effective velocities in fractured media a numerical study using the rotated staggered finite difference grid the modelling of elastic waves in fractured media with an explicit finite difference scheme causes instability problems on a staggered grid when the medium possesses high contrast discontinuities strong heterogeneities for the present study we apply the rotated staggered grid using this modified grid it is possible to simulate the propagation of elastic waves in a 2d or 3d medium containing cracks pores or free surfaces without hard coded boundary conditions therefore it allows an efficient and precise numerical study of effective velocities in fractured structures we model the propagation of plane waves through a set of different randomly cracked media in these numerical experiments we vary the wavelength of the plane waves the crack porosity and the crack density the synthetic results are compared with several static theories that predict the effective p and s wave velocities in fractured materials in the long wavelength limit for randomly distributed and randomly orientated rectilinear non intersecting thin dry cracks the numerical simulations of velocities of p sv and sh waves are in excellent agreement with the results of the modified or differential self consistent theory on the other hand for intersecting cracks the critical crack density porosity concept must be taken into account to describe the wave velocities in media with intersecting cracks we propose introducing the critical crack density concept into the modified self consistent theory numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case

vibrational modes of hydraulic fractures inference of fracture geometry from resonant frequencies and attenuation oscillatory seismic signals arising from resonant vibrations of hydraulic fractures are observed in many geologic systems including volcanoes glaciers and ice sheets and hydrocarbon and geothermal reservoirs to better quantify the physical dimensions of fluid filled cracks and properties of the fluids within them we study wave motion along a thin hydraulic fracture waveguide we present a linearized analysis valid at wavelengths greater than the fracture aperture that accounts for quasi static elastic deformation of the fracture walls as well as fluid viscosity inertia and compressibility in the long wavelength limit anomalously dispersed guided waves known as crack or krauklis waves propagate with restoring force from fracture wall elasticity at shorter wavelengths the waves become sound waves within the fluid channel wave attenuation in our model is due to fluid viscosity rather than seismic radiation from crack tips or fracture wall roughness we characterize viscous damping at both low frequencies where the flow is always fully developed and at high frequencies where the flow has a nearly constant velocity profile away from viscous boundary layers near the fracture walls most observable seismic signals from resonating fractures likely arise in the boundary layer crack wave limit where fluid solid coupling is pronounced and attenuation is minimal we present a method to estimate the aperture and length of a resonating hydraulic fracture using both the seismically observed quality factor and characteristic frequency finally we develop scaling relations between seismic moment and characteristic frequency that might be useful when interpreting the statistics of hydraulic fracture events

the spectrum of gps measurement errors and the accuracy of airborne gravity measurements recent observations georgiadou and kleusberg 1987 kleusberg et al 1989 suggest that errors in gps carrier phase observations at frequencies within the gravity passband of airborne gravity systems may be due mainly to multipath interference further the power spectral density psd of these errors has been found to fall off rapidly with increase in frequency throughout the anticipated gravity passband in the manner of a red spectrum rather than a white which remains constant it is shown that this implies a much greater allowable error in gps derived altitude reference than would be the case if the psd of altitude errors 1 was white 2 had the same shape as that of typical aircraft vertical motion or 3 was dominated by a sinusoidal wave located near the high frequency limit of the gravity passband this enhances the feasibility of airborne gravity for regional scale surveys and perhaps explains why actual measurements have been better than predicted for example given a uniform f 4 distri

low frequency fluid waves in fractures and pipes low frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid three different fluid wave regimes can exist in such objects depending on the various combinations of parameters such as fluid density fluid viscosity walls shear modulus channel thickness and frequency equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact solutions the dominant role of fractures in rock permeability at field scales and the strong amplitude and frequency effects of stoneley guided waves suggest the importance of including these wave effects into poroelastic theories

slow waves in fractures filled with viscous fluid stoneley guided waves in a fluid filled fracture generally have larger amplitudes than other waves and therefore their properties need to be incorporated in more realistic models in this study a fracture is modeled as an infinite layer of viscous fluid bounded by two elastic half spaces with identical parameters for small fracture thickness i obtain a simple dispersion equation for wave propagation velocity this velocity is much smaller than the velocity of a fluid wave in a biot type solution in which fracture walls are assumed to be rigid at seismic prospecting frequencies and realistic fracture thicknesses the stoneley guided wave has wavelengths on the order of several meters and an attenuation q factor exceeding 10 which indicates the possibility of resonance excitation in fluid bearing rocks the velocity and attenuation of stoneley guided waves are distinctly different at low frequencies for water and oil the predominant role of fractures in fluid flow at field scales is supported by permeability data showing an increase of several orders of magnitude when compared to values obtained at laboratory scales these data suggest that stoneley guided waves should be taken into account in theories describing seismic wave propagation in fluid saturated rocks

source mechanism of volcanic tremor low frequency 10 hz volcanic earthquakes originate at a wide range of depths and occur before during and after magmatic eruptions the characteristics of these earthquakes suggest that they are not typical tectonic events physically analogous processes occur in hydraulic fracturing of rock formations low frequency icequakes in temperate glaciers and autoresonance in hydroelectric power stations we propose that unsteady fluid flow in volcanic conduits is the common source mechanism of low frequency volcanic earthquakes tremor the fluid dynamic source mechanism explains low frequency earthquakes of arbitrary duration magnitude and depth of origin as unsteady flow is independent of physical properties of the fluid and conduit fluid transients occur in both low viscosity gases and high viscosity liquids a fluid transient analysis can be formulated as generally as is warranted by knowledge of the composition and physical properties of the fluid material properties geometry and roughness of the conduit and boundary conditions to demonstrate the analytical potential of the fluid dynamic theory we consider a single phase fluid a melt of mount hood andesite at 1250 c in which significant pressure and velocity variations occur only in the longitudinal direction further simplification of the conservation of mass and momentum equations presents an eigenvalue problem that is solved to determine the natural frequencies and associated damping of flow and pressure oscillations for a simple constant pressure reservoir conduit orifice fluid system a change in orifice size can cause the source signal duration due to a single disturbance to change from several seconds to in excess of an hour fluid kinematic viscosity 0 412 m2 s is both included and neglected in the analysis to illustrate its effect upon system damping tremor magnitude is related to the magnitude of the conduit wall motion occurring in response to oscillating fluid pressures the entire volcanic fluid system does not generally experience a transient flow condition at a given time closed end and constant pressure fluid system boundaries reflect pressure waves and isolate components of the fluid system total fluid movement may not be accurately monitored by tremor data alone since steady state and slowly changing flows are aseismic

interpretation of resonance frequencies recorded during hydraulic fracturing treatments hydraulic fracturing treatments are often monitored by strings of geophones deployed in boreholes instead of picking discrete events only we here use time frequency representations of continuous recordings to identify resonances in two case studies this paper outlines an interpretational procedure to identify their cause using a subdivision into source path and receiver side effects for the first case study two main resonances are observed both at depth by the downhole geophones and on the surface by two broadband arrays the two acquisition networks have different receiver and path effects yet recorded the same resonances these resonances are therefore likely generated by source effects the amplitude pattern at the surface arrays indicates that these resonances are probably due to pumping operations in the second case study selective resonances are detected by the downhole geophones resonances coming from receiver effects are either lower or higher frequency and wave propagation modeling shows that path effects are not significant we identify two possible causes within the source area namely eigenvibrations of fractures or non darcian flow within the hydraulic fractures in the first situation 15 10 m long fluid filled cracks could generate the observed resonances an interconnected fracture network would then be required corresponding to mesoscale deformation of the reservoir alternatively systematic patterns in non darcian fluid flow within the hydraulic fracture could also be their leading cause resonances can be used to gain a better understanding of reservoir deformations or dynamic fluid flow perturbations during fluid injection into hydrocarbon and geothermal reservoirs co2 sequestration or volcanic eruptions

microcrack induced elastic wave anisotropy of brittle rocks the failure of brittle rocks during compression is preceded by the formation growth and coalescence of microcracks elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock in general these microcracks are not randomly oriented and the rock displays an elastic anisotropy the elastic anisotropy due to cracks can be expressed in terms of a second rank and fourth rank crack density tensor for open cracks the contribution of the fourth rank crack density tensor to the elastic wave velocities is small these results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to berea sandstone inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress in agreement with current rock mechanics theory a reasonable fit to the data is obtained using only the second rank crack density tensor even though at high confining stress the cracks are expected to be in partial contact along their length this is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by white however measurements of off axis wave velocities are required to fully quantify the contribution of the fourth rank crack density tensor

airborne gravimetry from a small twin engine aircraft over the long island sound in january 1990 a test of the feasibility of airborne gravimetry from a small geophysical survey aircraft a cessna 404 was conducted over the long island sound using a bell aerospace bgm 3 sea gravity meter gravity has been measured from large aircraft and specially modified de havilland twin otters but never from small standard survey aircraft the gravity field of the long island sound is dominated by an asymmetric positive 30 rngal anomaly which is well constrained by both marine and land gravity measurements using a trimble 4000 gps receiver to record the aircraft s horizontal position and radar altimeter elevations to recover the vertical accelerations gravity anomalies along a total of 65 km were successfully measured the root mean square rms difference between the airborne results and marine measurements within 2 km of the flight path was 2 6 mgai for 15 measured values the anomalies recovered from airborne gravimetry can also be compared with the gridded regional free air gravity field calculated using all available marine and land gravity measurements the rms difference between 458 airborne gravity measurements and the regional gravity field is 2 7 mgai this preliminary experiment demonstrates that gravity anomalies with wavelengthsas short as 5 km can be measured from small aircraft with accuracies of 2 7 mgal or better the gravity measurements could be improved by higher quality vertical and horizontal positioning and tuning the gravimeter s stabilized platform for aircraft use

an airborne gravity study of eastern north carolina the naval research laboratory nrl has developed a prototype airborne gravity measurement system the core of the system is a lacoste and romberg air sea gravity meter mounted on a three axis stable platform corrections to the gravimeter data for altitude and variations in altitude are determined from a combination of highly precise radar and pressure altimeters the original prototype system was designed for use over oceanic areas we recently incorporated the pressure measurement to extend use of the airborne system to terrestrial regions where occasional radar altitudes over points of known topographic height can be obtained the radar heights are used to relate the pressure altitudes to absolute altitudes and to determine the slopes of the isobaric surfaces vertical accelerations due to horizontal velocity over a curved rotating earth the eotvos correction and precise two dimensional positions are determined from a texas instrument p code global positioning system the updated system was tested

experimental measurements of seismic attenuation in microfractured sedimentary rock ultrasonic compressional and shear wave attenuation in water saturated carrara marble increase with increasing crack density and decreasing effective pressure between 0 4 and 1 0 mhz empirical linear relationships between 1 q and crack density cd were found to be cd 1 96 or 0 63 x 1 q for compressional waves andcd 6 7 or 1 5 x 1 q for shear waves

modelling frequency dependent seismic anisotropy in fluid saturated rock with aligned fractures implication of fracture size estimation from anisotropic measurements measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity analysis of the data is based upon equivalent medium theories that describe the elastic response of a rock containing cracks or fractures in the long wavelength limit conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures the latter however control the fluid flow in many subsurface reservoirs therefore the fracture size is essential information for reservoir engineers in this study we apply a new equivalent medium theory that models frequency dependent anisotropy and is sensitive to the length scale of fractures the model considers velocity dispersion and attenuation due to a squirt flow mechanism at two different scales the grain scale microcracks and equant matrix porosity and formation scale fractures the theory is first tested and calibrated against published laboratory data then we present the analysis and modelling of frequency dependent shear wave splitting in multicomponent vsp data from a tight gas reservoir we invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves the derived fracture length matches independent observations from borehole data

scattering by hydraulic fractures finite difference modeling and laboratory data reservoir production can be stimulated by creating hydraulic fractures that effectively facilitate the inflow of hydrocarbons into a well considering the effectiveness and safety of the operation it is desirable to monitor the size and location of the fracture in this paper we investigate the possibilities of using seismic waves generated by active sources to characterize the fractures first we must understand the scattering of seismic waves by hydraulic fractures for that purpose we use a finite difference modeling scheme we argue that a mechanically open hydraulic fracture can be represented by a thin fluid filled layer the width or aperture of the fracture is often small compared to the seismic wavelength which forces us to use a very fine grid spacing to define the fracture based on equidistant grids this results in a large number of grid points and hence computationally expensive problems we show that this problem can be overcome by allowing for a variation in grid spacing in the finite

potential use of resonance frequencies in microseismic interpretation continuous passive recordings of microseismic experiments can be used to detect and trace the modifications in frequency content during hydraulic fracturing or heavy oil steam injection we analyze the performance of four different time frequency representations namely the short time fourier transform the s transform the continuous wavelet transform and the autoregressive method on a real microseismic data set of intermediate quality we show that time frequency transforms provide an efficient tool to highlight time varying resonance frequencies occurring during reservoir fracturing four distinct resonance frequencies at 17 35 51 and 60 hz are observed during two experiments using the same experimental setup

a novel ebsd based finite element wave propagation model for investigating seismic anisotropy application to finero peridotite ivrea verbano zone northern italy a novel electron backscatter diffraction ebsd based finite element fe wave propagation simulation is presented and applied to investigate seismic anisotropy of peridotite samples the fe model simulates the dynamic propagation of seismic waves along any chosen direction through representative 2d ebsd sections the numerical model allows separation of the effects of crystallographic preferred orientation cpo and shape preferred orientation spo the obtained seismic velocities with respect to specimen orientation are compared with voigt reuss hill estimates and with laboratory measurements the results of these three independent methods testify that cpo is the dominant factor controlling seismic anisotropy fracture fillings and minor minerals like hornblende only influence the seismic anisotropy if their volume proportion is sufficiently large up to 23 the spo influence is minor compared to the other factors the presented fe model is discussed with regard to its potential in simulating seismic wave propagation using ebsd data representing natural rock petrofabrics

evidence for magma intrusion during the mammoth lakes earthquakes of may 1980 and implications of the absence of volcanic harmonic tremor the compensated linear vector dipole clvd mechanism p wave radiation with conical nodal surfaces found for the mammoth lakes earthquakes of may 1980 has been attributed to dike intrusion by julian and his colleagues there is a concern about this interpretation because magma intrusion through a crack should radiate compressional first motion everywhere chouet s calculation on a magma intrusion model however showed that the main dynamic motion as well as the final static displacement have patterns similar to the clvd mechanism we found an example of observed radiation pattern similar to the clvd mechanism from eruption earthquakes at mount aso obtained by sassa and we interpret the observation as misidentification of the main motion as the initial motion in searching for a similar misidentification for the mammoth lakes earthquakes we found that there are numerous reports of compression for short period p waves at stations where long period p waves show unequivocal dilatation furthermore we found that the compressional short period first motion is systematically earlier than the dilatational one these observations can be explained if the source of magma intrusion generated compressional first motions which were very weak and of high frequency contents in the direction where long period p waves are dilatational the seismic moment of the mammoth lakes earthquakes suggests an involvement of magma volume of the order of 10 2 km3 however we have not yet observed long period events or volcanic harmonic tremors which are often observed at active volcanos we review recent advances in theories and observations on volcanic tremor and conclude that for the volume of magma reservoir suggested for the mammoth lakes area a fluctuation of pressure of the order of 10 2 bar would generate measurable tremor this conclusion is obtained under the assumption that both the viscosity of magma and the radiation loss of the magma reservoir are low enough for the excitation of a harmonic tremor we found that the concept of reduced displacement introduced by aki and koyanagi for body waves and by fehler for surface waves is very useful for estimating the physical parameters of a volcanic tremor source

krauklis wave initiation in fluid filled fractures by seismic body waves abstractkrauklis waves are a special wave mode that is bound to and propagates along fluid filled fractures they can repeatedly propagate back and forth along a fracture and eventually fall into resonance emitting a seismic signal with a dominant characteristic frequency they are of great interest because this resonant behavior can lead to strongly frequency dependent propagation effects for seismic body waves and may explain seismic tremor generation in volcanic areas or affect microseismic signals in fractured fluid reservoirs it has been demonstrated that krauklis waves can be initiated by a seismic source inside the fracture for example by hydrofracturing here the aim is to study krauklis wave initiation by an incident plane p or s wave in numerical simulations both seismic body waves are reflected and scattered at the fracture but also two krauklis waves are initiated with significant amplitude one at each fracture tip i e at the diffraction points of the fracture generally the incid

laboratory evidence for krauklis wave resonance in fractures and implications for seismic coda wave analysis abstractkrauklis waves are of major interest because they can lead to resonance effects in fluid filled fractures this resonance is marked by seismic signals with a dominant signature frequency which may reveal fracture related rock properties in our laboratory study we used homogeneous plexiglas samples containing a single well defined i e manufactured fracture we recorded the signals obtained from propagating ultrasonic p and s waves source frequency 0 6 1 and 2 25 mhz along a sample without a fracture and samples with a fracture with different inclination angles of 30 45 and 60 with respect to the short axis the experimental results obtained from an incident s wave confirmed that the presence of the fracture led to resonance effects at frequencies lower than the dominant source frequency which slowly decayed over time in the recorded seismic coda after the first arrival the resonance frequency was independent of the fracture orientation and the source frequency we have interpret

stoneley wave generation by an incident p wave propagating in the surrounding formation across a horizontal fluid filled fracture abstract this study investigates the generation of the low frequency borehole stoneley wave tube wave by a plane p wave propagating through the surrounding elastic formation which is intersected by a fluid filled fracture a model is constructed taking into account the dynamic fluid coupling between the borehole interior and the fluid filled fracture of infinite extent with parallel walls the basic mechanism of such coupling is due to the contraction of the fracture walls by the incident p wave leading to seismic radiation into the fracture the dynamic fluid flux from the fracture into the borehole interior and vice versa is the source of the low frequency stoneley wave an expression for the monopole pressure source exciting the tube wave is obtained the tube wave equation in the long wave approximation is derived in the presence of a fluid filled fracture of infinite extent amplitudes and waveforms of stoneley waves are analysed in the seismic wavelength range for p wave pulses of various shapes it is shown that the amplitude and waveform of the stoneley wave depends significantly on the two dimensionless parameters of the problem 1 the ratio of the borehole radius to the dominant wavelength of the incident pulse 2 the ratio of the fracture width to the borehole radius it is found that the amplitude of the generated stoneley wave can be of the order of the p wave amplitude in the borehole fluid stoneley waveforms are found to be completely different from those of the incident pulse

squirt flow in fully saturated rocks we estimate velocity frequency dispersion and attenuation in fully saturated rocks by employing the squirt flow mechanism of solid fluid interaction in this model pore fluid is squeezed from thin soft cracks into the surrounding large pores information about the compliance of these soft cracks at low confining pressures is extracted from high pressure velocity data the frequency dependence of squirt induced pressure in the soft cracks is linked with the porosity and permeability of the soft pore space and the characteristic squirt flow length these unknown parameters are combined into one expression that is assumed to be a fundamental rock property that does not depend on frequency the appropriate value of this expression for a given rock can be found by matching our theoretical predictions with the experimental measurements of attenuation or velocity the low frequency velocity limits as given by our model are identical to those predicted by gassmann s formula the high frequency limits may sign