essentially the “cascade” model, successfully captures the evolution of the earthquake source process and that the rupture initiation and the abrupt increase in the velocity amplitude observed on seismograms by previous researchers roughly corresponds to the rupture of the first subevent and the breaking of the largest subevent in the composite source model.

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Reconnaissance seismic refraction-reflection surveys in northwestern New Mexico

1984 ◽  
Vol 74 (4) ◽  
pp. 1263-1274
Author(s):  
Lawrence H. Jaksha ◽  
David H. Evans
Keyword(s):  
New Mexico ◽  
Wave Velocity ◽  
Lower Crust ◽  
Seismic Waves ◽  
Seismic Refraction ◽  
Velocity Model ◽  
P Wave ◽  
Uppermost Mantle ◽  
P Wave Velocity ◽  
Crustal Thinning

Abstract A velocity model of the crust in northwestern New Mexico has been constructed from an interpretation of direct, refracted, and reflected seismic waves. The model suggests a sedimentary section about 3 km thick with an average P-wave velocity of 3.6 km/sec. The crystalline upper crust is 28 km thick and has a P-wave velocity of 6.1 km/sec. The lower crust below the Conrad discontinuity has an average P-wave velocity of about 7.0 km/sec and a thickness near 17 km. Some evidence suggests that velocity in both the upper and lower crust increases with depth. The P-wave velocity in the uppermost mantle is 7.95 ± 0.15 km/sec. The total crustal thickness near Farmington, New Mexico, is about 48 km (datum = 1.6 km above sea level), and there is evidence for crustal thinning to the southeast.

scholarly journals Vertical to Horizontal Spectral Ratio (VHSR) Response of Seismic Wave Propagation in a Homogeneous Elastic – Poroelastic Medium Using The Spectral Finite Element Method

2021 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Sudarmaji Saroji ◽  
Budi Eka Nurcahya ◽  
Nivan Ramadhan Sugiantoro
Keyword(s):  
Finite Element Method ◽  
Elastic Medium ◽  
Seismic Waves ◽  
Low Frequency ◽  
Seismic Wave Propagation ◽  
P Wave ◽  
Poroelastic Medium ◽  
Compressional Waves ◽  
Spectral Finite Element Method ◽  
Spectral Finite Element

<p>Numerical modeling of 2D seismic wave propagation using spectral finite element method to estimate the response of seismic waves passing through the poroelastic medium from a hydrocarbon reservoir has been carried out. A hybrid simple model of the elastic - poroelastic - elastic with a mesoscopic scale element size of about 50cm was created. Seismic waves which was in the form of the ricker function are generated on the first elastic medium, propagated into the poroelastic medium and then transmitted to the second elastic medium. Pororoelastic medium is bearing hydrocarbon fluid in the form of gas, oil or water. Vertical and horizontal component of velocity seismograms are recorded on all mediums. Seismograms which are recorded in the poroelastic and second elastic medium show the existence of slow P compressional waves following fast P compressional waves that do not appear on the seismogram of the first elastic medium. The slow P wave is generated when the fast P wave enters the interface of the elastic - poroelastic boundary, propagated in the poroelastic medium and is transmited to the second elastic medium. The curves of Vertical to horizontal spectrum ratio (VHSR) which are observed from seismograms recorded in the poroelastic and the second elastic medium show that the peak of VHSR values at low frequency correlated with the fluid of poroelastic reservoir. The highest VHSR value at the low frequency which is recorded on the seismogram is above the 2.5 Hz frequency for reservoirs containing gas and oil in the second elastic medium, while for the medium containing water is the highest VHSR value is below the 2.5 Hz frequency.</p>

Average Q and yield estimates from the Pahute Mesa test site

1987 ◽  
Vol 77 (4) ◽  
pp. 1274-1294
Author(s):  
R. W. Burger ◽  
T. Lay ◽  
L. J. Burdick
Keyword(s):  
Time Domain ◽  
Near Field ◽  
Energy Levels ◽  
Source Model ◽  
Spectral Shape ◽  
Field Amplitude ◽  
Far Field ◽  
Source Models ◽  
Attenuation Models ◽  
Shape Data

Abstract Attenuation models, with and without frequency dependence, have been developed through analysis of time-domain amplitude measurements and teleseismic spectral shape data from Pahute Mesa nuclear explosions. The time-domain analysis is based on a near-field to far-field amplitude comparison. The near-field amplitude information is incorporated in two parameterized explosion source models (Mueller-Murphy and Helmberger-Hadley) based on analyses of near-field data. The teleseismic amplitude observations are from a large data set of WWSSN short-period analog recordings. For the narrow-band time-domain data, the various source and attenuation models are indistinguishable. We utilize the spectral shape data in the 0.5- to 4-Hz band as a constraint on the source-attenuation models at higher frequencies, concluding that either source model, when convolved with the appropriate frequency-dependent Q model, can be consistent with both the near-field and far-field time-domain amplitudes and the spectral shape data. Given the trade-off between source and attenuation models and the similarity of the different source models in the 0.5- to 4-Hz band, it is difficult to prefer clearly one source model over the other. The Mueller-Murphy model is more consistent with surface wave amplitude measurements because of larger predicted long-period energy levels. Whether or not frequency dependence is included in the attenuation model, the value of t* near 1 Hz is about 1.0 sec (assuming the Mueller-Murphy source model) or 0.8 sec (assuming the Helmberger-Hadley source model). This 0.2 sec difference results from greater 1-Hz energy levels for the Mueller-Murphy source model. Adopting an average attenuation model, predicted amplitudes and yields are shown to be within the uncertainty of the data for all the events analyzed.

AUTOREGRESSIVE ANALYSIS FOR THE DETECTION OF EARTHQUAKES WITH A RING LASER GYROSCOPE

2001 ◽  
Vol 01 (01) ◽  
pp. R41-R50 ◽  
Author(s):  
DUNCAN P. McLEOD ◽  
B. TOM KING ◽  
GEOFFREY E. STEDMAN ◽  
K. ULRICH SCHREIBER ◽  
TERRY H. WEBB
Keyword(s):  
Phase Angle ◽  
Ring Laser ◽  
Seismic Waves ◽  
P Wave ◽  
Quantum Limit ◽  
S Wave ◽  
Large Ring ◽  
Rotational Components ◽  
Ring Laser Gyroscope ◽  
Laser Gyroscope

The second-order autoregressive AR(2) model is used to analyze rotational data for seismic events captured by a large ring laser gyroscope. Both the Sagnac frequency and linewidth estimates obtained from this model sense the rotational components of seismic waves. An event of magnitude M L = 6.5 at a distance of D = 5.4° from a large ring laser gyroscope operating at its quantum limit is used to compare the AR(2) model with the previous analytical phase angle method of analysis. The frequency, linewidth and analytic phase angle data each satisfactorily estimate the rotation magnitude. The direct detection of rotational motion in the P wave coda is observed, demonstrating the conversion to transverse S wave polarizations by the local geology.

Scalar reverse‐time depth migration of prestack elastic seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1519-1527 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Waves ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
S Wave ◽  
Wave Source ◽  
Reflected Waves ◽  
S Waves ◽  
Elastic Data

Reflected P‐to‐P and P‐to‐S converted seismic waves in a two‐component elastic common‐source gather generated with a P‐wave source in a two‐dimensional model can be imaged by two independent scalar reverse‐time depth migrations. The inputs to migration are pure P‐ and S‐waves that are extracted by divergence and curl calculations during (shallow) extrapolation of the elastic data recorded at the earth’s surface. For both P‐to‐P and P‐to‐S converted reflected waves, the imaging time at each point is the P‐wave traveltime from the source to that point. The extracted P‐wave is reverse‐time extrapolated and imaged with a P‐velocity model, using a finite difference solution of the scalar wave equation. The extracted S‐wave is reverse‐time extrapolated and imaged similarly, but with an S‐velocity model. Converted S‐wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources. Synthetic examples show that the algorithm gives satisfactory results for laterally inhomogeneous models.

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