On the disturbance due to a point source in an inhomogeneous medium

Summary The problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c ₀(1 +m z) wherem is a constant andc ₀ is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem.     

Seismoelectric and electroseismic responses to a point source in a marine stratified model

We investigate the seismoelectric/electroseismic wavefields excited by a point source in an air/seawater/three-layered porous medium configuration containing a hydrocarbon layer. The results show that if an explosive source for excitation is used, receivers at seafloor can record the coseismic electromagnetic fields accompanying the P, S, fluid acoustic waves and the interface responses converted from the acoustic waves at seafloor interface and from the seismic waves at the interfaces beneath the seafloor. Employing a vertical electric dipole source shows that, with the exception of the interface responses converted from electromagnetic waves at seafloor, the interface responses converted from transmitted electromagnetic waves at the interfaces beneath the seafloor can also be identified. Given that the strength of the explosive source is within excitation capability of industry air guns, the generated interface responses from the hydrocarbon layer can be detected by current electromagnetic sensors considering the low ambient noise at the seafloor. Our results demonstrate the feasibility of the seismoelectric method applied to marine hydrocarbon exploration. Electroseismic modelling results suggest that it is not practical to employ this method to prospect marine hydrocarbon layer due to the weak interface response signal, unless a much larger current is injected into seafloor.     

Reflection of wide-angle acoustic waves from a high velocity interface

At angles other than normal incidence a pencil of plane acoustic waves, incident on a planar interface separating a low velocity medium from a high velocity medium, gives rise to a reflected pencil of waves which is laterally displaced from the illumination point of the incident pencil. The importance of this planar shift for understanding and interpreting wide-angle acoustic reflections is discussed, as is the variation of the equivalent depth below the interface at which a point-like reflection would be considered as an equivalent reflecting horizon.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA, where P is the propagation vector, and A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0), homogeneous plane waves (A ≠ 0, P and A parallel), and inhomogeneous plane waves (A ≠ 0, P and A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail. vcerveny@seis.karlov.mff.cuni.cz     

Comparison of amplitude decay rates in reflection,refraction, and local earthquake records

Three types of seismic data recorded near Coalinga, California were analyzed to study the behavior of scattered waves: 1) aftershocks of the May 2, 1983 earthquake, recorded on verticalcomponent seismometers deployed by the USGS; 2) regional refraction profiles using large explosive sources recorded on essentially the same arrays above; 3) three common-midpoint (CMP) reflection surveys recorded with vibrator sources over the same area. Records from each data set were bandpassed filtered into 5 Hz wide passbands (over the range of 1–25 Hz), corrected for geometric spreading, and fit with an exponential model of amplitude decay. Decay rates were expressed in terms of inverse codaQ (Q _c ^–1 ).Q _c ^–1 values for earthquake and refraction data are generally comparable and show a slight decrease with increasing frequency. Decay rates for different source types recorded on proximate receivers show similar results, with one notable exception. One set of aftershocks shows an increase ofQ _c ^–1 with frequency.Where the amplitude decay rates of surface and buried sources are similar, the coda decay results are consistent with other studies suggesting the importance of upper crustal scattering in the formation of coda. Differences in the variation ofQ _c ^–1 with frequency can be correlated with differences in geologic structure near the source region, as revealed by CMP-stacked reflection data. A more detailed assessment of effects such as the depth dependence of scattered contributions to the coda and the role of intrinsic attenuation requires precise control of source-receiver field geometry and the study of synthetic seismic data calculated for velocity models developed from CMP reflection data.     

Seismo-acoustic signals associated with degassing explosions recorded at Shishaldin Volcano,Alaska, 2003–2004

In summer 2003, a Chaparral Model 2 microphone was deployed at Shishaldin Volcano, Aleutian Islands, Alaska. The pressure sensor was co-located with a short-period seismometer on the volcano’s north flank at a distance of 6.62 km from the active summit vent. The seismo-acoustic data exhibit a correlation between impulsive acoustic signals (1–2 Pa) and long-period (LP, 1–2 Hz) earthquakes. Since it last erupted in 1999, Shishaldin has been characterized by sustained seismicity consisting of many hundreds to two thousand LP events per day. The activity is accompanied by up to ∼200 m high discrete gas puffs exiting the small summit vent, but no significant eruptive activity has been confirmed. The acoustic waveforms possess similarity throughout the data set (July 2003–November 2004) indicating a repetitive source mechanism. The simplicity of the acoustic waveforms, the impulsive onsets with relatively short (∼10–20 s) gradually decaying codas and the waveform similarities suggest that the acoustic pulses are generated at the fluid–air interface within an open-vent system. SO₂ measurements have revealed a low SO₂ flux, suggesting a hydrothermal system with magmatic gases leaking through. This hypothesis is supported by the steady-state nature of Shishaldin’s volcanic system since 1999. Time delays between the seismic LP and infrasound onsets were acquired from a representative day of seismo-acoustic data. A simple model was used to estimate source depths. The short seismo-acoustic delay times have revealed that the seismic and acoustic sources are co-located at a depth of 240±200 m below the crater rim. This shallow depth is confirmed by resonance of the upper portion of the open conduit, which produces standing waves with f=0.3 Hz in the acoustic waveform codas. The infrasound data has allowed us to relate Shishaldin’s LP earthquakes to degassing explosions, created by gas volume ruptures from a fluid–air interface.     

3D description and inversion of reflection moveout of PS‐waves in anisotropic media

Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t²(x²) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (V_P0 and V_S0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (V_P0, V_S0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves.     

THE INFLUENCE OF AN ASYMMETRY IN THE SEQUENCE ROCK/COAL/ROCK ON THE PROPAGATION OF RAYLEIGH SEAM WAVES*

Small offsets in hard coal seams can be detected with the aid of seam (channel) waves. Transmission and reflection of seam waves depend, among other parameters, upon the symmetry properties of the sequence rock/coal/rock. Two typical unsymmetrical sequences are found in European coal deposits: (i) coal seams with roof and floor of differing acoustic impedance and (ii) coal seams interlayered with rock and soil. Two-dimensional analog models with appropriate impedance contrasts are used to study the effect of the unsymmetrical layers upon the propagation of Rayleigh seam waves. Data analysis is based upon amplitude measurements both parallel and perpendicular to the layers and dispersion curves. The effect of unsymmetrical roof (rock 1) and floor (rock 2) was studied with models containing homogeneous coal seams. Leaky mode wave groups with phase velocities (c_R) in the range between the SV-wave velocities (β_{r1, 2}) of the two rock materials, i.e. β_r1≥c_R > β_r2, form a characteristic part of the Rayleigh seam wave signal. Using Knott's energy coefficient calculations it is shown that in that range energy leakage into the surrounding rock by refracted SV-waves is restricted to only one of the two interfaces, namely coal/rock 2. At the other interface, coal/rock 1, all waves are totally reflected. Thus, the high amplitudes of these leaky mode wave groups are explained by “quasi-normal mode” features. The influence of a dirt bed on wave propagation was studied in models where the roof and the floor have the same elastic properties. The maximum thickness of the dirt bed did not exceed 20% of the total seam thickness. The effect of the bed's location within the seam was also investigated. For all recorded normal-mode wave groups either the total seam or the coal layers could be regarded as wave guides. This was shown by the fact that the phases could be associated with the phase velocity dispersion curves calculated for the symmetrical sequence rock/coal/rock. These curves are relevant under the condition that the thickness of the coal layer assumed under the calculation coincides with the thickness of the effective wave guide of the respective wave groups. Wave groups guided in the total seam are not influenced by either the thickness or the position of the dirt bed. On the other hand, for wave groups guided in the coal layers, the quotient of signal amplitudes in the coal layers is influenced by the position of the dirt bed.     

A note on tsunami amplitudes above submarine slides and slumps

Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, which consider the effects of source finiteness and directivity. Five simple two-dimensional kinematic models of submarine slumps and slides are described mathematically as combinations of spreading constant or slopping uplift functions. Tsunami waveforms for these models are computed using linearized shallow water theory for constant water depth and transform method of solution (Laplace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, for a time window of the order of the source duration.The results show that, at the time when the source process is completed, for slides that spread rapidly (c_R/c_T≥20, where c_R is the velocity of predominant spreading), the displacement of the free water surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity the tsunami waveform has progressively larger amplitude, and higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for c_R/c_T1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.A comparison of peak tsunami amplitudes for five models plotted versus L/h (where L is characteristic length of the slide and h is the water depth) shows that for similar slide dimensions the peak tsunami amplitude is essentially model independent.     

Transient electromagnetic vs. seismic prospecting—a correspondence principle1

A correspondence principle is derived that relates the Green's functions (point-receiver responses to point-source excitations) for 2D transient diffusive electro-magnetic fields with electric field in the vertical plane to 2D seismic waves (in the acoustic approximation) with particle velocity in the vertical plane in arbitrarily inhomogeneous media. The constituent medium parameters in the two cases are related via two global proportionality constants. The kernels in the integral operators that express the diffusion phenomenon in terms of the wave phenomenon are of a smoothing nature. The fact that they are explicitly known can be of importance to the inverse operation. The correspondence principle is the fundamental tool in comparing the spatial resolving powers in the two methods of geophysical prospecting.     

Time domain scattering of acoustic plane waves by vertical faults

Acoustic plane wave scattering at a vertical fault structure represents the simplest two-dimensional model of geophysical exploration that can be investigated by analytical techniques. The exact and complete solution, in the time domain, for the scattering of the pressure field of an acoustic plane wave normally incident on a vertical fault structure is determined adapting previous results given for the frequency domain. The wave form of the pressure field of the incident plane wave is expressed by a causal time function that decays exponentially with time at every point above the fault (z<0). The zero-order term of the scattered pressure field has been computed above the fault. This zero-order term consists of an inverse Fourier transform which reduces to a closed expression forx=0, and contains an integral of a Hankel function forx#0. The high frequency part of the inverse Fourier transform forx#0 is computed employing asymptotic expressions for the Hankel function. The integral of the asymptotic expression of the Hankel function reduces to: (i) a Fresnel integral which contains a plane wave term for |x||z|; and (ii) a stationary point plane wave term plus an upper limit term for |x|=O(|z|). For the latter case the plane wave term cancels, leaving a cylindrical wave emanated from the edge of the fault. The wave front is well defined in shape, in phase and in amplitude. The amplitude of the scattered field is discontinuous atx=0, presents a jump and is well defined for |x| small and is rather smooth for |x| large.     

Iterative deconvolution of teleseismic P waves from the Thessaloniki (N. Greece) earthquake of June 20, 1978

Teleseismic long-period P waves from the June 20, 1978, Thessaloniki (N. Greece) earthquake (M _s=6.4) were modeled in an attempt to extract information about asperities or barriers on the fault plane. The analysis is based on the inversion method of complex P waves developed by Kikuchi and Kanamori (1982). A far-field source time function with a rise time of 2 sec and a process time of 5 sec is inferred, corresponding to a source dimension of about 10 km when a rupture velocity of 2 km/sec is assumed.The source depth of this shock, estimated by matching synthetic seismograms to observations, is found to be 8 km. The sum of the seismic moments of the individual subevents amounts to 3.3×10²⁵ dyn-cm.     

Energy of acoustic signals in a borehole

In the present article, the dependencies of the acoustic signal total energy and the energies of the wave packets of different types of the waves on the elastic parameters and permeability of rocks have been studied. We have considered traditional logging tools containing acoustical monopole source. Calculations were performed in a frequency range of dozens of kilohertz, typical for acoustic well logging. It was shown that in a typical high-velocity formation (v_s > v_f, where v_s and v_f are the velocities of the shear wave in the rock and of the compressional wave in the borehole fluid, respectively), the pseudo-Rayleigh waves, whose elastic properties depend mainly on the shear modulus of the rock, contributed significant energy to the total signal energy in the borehole. The energies of different wave packets depend on the permeability in different ways. The greatest sensitivity to permeability change has been shown by the acoustic signal total energy and the energy of the low-velocity part of the pseudo-Rayleigh wave packet. The theoretical analysis was illustrated by real sonic log data.     

Baroclinic energetics and zonal plane distribution of monsoon disturbances

The adiabatic, quasi-geostraphic, 25-layer, numerical, linear model with Ekman boundary layer friction is utilised to perform the baroclinic stability analysis of the mean monsoon zonal wind profile. It is shown thec _i is a function of the resultant wavenumber alone. This relation is able to explain the effects of the lateral walls on the unstable waves.The energetics and zonal plane distribution of the short and long preferred viscous waves are computed. The upward motion of the short wave together with the warm (cold) core lies to the west of the surface trough position above (below) 850 mb. Further, it is shown that the main source of kinetic energy for the wave lies in the middle layer (850–700 mb) which is transported to the lower and upper layers. Computed is found to be in good agreement with observed values.     

2012年江苏高邮、宝应交界MS4.9地震发震断层参数测定

基于一维单侧有限移动震源模式,根据地震波传播过程中的多普勒效应,分别利用P波和S波拐角频率的方位变化,反演2012年7月20日江苏高邮、宝应交界MS4.9地震的发震断层面参数。P波和S波拐角频率的反演结果一致显示:本次地震的断层面破裂方向为232°左右,破裂面呈NE-SW向;地震马赫数v/c为0.2左右,平均破裂速度小于S波速度,破裂长度较短,为0.2~0.3km左右。破裂面方位与震源机制解、宏观烈度调查和余震精定位的研究结果具有一致性,结合震区周边的地质构造背景,分析认为滁河断裂很可能是高邮、宝应交界MS4.9地震的发震构造。     

ON VERTICAL SEISMIC PROFILE PROCESSING*

From the wealth of information which can be deduced from VSP, the information most directly comparable to well logs is considered: P-wave and S-wave interval velocity, acoustic impedance, and the velocity ratio γ=V_s/V_p. This information not only allows better interpretation of surface seismic sections but also improves processing. For these results to be usable a number of precautions must be taken during acquisition and processing; the sampling in depth should be chosen in such a way that aliasing phenomena do not unnecessarily limit the spectra during the separation of upwards and downwards travelling waves. True amplitudes should be respected and checked by recording of signatures, and the interference of upwards and downwards travelling waves should be taken into account for the picking of first arrivals. The different steps in processing and the combination of results in the interpretation of surface seismic results are described with actual records.     

THE SPECTRAL FUNCTION OF A VERTICALLY INHOMOGENEOUS MEDIUM1

Elastic, acoustic and electromagnetic waves in media consisting of vertically inhomogeneous layers are considered in a common formulation. The spectral function of a vertically inhomogeneous medium is the downward energy flux due to an impulsive source at the top of the first layer. A propagation-invariant form is used to derive several identities for the reflection and transmission matrices. When the top layer is bounded by a free surface, one of the expressions reduces to a formula derived by Kunetz for the one-dimensional wave equation. A source radiating upwards and downwards gives a discontinuity in the propagation-invariant form which is equal to the source energy. A new formula is derived for when the source is located just beneath the top interface of the layers.     

Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL _s and time in terms of the mean-free timesL _s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ _i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q _s>Q _i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ _i, then as the distance increases, effects of scatteringQ _s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ _i should not be smaller than one tenth ofQ _s.Project Sponsored by the Joint Earthquake Science Foundation of China.