effective medium theories for fluid saturated materials with aligned cracks there is general agreement between different theories giving expressions for the overall properties of materials with dry aligned cracks if the number density of cracks is small there is also very fair agreement for fluid filled isolated cracks however there are considerable differences between two separate theories for fluid filled cracks with equant porosity comparison with recently published experimental data on synthetic sandstones gives a good fit with theory for dry samples however although the crack number density in the laboratory sample is such that first order theory is unlikely to apply expressions correct to second order in the number density provide a worse fit it also appears that the ratio of wavelength to crack size is not sufficiently great for any detailed comparison with effective medium theories which are valid only when this ratio is large the data show dispersion effects for dry cracks and scattering neither of which will occur at sufficiently long wavelengths data from the water saturated samples indicate that the effect of equant porosity is significant although the two theories differ strongly as to just how significant once again and in spite of the reservations mentioned above a reasonable fit between theory and observation can be shown

a microwave technique for mapping thin sea ice a technique is presented for mapping the distribution of new young and first year sea ice in seasonal sea ice zones that utilizes microwave spectral and polarization information from the defense meteorological satellite program special sensor microwave imager the motivation for this work stems from the need for accurate estimates of open water and thin ice within the arctic ice pack the technique utilizes the microwave polarization and spectral characteristics of these three ice types through two microwave radiance ratios the 19 4 ghz polarization and the spectral gradient ratio which is a measure of the spectral difference between the 19 4 ghz and the 37 0 ghz vertically polarized radiance components the combined use of the spectral gradient ratio and polarization reduces the low ice concentration bias generally associated with the presence of thin ice types the microwave polarization which is sensitive to changes in ice thickness and ice surface characteristics is used to classify new young and first year ice types the polarization varies from about 0 3 for calm ice free water to about 0 15 for new ice and to 0 03 for thick first year ice on the basis of this parameterization improved sea ice concentration maps and maps of new young and first year ice type distributions are derived examples from the bering sea are presented and comparisons are made with analyzed noaa avhrr imagery

wave attenuation in partially saturated porous rocks new observations and interpretations across scales abstract seismic waves propagating in porous rocks saturated with two immiscible fluids can be strongly attenuated predicting saturation effects on seismic responses requires a sound understanding of attenuation and velocity dependencies on the fluid distribution decoding these effects involves interpreting laboratory experiments analyzing well log data and performing numerical simulations despite striking differences among scales flow regimes and frequency bands some aspects of wave attenuation can be explained with a single mechanism wave induced pressure diffusion different facets of wave induced pressure diffusion can be revealed across scales

water saturation effects on p wave anisotropy in synthetic sandstone with aligned fractures the seismic properties of rocks are known to be sensitive to partial liquid or gas saturation and to aligned fractures p wave anisotropy is widely used for fracture characterization and is known to be sensitive to the saturating fluid however studies combining the effect of multiphase saturation and aligned fractures are limited even though such conditions are common in the subsurface an understanding of the effects of partial liquid or gas saturation on p wave anisotropy could help improve seismic characterization of fractured gas bearing reservoirs using octagonal shaped synthetic sandstone samples one containing aligned penny shaped fractures and the other without fractures we examined the influence of water saturation on p wave anisotropy in fractured rocks in the fractured rock the saturation related stiffening effect at higher water saturation values is larger in the direction across the fractures than along the fractures consequently the anisotropy parameter decreases as a result of this fluid stiffening effect these effects are frequency dependent as a result of wave induced fluid flow mechanisms our observations can be explained by combining a frequency dependent fractured rock model and a frequency dependent partial saturation model

polynya dynamics a review of observations and modeling 1 polynyas are nonlinear shaped openings within the ice cover ranging in size from 10 to 105 km2 polynyas play an important climatic role first winter polynyas tend to warm the atmosphere thus affecting atmospheric mesoscale motions second ocean surface cooling and brine rejection during sea ice growth in polynyas lead to vertical mixing and convection contributing to the transformation of intermediate and deep waters in the global ocean and the maintenance of the oceanic overturning circulation since 1990 there has been an upsurge in polynya observations and theoretical models for polynya formation and their impact on the biogeochemistry of the polar seas this article reviews polynya research carried out in the last 2 decades focusing on presenting a state of the art picture of the physical interactions between polynyas and the atmosphere sea ice ocean system observational and modeling studies the surface heat budget and water mass transformation within these features are addressed

method for detection of leads from sentinel 1 sar images the university of bremen the german excellence initiative deutsche forschungsgemeinschaft dfg

delineating fracture zones using surface tunnel surface seismic data p s and s p mode conversions a surface tunnel surface seismic experiment was conducted at the aspo hard rock laboratoryto study the seismic response of major fracture systems intersecting the tunnel a newly developedthree com

oxygen and carbon stable isotopes in coast redwood tree rings respond to spring and summer climate signals 1 interannual variability in the oxygen and carbon isotope composition of tree ring cellulose was investigated in coast redwood sequoia sempervirens from three sites in coastal northern california middle and late wood samples from annual tree rings were compared to regional climate indices and gridded ocean atmosphere fields for the years 1952 2003 the strongest climate isotope relationship r 0 72 was found with summer june september daily maximum temperature and middle wood 13 which also responds positively to coastal sea surface temperature and negatively to summer low cloud frequency late wood 18o reflects a balance between 18o enriched summer fog drip and depleted summer rainwater while a combined analysis of late wood 18o and 13c revealed sensitivity to the sign of summer precipitation anomalies empirical orthogonal function analysis of regional summer climate indices and coast redwood stable isotopes identified multivariate isotopic responses to summer fog and drought that correspond to atmospheric circulation anomalies over the ne pacific and nw u s the presence of regional climate signals in coast redwood stable isotope composition consistent with known mechanistic processes and prior studies offers the potential for high resolution paleoclimate reconstructions of the california current system from this long lived tree species

frequency dependent anisotropy due to meso scale fractures in the presence of equant porosity fractured rock is often modelled under the assumption of perfect fluid pressure equalization between the fractures and equant porosity this is consistent with laboratory estimates of the characteristic squirt flow frequency however these laboratory measurements are carried out on rock samples which do not contain large fractures we consider coupled fluid motion on two scales the grain scale which controls behaviour in laboratory experiments and the fracture scale our approach reproduces generally accepted results in the low and high frequency limits even under the assumption of a high squirt flow frequency we find that frequency dependent anisotropy can occur in the seismic frequency band when larger fractures are present shear wave splitting becomes dependent on frequency with the size of the fractures playing a controlling role in the relationship strong anisotropic attenuation can occur in the seismic frequency band the magnitude of the frequency dependence is influenced strongly by the extent of equant porosity with these results it becomes possible in principle to distinguish between fracture and microcrack induced anisotropy or more ambitiously to measure a characteristic fracture length from seismic data

mapping of apparent magnetic susceptibility and the identification of fractures a case study from the eye dashwa lakes pluton atikokan ontario in situ magnetic susceptibility measurements are only possible on outcrops which are often limited by overburden and water bodies an alternative approach is to derive an apparent susceptibility map from total magnetic intensity tmi surveys which was done in this study for the eye dashwa lakes pluton near atikokan ontario susceptibility logs of cores directly link alteration to systematic changes in the amount and composition of magnetic minerals the surficial distribution of alteration zones was originally estimated from a limited number of in situ magnetic susceptibility measurements here through forward modeling of the tmi data set susceptibility data are used to validate the apparent susceptibility data set the modeling accounts for the bathymetric surface of all lakes that cover the area a two step process of bulk and local scale modeling was used to estimate apparent susceptibility patterns bulk magnetic susceptibility is used as an indicator of overall alteration content and local scale apparent magnetic susceptibility values are computed using a forward modeling routine the new apparent magnetic data set indicates northwest and northeast linears which are the same as those seen in previous studies

water saturation effects on elastic wave attenuation in porous rocks with aligned fractures summary elastic wave attenuation anisotropy in porous rocks with aligned fractures is of interest to seismic remote sensing of the earth s structure and to hydrocarbon reservoir characterization in particular we investigated the effect of partial water saturation on attenuation in fractured rocks in the laboratory by conducting ultrasonic pulse echo measurements on synthetic silicacemented sandstones with aligned penny shaped voids fracture density of 0 0298 0 0077 chosen to simulate the effect of natural fractures in the earth according to theoretical models our results show for the first time contrasting variations in the attenuation q 1 o fp and s

seismic attenuation due to wave induced flow analytical expressions for three p wave attenuation mechanisms in sedimentary rocks are given a unified theoretical framework two of the models concern wave induced flow due to heterogeneity in the elastic moduli at mesoscopic scales scales greater than grain sizes but smaller than wavelengths in the first model the heterogeneity is due to lithological variations e g mixtures of sands and clays with a single fluid saturating all the pores in the second model a single uniform lithology is saturated in mesoscopic patches by two immiscible fluids e g air and water in the third model the heterogeneity is at microscopic grain scales broken grain contacts and or micro cracks in the grains and the associated fluid response corresponds to squirt flow the model of squirt flow derived here reduces to proper limits as any of the fluid bulk modulus crack porosity and or frequency is reduced to zero it is shown that squirt flow is incapable of explaining the measured level of loss 10 sup 2 q sup 1 10 sup 1 within the seismic band of frequencies 1 to 10 sup 4 hz however either of the two mesoscopic scale models easily produce enough attenuation to explain the field data

east antarctic sea ice albedo thickness distribution and snow cover characteristics of springtime sea ice off east antarctica were investigated during a cruise of the australian national antarctic research expedition in october through december 1988 the fractional coverage of the ocean surface the ice thickness and the snow cover thickness for each of several ice types were estimated hourly for the region near the ship these observations were carried out continuously during the 4 weeks the ship was in the ice thin and young ice types were prevalent throughout the region and the observations show a systematic increase in the total area weighted pack ice thickness including open water area from only 0 2 m within 50 km of the ice edge to 0 45 m close to the coast ice thickness averaged over the ice covered region only is also relatively thin ranging from 0 35 m near the ice edge to 0 65 m in the interior these values are probably typical of average winter thickness for the area the average snow cover thickness on the ice increased from 0 05 m near the ice edge to 0 15 m in the interior average ice concentration increased from less than 6 10 near the ice edge to 8 10 in the interior the ship observed concentrations were in good agreement with concentrations derived from passive microwave satellite imagery except in some regions of high concentration in these regions the satellite derived concentrations were consistently lower than those estimated from the ship possibly because of the inability of the satellite sensors to discriminate the appreciable percentage of very thin ice observed within the total area spectral albedo was measured for nilas young grey ice grey white ice snow covered ice and open water at wavelengths from 420 to 1000 nm allwave albedo was computed by using the spectral measurements together with estimates of near infrared albedo and modeled spectral solar flux area averaged albedos for the east antarctic sea ice zone in spring were derived from representative allwave albedos together with the hourly observations of ice types these area averaged surface albedos increased from about 0 35 at the ice edge to about 0 5 at 350 km from the edge remaining at 0 5 to the coast of antarctica the low average albedo is in part due to the large fraction of open water within the pack but extensive fractions of almost snow free thin ice also play an important role

seismic attenuation in porous rocks with random patchy saturation saturation of porous rocks with a mixture of two fluids has a substantial effect on seismic wave propagation in particular partial saturation causes significant attenuation and dispersion of the propagating waves due to the mechanism of wave induced fluid flow such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a regular way however recent experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion based on an approximation for the coherent wavefield in random porous media we develop a model which assumes a continuous distribution of fluid heterogeneities as this continuous random media approach assumes that there will be a distribution of different patch sizes it is expected to be better suited to modelling experimental data we also show how to relate the random functions to experimentally measurable parameters

interpreting laboratory velocity measurements in partially gas saturated rocks it is an old problem in rock physics that the saturation dependence of high frequency laboratory velocities does not match the biot gassmann theory commonly used to predict the effects of gas on seismic velocities a new interpretation of laboratory velocity data shows that the saturation dependence is controlled by two previously published high frequency acoustic mechanisms 1 a gas pocket model that describes pressure equilibration between liquid and gas saturated regions of the pore space and 2 local fluid flow induced by pressure equilibration in pores with different aspect ratios when these two mechanisms are added to biot theory the result describes published velocity versus gas saturation data for a wide range of rock types these two mechanisms are negligible at the lower frequencies of seismic data so the saturation dependence of laboratory velocities cannot be used to predict the saturation dependence at seismic frequencies the one laboratory measurement that is relevant for predicting the seismic velocity is the ultrasonic velocity of the dry rock the dry rock velocities should be used in the biot gassmann theory to predict the full saturation dependence of the seismic velocities

a 5 year satellite climatology of winter sea ice leads in the western arctic the distribution of openings leads and polynyas in polar sea ice is not well known this study estimates the large scale distribution and variability of leads in the arctic of the western hemisphere in winter using a 5 year record of defense meteorological satellite program thermal and visible band imagery the occurrence density and orientation of leads are derived from gridded maps made at 10 day intervals their mean value and interannual seasonal and monthly variabilities are estimated lead densities are observed to be highest in early winter decreasing 20 from november through april the highest densities are observed in the central canada basin and the lowest are in the east siberian sea there is limited interannual variability in the positions of maximum and minimum densities preferred lead orientations are identified as generally north south in the beaufort sea sector and east west in the east siberian sea sector with transitional orientations in the intermediate area the mean distributions of lead density and orientation are observed to be associated with large scale mean fields of ice divergence and shear respectively

elastic wave propagation in media with parallel fractures and aligned cracks a model of parallel slip interfaces simulates the behaviour of a fracture system composed of large closely spaced aligned joints the model admits any fracture system anisotropy triclinic the most general monoclinic orthorhombic or transversely isotropic and this is specified by the form of the 3 3 fracture system compliance matrix the fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy to compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 3 matrices when the fractures are assumed on average to have rotational symmetry transversely isotropic fracture system behaviour and the background is assumed isotropic the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters in addition to the two isotropic parameters of the isotropic background dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints i e there are two additional parameters due to the presence of the microcracks which play roles in the stress strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints thus knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation as the aligned microcracks which were assumed to be ellipsoidal with very small aspect ratio are allowed to become non fiat i e have a growing aspect ratio the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks the divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0 3

annual accumulation at two sites in northwest greenland during recent centuries during summer 1995 150 m firn and ice cores were drilled to determine annual accumulation rates at two greenland sites 73 84 n 49 49 w nasa u site and 78 53 n 56 83 w humboldt glacier site annual layers were identified in the cores using multiple parameters 18 o and concentrations of dust h 2 o 2 nh 4 ca 2 and no 3 using all parameters together to define annual layers resulted in a 350 year record for the nasa u core with no dating uncertainty for the lower accumulation humboldt core the dating uncertainty is about 5 years over the 852 year period of record with no uncertainty over the past 200 years annual accumulation over the periods of record at the two sites averaged about 0 34 and 0 14 m water equivalent respectively a set of 20 m firn cores drilled near the main 150 m cores showed that interannual variability of accumulation exceeded spatial variability at nasa u the humboldt cores showed equal spatial and interannual variability the accumulation rates at both sites showed a low frequency variation of about 100 years and both sites showed 200 year cumulative fluctuations of about 2 m from mean accumulation rates compared to central greenland and to nasa u the humboldt core showed higher annual accumulation rates around 1760 1810 possibly indicating a changed circulation pattern for the more northern part of greenland in that period

experimental observation of water saturation effects on shear wave splitting in synthetic rock with fractures aligned at oblique angles fractured rocks are known to exhibit seismic anisotropy and shear wave splitting sws sws is commonly used for fractured rock characterization and has been shown to be sensitive to fluid type the presence of partial liquid gas saturation is also known to affect the elastic properties of rocks the combined effect of both fractures and partial liquid gas saturation is still unknown using synthetic silica cemented sandstones with aligned penny shaped voids we conducted laboratory ultrasonic experiments to investigate the effect fractures aligned at an oblique angle to wave propagation would have on sws under partial liquid gas saturation conditions the result for the fractured rock shows a saturation dependence which can be explained by combining a fractured rock model and a partial saturation model at high to full water saturation values sws decreases as a result of the fluid bulk modulus effect on the quasi shear wave this bulk modulus effect is frequency dependent as a result of wave induced fluid flow mechanisms which would in turn lead to frequency dependent sws this result suggests the possible use of sws for discriminating between full liquid saturation and partial liquid gas saturation

elastic anisotropy due to aligned cracks in porous rock all theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way for example to the case of stiff pore fluids or of the absence of equant porosity or of a moderately high frequency band because of these restrictions previous theory is not suitable for application to the upper crust where the pore fluid is brine kf k820 the equant porosity is often substantial p 0 1 and the frequency band is sonic to seismic this work removes these particular restrictions recognizing in the process an important mechanism of dispersion a notable feature of these more general expressions is their insensitivity at low frequency to the aspect ratio of the cracks only the crack density is critical an important conclusion of this more general model is that many insights previously achieved concerning the shear wave splitting due to vertical aligned saturated cracks are sustained however conclusions on crack orientation or crack aspect ratio which were derived from p wave data or from shear wave critical angles may need to be reconsidered further the non linear coupling between pores and cracks due to pressure equalization effects means that the linear schoenberg muir calculus may not be applied to such systems the theory receives strong support from recent data by rathore et al on artificial samples with controlled crack geometry

surface based passive microwave observations of sea ice in the bering and greenland seas measurements of brightness temperatures of sea ice were carried out during both the mizex field experiments in 1983 the first in februrary in the bering sea and the second in june july in the northern greenland sea in the bering sea thin growing sea ice types from black ice to 400 mm thick snow covered floes were investigated brightness temperatures increased with ice thickness up to 100 mm from values of 100 k for open water to as high as 250 k e 0 97 for thick ice and a moderate dependence on snow thickness was found in the greenland sea thick first year and multiyear ice types were studied brightness temperatures were quite variable depending on the daily melt freeze cycle superimposed on the seasonal warming ranging from near blackbody values for melting conditions to multiyear like spectra when the surface layers refroze the melt season was sufficiently advanced however that first year and multiyear ice could not be differentiated radiometrically

aircraft and satellite passive microwave observations of the bering sea ice cover during mizex west passive microwave measurements of the bering sea ice cover were made with the nasa cv 990 airborne laboratory and with the nimbus 7 scanning multichannel microwave radiometer smmr during february 1983 as part of the bering sea marginal zone experiment mizex west microwave data obtained with the cv 990 include radiances from both imaging and dual polarized fixed beam radiometers spanning a range of frequencies from 10 to 183 ghz the imagery at 19 and 92 ghz provide a description of the marginal ice zone delineating regions of open water ice compactness and ice edge structure comparison of these images with ice concentration maps derived from the smmr data shows that the maps provide an accurate description of the ice edge and interior pack polynyas analysis of the fixed beam data shows that spectral differences increase with a decrease in ice thickness and the polarization at both 18 and 37 ghz distinguishes among new young and first year sea ice types finally these results are shown to agree with surface based radiometric measurements

warm water cells in the north water northern baffin bay during winter sea surface temperatures above the freezing point of seawater 1 8 c were observed in the north water during winter and early spring the result indicates a possibility of upwelling warm water presumably of atlantic origin brought from lower depths to the surface the warm water temperatures ranged from 1 7 to 0 1 c the highest occurrence frequency lay in the temperature interval from 1 0 to 0 8 c most warm water cells were found along the greenland coast in smith sound lady ann strait and barrow strait they occurred most frequently in smith sound west of cape alexander the highest temperatures of 0 1 c occurred however south of cape alexander the occurrence frequency and the total area of warm water patches decreased toward spring the predominantly northerly wind that is channeled in smith sound accounts for a mean ice drift of approximately 17 km d 1 this ice drift causes an ice divergence in smith sound and along the greenland coast the existence of warm water areas can be explained by the strong northerly wind resulting in a coriolis force that induces coastal upwelling the wind induced offshore transport of 3 5 105 m3 s 1 in the north water compensated by the upwelling of atlantic baffin bay water 0 c along the greenland coast will suffice to keep 10 of the north water ice free the combination of ice divergence and forced convection of warm water can be considered as a prime cause of the polynyas in the north water

permeability dependence of seismic amplitudes can permeability be determined from seismic data this question has been around since maurice biot working for shell in the 1950s introduced the idea that seismic waves induce fluid flow in saturated rocks due to fluid pressure equilibration between the peaks and troughs of a compressional wave or due to grain accelerations in the case of a shear wave biot 1956 established a frequency dependent analytical relation between permeability and seismic attenuation however laboratory sonic log crosswell vsp and surface seismic have all demonstrated that biot s predictions often greatly underestimate the measured levels of attenuation dramatically so for the lower frequency measurements yet if an unresolved link truly exists between seismic amplitudes and permeability the potential benefit to the oil industry is enormous for this reason the department of energy doe brought together 15 participants from industry national laboratories and universities to concentrate for two days on whether permeability information is conceivably contained in and retrievable from seismic data the present article represents much of the workshop discussion which took place 5 6 december 2001 in berkeley california but is not strictly limited to it not all connections between hydrological and seismic properties are considered three dimensional seismic images and time lapse seismic monitoring are routinely used by reservoir engineers in constructing and constraining their reservoir model such imaging applications of seismic surveys to hydrological modeling are not discussed furthermore in fractured reservoirs it is reasonable to postulate that any locally determined seismic anisotropy defines a symmetry class for the geologic material that must also be satisfied by the permeability tensor neither are such material symmetry constraints discussed the focus here is only on whether the permeability of the rocks through which seismic waves propagate directly influences the decay of the wave amplitudes with distance key to addressing this question is an up to date discussion of the likely attenuation

sensitivity of 3d 3c synthetic seismograms to anisotropic attenuation and velocity in reservoir models abstractanisotropic attenuation in fluid saturated reservoirs with high fracture density may be diagnostic for reservoir characterization wave induced mesoscale fluid flow is considered to be the major cause of intrinsic attenuation at exploration seismic frequencies we perform tests of the sensitivity of anisotropic attenuation and velocity to reservoir properties in fractured hti media based on the mesoscale fluid flow attenuation mechanism the viscoelastic t matrix a unified effective medium theory of global and local fluid flow mechanisms is used to compute frequency dependent anisotropic attenuation and velocity for ranges of reservoir properties including fracture density orientation fracture aspect ratio fluid type and permeability the 3d 3c staggered grid finite difference anisotropic viscoelastic modeling with a crank nicolson scheme is used to generate seismograms using the frequency dependent velocity and attenuation computed by the viscoelastic t matrix a standard linear solid mo

validation of the boundary conditions to model the seismic response of fractures fractures in fluid saturated poroelastic media can be modeled as extremely thin highly permeable and compliant layers or by means of suitable boundary conditions that approximate the behavior of such thin layers since fracture apertures can be very small the numerical simulations would require the use of extremely fine computational meshes and the use of boundary conditions would be required in this work we study the validity of using boundary conditions to describe the seismic response of fractures for this purpose we compare the corresponding scattering coefficients to those obtained from a thin layer representation the boundary conditions are defined in terms of fracture apertures that in the most general case impose discontinuity of displacements fluid pressures and stresses across a fracture furthermore discontinuities of either fluid pressures stresses or both can be removed or displacement jumps proportional to the stresses and or pressures can be expressed via shear and normal dry compliances in order to simplify in the examples we vary the permeability thickness and porosity of the fracture and the type of fluid saturating the background medium and fractures we observe good agreement of the scattering coefficients in the seismic range obtained with the two different approaches

effect of fracture fill on frequency dependent anisotropy of fractured porous rocks in fractured reservoirs seismic wave velocity and amplitude depend on frequency and incidence angle the frequency dependency is believed to be principally caused by the wave induced flow of pore fluid at the mesoscopic scale in recent years two particular phenomena patchy saturation and flow between fractures and pores have been identified as significant mechanisms of wave induced flow however these two phenomena are studied separately recently a unified model was proposed for a porous rock with a set of aligned fractures with pores and fractures filled with two different fluids existing models treat waves propagating perpendicular to the fractures in this paper we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction we first consider the limiting cases through poroelastic backus averaging and then we obtain the five complex and frequency dependent stiffnesses of the equivalent ti medium as a function of the frequency the numerical results show that when the bulk modulus of the fracture filling fluid is relatively large the dispersion and attenuation of p waves are mainly caused by fractures and the values decrease as angles increase almost vanishing when the incidence angle is 90 propagation parallel to the fracture plane while the bulk modulus of fluid in fractures is much smaller than that of matrix pores the attenuation due to the partial saturation mechanism makes the fluid flow from pores into fractures which is almost independent of the incidence angle this article is protected by copyright all rights reserved