Airy Phase Research Articles

Sediment tomography in the East China Sea: Compressional wave speed and attenuation inversions from mode travel time dispersion and Airy phase measurementsa)

This paper discusses ongoing data analysis results from the acoustic bottom interaction experiment conducted in May–June 2001 in the East China Sea as part of the Asian Seas International Acoustics Experiment (ASIAEX‐2001). Using time‐frequency scalograms of broadband signals, the modal arrivals and group speed minimums (Airy Phase) of several modes are clearly observed. The structure of the Airy Phase signal forms the basis of this inversion technique. Utilizing the Airy Phase group speed minimums and corresponding pressure amplitudes of each observable mode, the sediment compressional wave speed and attenuation as a function of depth are derived. The group speed minimum for each mode provides additional information on the compressional wave speed in the modal sediment depth penetration interval. Inverted speeds and estimated modal penetration depths are then used to develop the sediment profile. The estimated resolution is dependent on the number and frequency span of the observable modes. This method has the advantage of utilizing only one hydrophone to obtain rapid estimates of sediment properties. Additionally, it also complements other inversion schemes that can benefit from accurate a priori environmental information by limiting the size of the search parameter space. Estimated sediment properties from several areas are presented with verification from coring results. [Work supported by ONR.] a)For Acoustical Oceanography Best Student Paper Award.

Observations of sediment shear velocity in the San Diego Trough

We report observations of shallow seafloor shear velocity structure in the San Diego Trough, whose depth is about 1100 m. Dispersed Scholte waves were generated using a new implosive source, described elsewhere in this meeting, and observed using ocean-bottom seismographs. Preliminary estimates of the surficial shear velocities are in the 16–25 m/s range, which is very low. The Scholte waves are observed in the 1–8 Hz frequency range and dispersion is well-developed after 100 m of propagation. Higher modes appear in addition to the fundamental mode, which exhibits a smooth increase in frequency from 2 to an Airy phase at about 3 Hz. The group velocity of the Airy phase approximates the surficial shear velocity. In the work area, the topographic relief is only a few meters. Geologically, the sediments are turbidites distributed by a channel and levee system. High-resolution multibeam bathymetry is available from NOAA and is being used to aid geological interpretation.

Acoustic wave propagation in one-dimensional random media: the wave localization approach

Multiple wave scattering in strongly heterogeneous media is a very complicated phenomenon. Although a statistical approach may yield a considerable simplification of the mathematics, no guarantee exists that the theoretically predicted and the observed quantities coincide. The solution of this problem is to use self averaging quantities only. A multiple scattering theory that makes use of such self averaging quantities is the so called wave localization theory. This theory allows one to study both numerically and theoretically the influence of the presence of heterogeneities on the frequency dependent dispersion and apparent attenuation of a pulse traversing a random medium. I calculate the localization length (penetration depth), the inverse quality factor and both the group and phase velocities for several chaotic media described by different autocorrelation functions. Calculations are limited to 1 D acoustic media with constant density. However, media studied range from very smooth to fractal like and incidence is not limited to be vertical. I then compare the theoretical results with estimates of the same quantities obtained from numerical simulations. The following can be concluded. (1) Theoretical predictions and numerical simulations agree in nearly the whole frequency domain for angles of incidence ≤30° and relative standard deviations of the fluctuations of the incompressibility ≤30 per cent. (2) An inspection of the inverse quality factor confirms that the apparent attenuation is strongest in the domain of Mie scattering except for fractal like media. In such media, no particular ratio of the wavelength to the typical scale length of heterogeneities is preferred since no such typical scale length exists. Hence, the inverse quality factor is constant over a large frequency band. (3) The group and phase velocities obtained agree with the effective medium theory and the Kramers–Krönig relations. That is, both converge to the effective medium velocity and the geometric velocity in the low and high frequency domains respectively. However, for intermediate frequencies, the exact behaviour strongly depends on the type of medium. Differences are related mainly to the number of extrema and Airy phases.

Detection of mantle plumes in the lower mantle by diffraction tomography: theory

We investigate the properties of long-period seismic waves scattered by idealized plume conduits in the lower mantle. We build a schematic, yet realistic, model of the seismic velocity and density anomalies caused by a thermal plume. We devise a method to construct realistic seismograms of P-waves scattered by this anomaly. The results show that the scattered wave takes the form of an Airy phase, which arrives after the direct P-wave, at a time that corresponds to the shortest time it takes for the P-wave to travel from the source to the plume, and from there to the station. The predicted amplitude at a long period ( T≃20 s) is in the range of 1–5% of the amplitude of the direct wave. We explore the variation of the amplitude as a function of the geometrical parameters, and show that it is well explained by considering the contribution of the column of the plume in a T/4 Fresnel zone around the fastest scattered ray. We compare the amplitudes and waveforms obtained in the Rayleigh and Mie approximations, and find that, for realistic geometries, wider plumes yield a larger signal. Nevertheless, the predicted amplitudes are too small to yield a detectable signal. In the Born approximation, the image reconstruction of nearly vertical features reduces to a 2D linear inversion. We present a method, based on LSQR, to produce such images from the global set of long-period seismograms. In a companion paper [Ying Ji, H.-C. Nataf, Earth Planet. Sci. Lett., this issue], this method is applied to real data that sample the lower mantle beneath Hawaii.

Regional seismic discriminants using wave-train energy ratios

AbstractWe have examined broadband regional waveforms of recent (since 1988) Nevada Test Site (NTS) underground explosions and earthquakes throughout the southwestern United States and Baja, Mexico, recorded by TERRAscope and other IRIS stations in order to characterize seismic sources for the purposes of event identification. As expected, earthquakes tended to be richer in long-period surface-wave and short-period shear-wave energy relative to explosions of comparable P-wave strength. Also, explosions, in general, were found to be richer in 1- to 6-sec surface-wave (Rg) energy and other late-arriving coda energy than were earthquakes. Most earthquakes show relatively little long-period (T > 6 sec) Rg and surface-wave coda energy, which we attribute to their deeper source depths, whereas known shallow earthquakes do exhibit these phases. We have developed several seismic discriminants based on our observations. The most promising discriminant is the ratio of short-period (f ≧ 1.0 Hz), vertical component, Pnl wave-train energy (EspPz) to long-period (0.05 to 0.167 Hz), three-component, surface-wave energy (Elp−3). For this ratio, explosions tend to have a higher value than do earthquakes. This discriminant works on the same premise as the teleseismic mb:MS ratio, for which earthquakes are richer in long-period surface-wave energy relative to explosions with the same body-wave magnitude. The long-period passband was chosen to limit the effect of longer-period noise and to remove the effect of the coda surface waves. Another potential discriminant examined is the ratio of short-period (f ≧ 1.0 Hz), vertical-component, P-wave to S-wave energy (EspPz:EspSz). We find that this criterion only yields marginal separation of the source populations but becomes more effective at higher frequency bands (f ≧ 4.0 Hz) or when looking at single-station observations. It does, however, help to quantify significant short-period waveform differences between the three test subsites, with Pahute Mesa shots generating relatively little S-wave energy compared to those of Yucca Flat for which the S wave (or Lg) is often the largest phase, while Rainier's shots are intermediate in character with distinct but less prominent S waves. This S-wave generation is thought to be caused by near-source scattering to converted phases and appears to be highly dependent on the near-source geology. These two discriminants are useful in that they are simple and fast to calculate. Using regional stations for sources 200 to 1300 km away, the magnitude threshold for the EspPz:Elp−3 discriminant is roughly ML ≧ 4.0, the limiting factor being the signal level of the Airy phase, while that for the EspPz:EspSz discriminant is roughly ML ≧ 3.0 for the same distance ranges.

Guided seismic waves in layered poroviscoelastic media for continuity logging applications: model studies1

AbstractThe gas industry is continuing to concentrate its research and development efforts on new and advanced technology to improve reservoir descriptions through the producing life and development history of heterogeneous gas reservoirs. A very important aspect of this need is the ability to reduce the uncertainty of estimating probable reserves and to lower the operating costs to recover incremental reserves in producing and depleted gasfields. Established methods for reducing uncertainty in heterogeneous reservoir compartments, such as VSP and cross‐well techniques may enhance resolution, but they are currently not economically justifiable in on‐shore gasfields. Continuity logging using guided waves is an alternative approach to analysing inter‐well seismic data to confirm the continuity of heterogeneous gas reservoir compartments; in particular, the continuity of sand and shale stratigraphy in gas reservoirs.The solution of a coupled system of differential equations based on Biot and homogenization theories is adapted to calculate guided seismic waves trapped in low‐velocity layers. The general solution is for a 3D source in a horizontally layered poroviscoelastic medium having isotropic and laterally homogeneous material properties. A unified representation of the medium that includes fluid‐solid interactions and viscoelastic losses is incorporated into the solution. The guided‐wave part of the vector wave field and fluid‐pressure of the complete wave motion in layered dissipative media is verified and used to simulate dispersion and attenuation of guided seismic waves for continuity logging applications. The results of this work suggest that the multimode wave solution is appropriate to simulate guided seismic wave signatures to indicate continuity of layered earth structures in poroviscoelastic reservoirs. In particular, the normal mode information can be used for planning continuity logging surveys and for interpreting the corresponding seismic data. Further, fluid‐pressure waveforms show that maximum amplitude normal modes can be detected at layer interfaces in fluid‐filled porous media, and the corresponding Airy phase wave groups may carry information on the formation permeability.

Surface wave propagation in central Asia: Observations of scattering and multipathing with the Kyrgyzstan broadband array

We studied the propagation of Rayleigh waves at regional distances in central Asia using a combination of array processing techniques and surface wave analysis. We present results from the detailed analysis of three representative events recorded by a 10‐station, broadband network that has been running in the central Asian country of Kyrgyzstan since 1991: an Ms = 5.1 event near Ashkhabad, Turkmenistan; an Ms = 5.8 event in south central Tibet; and the October 7, 1994, nuclear explosion at Lop Nor. We find there is a remarkable difference in the propagation characteristics of surface waves along these three paths. The path from the event in Turkmenistan is simple and is well approximated by propagation through a laterally homogeneous medium. Array processing shows the entire Rayleigh wave train stacks coherently and arrives from an azimuth close to that predicted by a great circle path. Furthermore, estimates of dispersion curves and fundamental mode signals determined for individual stations show little variation across the array. The Tibet and Lop Nor paths are completely different. We find strong evidence for complicated multipathing and scattering effects along both of these paths. We observe a three‐stage pattern in the Tibet case: (1) the early, lowest‐frequency part of the Rayleigh wave packet arrives as a coherent signal from close to the great circle path azimuth; (2) this is overpowered in the period range around 20 s by a strong multipath signal that propagates across the array from a much more southerly azimuth; and (3) periods below 20 s rapidly become incoherent, and the signal does not have a well‐defined direction of propagation. The Lop Nor path shows similar complexity. On this path there is little dispersion for measurable periods greater than 10 s, so the low‐frequency energy arrives in an Airy phase. The Airy phase stacks somewhat coherently (it stacks, but significant power is lost in the best beam), and slowness analysis shows it arrives from an azimuth 14° north of the great circle path azimuth. Like the Tibet event, the direction of propagation of the shorter periods cannot be resolved. These results are consistent with crustal structure in central Asia. The multipathing and scattering from the Tibet and Lop Nor events are not surprising given these waves propagate across highly variable crust and high topography resulting from the collision of India with Eurasia. The relative simplicity of the Turkmenistan event path reinforces this as almost all of that path traverses the relatively undeformed Turan platform of Uzbekistan.

Broad-Band Modelling of Regional Seismograms: the Basin and Range Crustal Structure

Three-component broad-band displacement seismograms with paths sampling the Basin and Range province are studied to constrain the crustal structure. To find an average model that fits the data in both absolute time and waveform, we generate broad-band reflectivity synthetics and conduct sensitivity tests on different parts of a layered crustal model, where only a few layers are involved. Generalized rays are used to help identify the various phases. It proves useful to decompose a regional seismogram into segments so that the impact of model parameters on each segment can be clearly identified. Thus, for mid-crustal earthquakes, it is established that the top crustal layer controls the Rayleigh wave, the Airy phase, in shape over the range from 300 to 600 km, and the crustal layer just above the source depth controls its timing. The P_nl waves, the P_n and P_L portion, are controlled in broad-band character by the mid-crust while the top layer contributes to their long-period motion. These crustal parameters control the tangential motion similarly. The SV wave, the segment between the P_nl wave and the Rayleigh wave, is mostly controlled by the shear velocity of the lower crust. In judging the goodness of fit between the array observations and synthetic waveforms, we allow individual data segments to shift relative to the 1-D synthetics by a few seconds to account for some lateral variation. The amount of time shift is found by the cross-correlation in displacement between the data segment and the synthetics. Applying these tests in a forward modelling approach, we find that a simple two-layer crustal model is effective in explaining this data set. In this model, the main crustal layer has P and S velocities of 6.1 km s^(-1) and 3.6 km s^(-1), similar to those found by Langston & Helmberger (1974). A surface layer of thickness 2.5 to 3.5 km is required to fit the Rayleigh waves. The refined model can be used as a reference model for further studies in this region.

Seismic-source and wave-propagation effects ofLgwaves in Scandinavia

A set of 517 recordings of Lg waves from 151 earthquakes in and around Norway has been used for determination of seismic moment Mo, corner frequency fo and anelastic attenuation Q(f). The data used have been recorded at source-receiver distances of 20 to 1200 km, with ML magnitudes between 0.8 and 5.0, and the parameters were estimated by inverting Fourier spectra from all of the recordings simultaneously. The observed spectra were represented by a source term, a spreading term, and an attenuation term, and the inversion was made assuming the geometrical spreading to be known. Because of the non-linear behaviour of the spectral shape, the inversion was done iteratively by minimizing the differences between observed and computed spectra. A standard ω−2 source model was used in the inversion, supported by near-field observations of small-magnitude earthquakes at the regional NORESS array. A model for geometrical spreading was then established by investigating the decay of Lg waves using synthetic data modelled without anelastic attenuation, for a realistic crustal structure with a Moho depth of 40 km. The results support the standard model of spherical spreading at short distances and cylindrical spreading at longer distances, but with a transition distance closer to 200 km than to the more commonly used value of 100 km. The decay rate beyond this distance was found to be close to ,−1/2 in the frequency domain, equal to the theoretical value for cylindrical spreading, and ,−3/4 in the time domain, where the theoretical value for an Airy phase is ,−5/6. The data used in the inversion were amplitude-displacement spectra corrected for instrument response and site effects, reduced (by smoothing) to 64 spectral values and weighted to represent equidistantly spaced points in the log-frequency domain. Only spectral values with signal-to-noise ratios of at least four were accepted, with an upper limit set to 10Hz, and a lower frequency limit determined by the instrument response. The computed MO values are quite stable, and exhibit a linear dependency on ML. The corner frequencies are less well constrained, however, especially for smaller events. In using a model of the type fO∝MO−δ we found a δ around 3.4, indicating slightly increasing stress drop, with values of less than 10 MPa in all cases (using a Brune model). The resulting Q models of the type Q(f) = qfη yield q values around 440 and η values around 0.7. This is reasonably close to other anelastic attenuation models found in this area.

Determining surface-wave magnitudes from regional Nevada Test Site data

We re-examine the use of surface-wave magnitudes to determine the yield of underground nuclear explosions and the associated magnitude-yield scaling relationship. We have calculated surface-wave magnitudes for 190 Nevada Test Site (NTS) shots using regional long-period seismograms from a combined super-network of 55 North American stations. Great effort went towards making the data set comprehensive and diverse in terms of yield, source location and shot medium in order to determine the portability of surface-wave magnitude scales. In particular, we examine Pahute Mesa, Rainier Mesa and Yucca Flat explosions detonated above and below the water table, and which range over three orders of magnitude in yield. By observation we find a low-yield measure threshold of approximately one kiloton (kt) for (assumedly) moderately well-coupled explosions recorded at near-regional (<500 km) stations, which have little microseismic noise. In order to utilize regional surface waves (Δ < 15°) for quantifying sources and for discrimination purposes, we have developed related methods for determining time-domain surface-wave magnitudes and scalar moments from regional Rayleigh waves. Employing regional surface-wave data lowers the effective magnitude threshold. One technique employs synthetic seismograms to establish a relationship between the amplitude of the regional Airy phase, or Rayleigh pulse of the Rayleigh wavetrain and an associated surface-wave magnitude, based on conventional M_S determinations, calculated from synthetic seismograms propagated to 40°. The other method uses synthetic seismograms in a similar fashion, but the relationship used is a more straightforward one between scalar moment and peak Rayleigh wave amplitude. Path corrections are readily implemented to both methods. The inclusion of path corrections decreases the M_S variance by a factor of two and affects the absolute scaling relationship by up to a factor of 0.1 magnitude units. This latter effect is attributed to the particular station network used and the Green's functions used to obtain the 40° M_S values. Using a generic structure for the distance travelled past the actual source-receiver path minimizes the difference between magnitudes determined with and without path corrections. The method gives stable M_S values that correlate well with other magnitude scale values over a range of three orders of magnitude in source yield. Our M_S values scale very similarly to more standard teleseismic M_S values from other studies, although the absolute MS values vary by ±M0.5 magnitude units about ours. Such differences are due in part to the choice of MS formula used. For purposes of future user comparisons, we give conversion values to the previous studies. Our most refined M_S values give the relationship M_S = 1.00 x log_10 (yield) +B, where B is dependent upon source region and shot medium. This yield exponent of unity holds for events of all sizes and is in line with M_S-yield scaling relations found by other studies. When events are grouped with respect to source region, significantly better fits to these individual-site linear-regression curves are obtained compared to the fits obtained using a single, all-inclusive- model. This observation implies that shot-site parameters and source structure can significantly affect surface-wave-magnitude measurements. We present these M_S values primarily to augment the extensive historical analysis of explosion data based on surface-wave magnitudes by using regional data to increase the number of events with surface-wave magnitudes. These magnitudes are consistant with the teleseismically determined magnitudes of larger events. We present our preferred surface-wave moment values in a sequel paper.

地盤の2次元性と非線形性を考慮したボアホール地震観測記録に基づく地盤の増幅特性のシミュレーション : 足柄平野久野地区の鉛直アレーで観測された弱震動と強震動の分析

We studied amplification characteristics of soil sediments by using strong and weak motion records observed on the surface, at 30m below, and at 97.6m below the surface at Kuno district in the Ashigara Valley. We found that the amplification factors for the main part of the weak and strong motions can be simulated from the one-dimensional soil analysis by considering the non-linear behavior of soil sediments during the strong motion shaking for not only alluvial surface layers but also diluvial layers. In order to simulate the amplification factors better, we performed two-dimensional finite element soil analysis in which we assume a soil model whose thickness of the first surface layer at the observation site is 8m and that at 50m away from it is 6m. As a result, we could simulate the amplification factors more precisely, because the short period surface waves whose Airy phase has about the period of 0.5 sec are generated due to such a small irregularity of the surface soil sediments.

Dispersion and attenuation of acoustic guided waves in layered fluid-filled porous media

The analysis of acoustic wave propagation in fluid-filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low-velocity layered media. Constitutive relations, the balance equation, and the generalized Darcy law of the modified Biot theory yield a coupled system of differential equations which governs the wave motion in each layer. The displacement and stress fields satisfy the boundary conditions of continuity of displacements and tractions across each interface, and the radiation condition at infinity. To avoid precision problems caused by the growing exponential in individual matrices for large wave numbers, the global matrix method was implemented as an alternative to the traditional propagation approach to determine the periodic equations. The complex wave numbers of the guided wave modes were determined using a combination of two-dimensional bracketing and minimization techniques. The results of this work indicate that the acoustic guided wave attenuation is sensitive to the in situ permeability. In particular, the attenuation changes significantly as the in situ permeability of the low-velocity layer is varied at the frequency corresponding to the minimum group velocity (Airy phase). Alternatively, the attenuation of the wave modes are practically unaffected by those permeability variations in the layer at the frequency corresponding to the maximum group velocity.

Analysis of Rayleigh wave refraction from three-component seismic spectra

SUMMARY Lateral refraction of intermediate period surface waves is caused by horizontal gradients in local phase velocity in the vicinity of the source-receiver minor arc. For smooth structural perturbations, this is manifested by an off-azimuth arrival (azimuth deviation) of the Airy phase. We present a method for estimating azimuth deviation as a function of frequency for Rayleigh waves observed on a three-component seismogram. By taking advantage of the different dispersion characteristics of the Rayleigh and Love wave group arrivals, the method essentially constructs an optimal narrow-band taper for each frequency component, in order to minimize the effect of Love wave contamination in the Rayleigh wave azimuth estimation. We have measured the frequency-dependent azimuth deviation of fundamental mode Rayleigh waves of period 20-100s under a variety of conditions. The most coherent results are obtained for (1) seismic records with a relatively high Rayleigh wave excitation, (2) ray paths which are confined to purely oceanic or purely continental lithosphere, and (3) ray paths of intermediate offset (30°-50°).

Reappraisal of major African earthquakes, south of 20°N, 1900–1930

We have re-examined those earthquakes in Africa south of 20°N, in the period 1900–1930, that appear from instrumental or macroseismic evidence to have a magnitude of 5 3/4 or greater. We identify more than 50 such events, about twice as many as listed by Gutenberg and Richter (1954). We find that the combined use of early instrumental readings and macroseismic information gleaned from previously untapped sources gives the best control of location. Instrumental relocation is difficult because of the lack of stations in Africa and the very uneven global distribution. For the low-gain, medium-period instruments then in use, the best control often comes from using the maximum Airy phase of surface waves. Similarly, there is a lack of sources of macroseismic information, and the simple building practice makes it difficult to assess intensity. We have recalculated magnitude Ms uniformly using the Prague formula. We discuss these problems and show that it is likely that our list is complete only down to magnitude about 6, and that the seismic record for Africa before this century will probably remain incomplete for events of all magnitudes.

The effect of the Airy phase during the propagation of edge waves

Peculiarities of the edge wave evolution a great distance away from the source are considered. It is shown that waveguide dispersion may result in discrimination of the region in a wave train corresponding to the Airy phase. The effect of the discrimination of the Airy wave in the remote zone for the model of a ‘step-like shelf’ is compared with real edge waves (using the marigrams of tsunami observed in the Sea of Japan in 1983).

Propagation Characteristics of Intermediate-Period (1-10 Seconds) Surface Waves in the Kanto Plain, Japan

Propagation characteristics of the intermediate-period (1-10 s) surface waves predominated in strong motion records are analyzed on the basis of an array observation deployed in metropolitan Tokyo area, Japan. Seismic energy source is the main shock of the 1984 western Nagano earthquake (M 6.8) with a focal depth of 2 km; epicentral distances (Δ) for the stations are about 157-205 km. Phase analyses using the sub-array at KOG (Δ_??_7175 km) indicate that dominant phases in the period range 1-10 s are Love and Rayleigh waves with clear dispersion. Apparent of their phases are lying in the range of 800-2, 100 m/s. They are matched with the fundamental mode of Love waves for transverse motion but are stretching over the two modes of Rayleigh waves (M11 and M21) for radial component; the crustal model, on which the normal mode solution is based, includes thick (-52, 000 m) sedimentary layers lying on the Pre-Tertiary bedrock. The above results in conjunction with direction of wave propagation and particle orbit of the ground motion suggest that the intermediate-period surface waves are perturbed by other phases such as diffracted surface waves which are owed to lateral heterogeneities in the uppermost crust. Correspondence of major phases in the strong motion records of the long-span array gives rise to inter-station group velocities of the surface waves of the intermediate-period. Thus derived group enable us to interpret that the well-dispersed later phases are on a branch near the Airy phase of which propagation velocity is 300-800 m/s.

Reappraisal of major African earthquakes, south of 20�N, 1900?1930

We have re-examined those earthquakes in Africa south of 20°N, in the period 1900–1930, that appear from instrumental or macroseismic evidence to have a magnitude of 5 3/4 or greater. We identify more than 50 such events, about twice as many as listed by Gutenberg and Richter (1954). We find that the combined use of early instrumental readings and macroseismic information gleaned from previously untapped sources gives the best control of location. Instrumental relocation is difficult because of the lack of stations in Africa and the very uneven global distribution. For the low-gain, medium-period instruments then in use, the best control often comes from using the maximum Airy phase of surface waves. Similarly, there is a lack of sources of macroseismic information, and the simple building practice makes it difficult to assess intensity. We have recalculated magnitude Ms uniformly using the Prague formula. We discuss these problems and show that it is likely that our list is complete only down to magnitude about 6, and that the seismic record for Africa before this century will probably remain incomplete for events of all magnitudes.

PREDICTION OF LOVE WAVE SPECTRA GENERATED DUE TO DIPPING LAYER

Surface wave near a dipping layer is predicted by multiplying the proposed magnification factor with spectra of incident wave components. The magnification factor is expressed as the product of the influence coefficient of Love wave and the magnification factor in the surface layer. The influence coefficient of Love wave is formulated as an explicit form. It is found that the incident wave whose period is longer than Airy phase consist mostly of surface wave and predicted spectra of surface wave is close to the one of the surface wave separated from the observed earthquake motion.

Shear wave logging in semi-infinite saturated porous formations

Recent theoretical and experimental studies have demonstrated the interest of using nonaxisymmetric sources, such as dipole and quadrupole, to record shear wave events in any kind of formation (fast or slow). Nonaxisymmetric sources excite surface waves whose Airy phase is predominant in the records at intermediate frequencies (≂3 to 6 kHz). They are referred to as the flexural and screw modes, respectively, for the dipole and the quadrupole sources. Their dispersion and attenuation are studied in a fluid-filled borehole embedded in a homogeneous saturated porous formation. The two-phase medium is modeled using Biot’s theory modified in accordance with the homogenization theory. Calculation of synthetic full waveform logs is also performed using the discrete wavenumber method. Whatever the formation, the most reliable information that can be extracted from low-frequency parts of the wavetrains is the formation shear wave velocity and attenuation. It is of great interest in the inversion of Stoneley wave velocity and attenuation for the evaluation of in situ permeability. In the presence of fast formations, the attenuation of the Airy phase of both the flexural and screw modes is sensitive to the in situ permeability. The same conclusion holds for the slow formations only when they are saturated by a fluid of low viscosity and high compressibility.

CHARACTERISTICS OF LOVE WAVE GENERATED AROUND A DIPPING BASEMENT

Source mechanism and characteristics of the horizontally propagating waves generated around a dipping basement due to the incident SH wave are investigated. A new analitical method which combines boundary elements, finite elements and energy transmitting boundary is proposed. Two layered media, the upper layer of which has semi-infinite boundary in one side and a dipping interface in the other side, is used in the analysis. It is found that the incident SH wave is mostly transformed into Love wave whose period is close to Airy phase at the horizontal part of the surface layer in the case that both the ratio of wave impedance and the inclination of basement are small; all reflected SH wave is predominant in the other case.