The relationships between the velocities,attenuations and petrophysical properties of reservoir sedimentary rocks1

We have measured the velocities and attenuations of compressional and shear waves in 29 water-saturated samples of sandstones and shales at a confining pressure of 60 MPa and at frequencies of about 0.85 MHz. The measurements were made using a pulse echo method in which the samples (diameter 5 cm, length 1.5 cm to 2.5 cm) were placed between perspex buffer rods inside a high-pressure cell. The velocity of each seismic wave was determined from the traveltime difference of equivalent phase points (corrected for diffraction effects) of the signals reflected from the top and from the base of each sample. Attenuation was determined in a similar way by comparison of the diffraction corrected amplitudes of the signals. The attenuation data are presented as ‘quality factors’: Q_p and Q_s for compressional and shear waves respectively. The results show that Q_s is strongly correlated with V_s, that Q_p is weakly correlated with V_p, and that Q_p is strongly correlated with Q_s. Q_p is strongly dependent on the volume percentage of the assemblage of intra-pore minerals, whether they are clays or carbonates. It is concluded that the attenuation mechanism is due to the local fluid flow arising from the differential dilation of the solid rock frame and the intra-pore mineral assemblage, which is a result of their very different elastic moduli.     

IMPROVEMENTS IN THE OBSERVATION OF SHEAR WAVES*

The observation of shear waves is finding more interest in seismic exploration, especially for the determination of additional lithologic parameters, e.g. V^p/V^s. We demonstrate the observation of converted waves in routine seismic work by means of horizontal geophones. Field technique and data processing permit acquisition and interpretation of converted waves in connection with routine seismic measurements. A special interpretation of the recorded converted waves results in the shear wave velocity and the V^p/V^s relation.     

VISCOELASTIC SEISMIC RESPONSES OF 2D RESERVOIR MODELS1

The use of relaxation mechanisms has recently made it possible to simulate viscoelastic (Q) effects accurately in time-domain numerical computations of seismic responses. As a result, seismograms may now be synthesized for models with arbitrary spatial variations in compressional- and shear-wave quality factors (Q₉, and Q_s, as well as in density (ρ) and compressional- and shear-wave velocities (V_p, and V_s). Reflections produced by Q contrasts alone may have amplitudes as large as those produced by velocity contrasts. Q effects, including their interaction with V_p, V_s and p, contribute significantly to the seismic response of reservoirs. For band-limited data at typical seismic frequencies, the effects of Q on reflectivity and attenuation are more visible than those on dispersion. Synthetic examples include practical applications to reservoir exploration, evaluation and monitoring. Q effects are clearly visible in both surface and offset vertical seismic profile data. Thus, AVO analyses that neglect Q may produce erroneous conclusions.     

Modelling shear waves in OBS data from the Vøring basin (Northern Norway) by 2-D ray-tracing

Three component recordings from an array of five ocean bottom seismographs in the northwestern part of the Vøring basin have been used to obtain a 2-D shear-wave (S-wave) velocity-depth model. The shear waves are identified by means of travel-time differences compared to the compressional (P) waves, and by analyzing their particle motions. The model has been obtained by kinematic (travel-time) ray-tracing modelling of the OBS horizontal components.The shear-wave modelling indicates that mode conversions occur at several high velocity interfaces (sills) in the 4–10 km depth range, previously defined by a compressional-wave velocity-depth model using the same data set.An averageV _p /V _s ratio of 2.1 is inferred for the layers above the uppermost sill, indicative of both poorly consolidated sediments and a low sand/shale ratio. A significant decrease in theV _p /V _s ratio (1.7) below the first sill may in part be atributed to well consolidated sediments, and to a change in lithology to more sandy sediments. This layer is interpreted to lie within the lower Cretaceous sequence. At 5–10 km depthV _p /V _s ratios of 1.85 indicate a lower sand/shale ratio consistent with the expected lithologies. The averageV _p /V _s ratio inferred for the crust is 1.75, which is consistent with values obtained north of Vøring, in the Lofoten area. An eastward thinning of the crystalline basement is supported by the shear-wave modelling.     

SEISMIC AND ELECTRICAL PROPERTIES OF UNCONSOLIDATED PERMAFROST1

A model has been developed to relate the velocities of acoustic waves V_p and V_s in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave-scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts V_p and V_s to be decreasing functions of both the porosity and the water-to-ice ratio. The theory has been applied to laboratory measurements of V_p and V_s in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples. Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.     

A PHYSICAL MODEL STUDY OF SCATTERING OF WAVES BY ALIGNED CRACKS: COMPARISON BETWEEN EXPERIMENT AND THEORY1

An approximation to plane-wave propagation through a composite material is examined using a physical model with oriented but randomly distributed penny-shaped rubber inclusions within an isotropic epoxy resin matrix. A pulse transmission method is used to determine velocities of shear and compressional waves as a function of angle of incidence and crack density. The experimental and theoretical results of Hudson were compared and limitations within the crack parameters used in this study have been determined. Results from both polarized shear waves (S1, S2) compare favourably with the theory for a composite with up to 7% crack density, but theory and experiment diverge at higher crack densities. On the other hand, compressional-wave velocities at low crack densities (1% and 3%) compare favourably with the theory. It is also shown that the velocity ratio V_p/V_s for two extreme cases, i.e. propagation normal and parallel to the cracks, as a function of crack density and porosity, has a strong directional dependence.     

ACOUSTIC MODELING OF THE SEAFLOOR*

Data from routine seismic surveys contain considerable information about the geo-acoustic properties of the seafloor. Waves are reflected at a wide range of angles of incidence from near-vertical reflections (higher multiples) to supercritical reflections (primary and lower multiples). The reflection coefficient is approximately constant for small angles of incidence (< 10°) but varies greatly for larger angles of incidence. Near-vertical reflections are used to determine the seafloor density. The P-velocity in the seafloor is determined in advance from the critical distance using the amplitude variation of the primary as well as the multiples. The V_p/V_S ratio is determined by modeling the amplitude variation with the angle of incidence. The primary reflection from the seafloor and the first three multiples are included in the modeling. Seismic data obtained with both conventional and superlong airgun arrays have been modeled. Data collected from the Barents Sea show that even if the P-velocity is the same at different sites, the V_p/V_s ratio, density and Poisson's ratio vary significantly. The most extreme example shows that for a P-velocity of 2.80 km/s the V_p/V_s ratio varies between 1.9 and 6.0. The corresponding densities vary from 2.36 g/cm³ to 1.80 g/cm³ and the Poisson's ratio varies from 0.31 to 0.49. The acoustic modeling offers a method of assessing the mean geotechnical or mechanical properties of larger volumes of marine sediments in terms of incompressibility, shear modulus and Poisson's ratio.     

Sediment Thicknesses and Q<Subscript>s</Subscript> vs. Q<Subscript>p</Subscript> Relations in the Kachchh Rift Basin,Gujarat, India Using Sp Converted Phases

Delineation of the top sedimentary structure and its Q_s vs. Q_p relationship using the travel-time difference of direct S and converted Sp phase is key to understanding the seismic hazard of any sedimentary basin area. We constructed filtered displacement waveforms from local ETNA Episensor acceleration recordings as well as local velocity recordings of aftershocks of the 2001 Bhuj earthquake recorded by the Kachchh seismological network of the National Geophysical Research Institute (NGRI), Hyderabad, India during 2001–2004. Stations are within 15–70km of epicenters, and the resulting displacement waveforms are generally simple, displaying prominent P, Sp, and S wave pulses. Particle motion of P and S waves suggest near-vertical raypaths consistent with preliminary depth estimates. The direct S wave on the horizontal component is characterized by lower frequency content than the converted Sp phase on the vertical component. This difference in frequency content between S and Sp phases can be explained in terms of different attenuation effects for P and S waves in the unconsolidated sediments. The Sp phase is generated by S-to-P phase conversion at the base of Mesozoic sediments of the Kachchh basin. Travel-time inversion (VELEST) of 2565 P and 2380 S arrivals from 658 well located aftershocks recorded at 8–14 three-component local seismic stations led to 1 D velocity models indicated very slow sediments in the upper 0–2 km depth range (Vp: 2.92 km/s and Vs: 0.90 km/s) and an increasing trend of velocities with depth at 2–40 km depth. The estimated sediment thicknesses beneath 12 accelerograph and 6 seismograph sites from the estimated velocity model and the travel-time difference between S and converted Sp phases reaches a maximum of (1.534 ± 0.117) km beneath Bandri (near the location of 2001 Bhuj mainshock) and attains a minimum sediment thickness of (0.858 ± 0.104) km beneath Ramvav and Burudia. The spectral ratios between Sp and S from 159 three-component accelerograms have been used to study seismic wave attenuation in the Kachchh rift basin. The estimated Q_s vs. Q_p relations for 12 accelerograph sites vary from Q_s = 0.184 Q_p (at Chobari) to Q_s = 0.505 Q_p (at Dudhai). For stations Chobari, Chopdwa, Jahawarnagar, Vondh and Tapar, the spectral ratio slopes and hence the calculated Q_s vs. Q_p relations are effectively the same, and the correlation coefficients are quite high (0.91–0.93). Stations Adhoi, Manfara, New Dudhai, Dudhai and Sikara have similar Q_s vs. Q_p relationships to each other and also have high correlation coefficients (0.78–0.87). The spectral ratios for stations Anjar and Ramvav are small and poorly constrained, resulting in less reliable Q_s vs. Q_p relations. This could be due to noisy data, fewer available waveforms, or scattering due to velocity heterogeneities and/or interface irregularities.     

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.     

COMMON REFLECTION POINT DATA-STACKING TECHNIQUE FOR CONVERTED WAVES1

For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PS- and SP-type in a stack of horizontal layers. The coordinates of the conversion points for waves of PS- or SP-type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio v_p/v_s. Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of v_p/v_s is required to obtain the CCP for a given reflector depth. A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix-type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.     

Vp‐Vs relationship and amplitude variation with offset modelling of glauconitic greensand‡

The relationship between V_p and V_s may be used to predict V_s where only V_p is known. V_p/V_s is also used to identify pore fluids from seismic data and amplitude variation with offset analysis. Theoretical, physical, as well as statistical empirical V_p‐V_s relationships have been proposed for reservoir characterization when shear‐wave data are not available. In published work, the focus is primarily on the V_p‐V_s relationship of quartzitic sandstone. In order to broaden the picture we present V_p‐V_s relationships of greensand composed of quartz and glauconite by using data from the Paleocene greensand Nini oil field in the North Sea. A V_p‐V_s relationship derived from modelling is compared with empirical V_p‐V_s regressions from laboratory data as well as from log data. The accuracy of V_s prediction is quantified in terms of root‐mean‐square error. We find that the V_p‐V_s relationship derived from modelling works well for greensand shear‐wave velocity prediction. We model the seismic response of glauconitic greensand by using laboratory data from the Nini field. Our studies here reveal that brine‐saturated glauconitic greensand can have a similar seismic response to that from oil‐saturated quartzitic sandstone and that oil‐saturated strongly cemented greensand can have a similar amplitude variation with offset response to that from brine‐saturated weakly cemented greensand.     

Use of mode-converted waves in marine seismic data to investigate the lithology of the sub-bottom sediments in Isfjorden,Svalbard

The compression wavefield is efficiently converted to shear-wave energy at post-critical angles in areas of high impedance contrast at the sea floor. We have analysed mode-converted shear waves in a data set acquired with a hybrid marine/land geometry in Isfjorden, Svalbard. Through a kinematic 2D ray-tracing modellingV _p/V_s ratios for part of the uppermost 5km of the crust are obtained. Low values (V _p /V _s =1.65) are tentatively associated with the section of Devonian sandstones which appears to attain a minimum thickness of 1.5km below 3 km depth about 10km west of Kapp Thorden.     

τ-p SEISMIC DATA FOR VISCOELASTIC MEDIA – PART 1: MODELLING1

Viscoelastic modelling reveals that the interaction of compressional-wave velocity C_p, compressional-wave quality factor Q_p, shear-wave velocity C_s, shear-wave quality factor Q_s and Poisson's ratio as a function of time intercept τ and ray parameter p, is complicated; however, distinct, potentially diagnostic behaviours are seen for different combinations of viscoelastic parameters. Synthetic seismograms for three viscoelastic reservoir models show that variations in the Poisson's ratio produce visible differences when compared to the corresponding elastic synthetic seismograms; these differences are attributable to interaction of the elastic parameters with Q_p and Q_s. When the P-wave acoustic impedance contrast is small, viscoelastic effects become more apparent and more useful for interpretation purposes. The corresponding amplitude and net phase spectra reveal significant differences between the elastic and the viscoelastic responses. When P-wave reflectivities are large, they tend to dominate the total response and to mask the Q reflectivity effects. The attenuation effects are manifested as an amplitude decay that increases with both time and ray parameter. The sensitivity of the computed seismic responses for various combinations of viscoelastic parameters suggests the opportunity for diagnostic interpretation of τ-p seismic data. The interpretation of the viscoelastic parameters can permit a better understanding of the rock types and pore fluid distribution existing in the subsurface.     

SEISMIC REFRACTION METHOD TO STUDY THE FOUNDATION ROCK OF A DAM*

Dynamic elastic moduli like E, μ, K and μ of the foundation rock of a dam have been determined by finding V_p- and V_s-velocities by seismic refraction with a hammer as source. Some parameters such as “fracture frequency” and “rock quality designation” (RQD) of the foundation rock have been derived using “average regression curves” and V_p-velocities. By comparing K/μ with V_p/V_s, a few locations showing weathered conditions have been demarcated. This compares well with RQD values of those locations.     

τ-p SEISMIC DATA FOR VISCOELASTIC MEDIA - PART 2: LINEARIZED INVERSION1

An approach to extraction of viscoelastic parameters from seismic data is implemented and succesfully tested. Viscoelastic inversion is performed using adaptive damping factors to control the sensitivity of the viscoelastic parameters in relation to the τ-p seismic data. A priori information is incorporated through the damping factors as standard deviations of the data and of the viscoelastic model parameters. The stability of the inversion process is controlled by the variation of the damping factors as a function of the residual errors and parameter updates at each iteration. Tests on synthetic and real data show that P- and S-wave quality factors, Q_p and Q_s, in addition to P- and S-wave velocities and density C_p, C_s and p, can be extracted from τ-p seismic information. Singular value decomposition analysis demonstrates that estimated Q_p and Q_s values are more affected by the presence of data inaccuracies and noise than are those of C_p and p. C_s and Q_s are not uniquely recovered due to the limited contribution of P-S converted waves. Knowledge of the viscoelastic parameters is of particular importance in accurately describing petrophysical properties of rocks and pore fluids existing in the subsurface; this is demonstrated with real data from the Gulf of Mexico.     

Vp and Vp/Vs structures in the crust and upper mantle of the Taiwan region, China

A tomographic study of the V _p and V _p/V _s structures in the crust and upper mantle beneath the Taiwan region of China is conducted by simultaneous inversion of P and S arrival times. Compared with the previous tomographic results, the spherical finite difference technique is suitable for the strong heterogeneous velocity structure, and may improve the accuracy in the travel time and three-dimensional ray tracing calculations. The V _p and V _p/V _s structures derived from joint inversion and the relocated earthquakes can provide better constraints for analyzing the lateral heterogeneity and deep tectonic characters in the crust and upper mantle. Our tomographic results reveal significant relations between the seismic wavespeed structure and the tectonic characters. In the shallow depth, sedimentary basins and orogen show distinct wavespeed anomalies, with low V _p, high V _p/V _s in basins and high V _p, low V _p/V _s in orogen. As the suture zone of Eurasian Plate and Philippine Sea Plate, Longitudinal Valley is characterized by a significant high V _p/V _s anomaly extending to the middle-lower crust and upper mantle, which reflects the impact of rock cracking, partial melting, and the presence of fluids. In the northeast Taiwan, the V _p, V _p/V _s anomalies and relocated earthquakes depict the subducting Philippine Sea Plate under the Eurasian Plate. The high V _p of oceanic plate and the low V _p, high V _p/V _s atop the subducted oceanic plate extend to 80 km depth. Along the east-west profiles, the thickness of crust reaches 60 km at the east of Central Range with eastward dipping trend, which reveals the eastward subduction of the thickened and deformed crust of the Eurasian continental plate. Supported by Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX3-SW-234-2), National Basic Research Program of China (Grant No. 2007CB411701), National High Technology Research and Development Program of China (Grant No. 2006AA09A101-0201) and National Natural Science Foundation of China (Grant Nos. 40804016, 40704013)     

CONVERSION POINTS AND TRAVELTIMES OF CONVERTED WAVES IN PARALLEL DIPPING LAYERS1

For converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio v_p/v_s. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration. The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two-term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates.     

OUTBURST FLOODS FROM GLACIER-DAMMED LAKES: THE EFFECT OF MODE OF LAKE DRAINAGE ON FLOOD MAGNITUDE

Published accounts of outburst floods from glacier-dammed lakes show that a significant number of such floods are associated not with drainage through a tunnel incised into the basal ice—the process generally assumed—but rather with ice-marginal drainage, mechanical failure of part of the ice dam, or both. Non-tunnel floods are strongly correlated with formation of an ice dam by a glacier advancing from a tributary drainage into either a main river valley or a pre-existing body of water (lake or fiord). For a given lake volume, non-tunnel floods tend to have significantly higher peak discharges than tunnel-drainage floods. Statistical analysis of data for floods associated with subglacial tunnels yields the following empirical relation between lake volume V and peak discharge Q_p : Q_p = 46V^0.66 (r² = 0.70), when Q_p is expressed in metres per second and V in millions of cubic metres. This updates the so-called Clague–Mathews relation. For non-tunnel floods, the analogous relation is Q_p = 1100V^0.44 (r² = 0.58). The latter relation is close to one found by Costa (1988) for failure of constructed earthen dams. This closeness is probably not coincidental but rather reflects similarities in modes of dam failure and lake drainage. We develop a simple physical model of the breach-widening process for non-tunnel floods, assuming that (1) the rate of breach widening is controlled by melting of the ice, (2) outflow from the lake is regulated by the hydraulic condition of critical flow where water enters the breach, and (3) the effect of lake temperature may be dealt with as done by Clarke (1982). Calculations based on the model simulate quite well outbursts from Lake George, Alaska. Dimensional analysis leads to two approximations of the form Q_p ∝ V^qf(h_i, θ₀), where q = 0.5 to 0.6, h_i is initial lake depth, θ₀ is lake temperature, and the form of f (h_i, θ₀) depends on the relative importance of viscous dissipation and the lake's thermal energy in determining the rate of breach opening. These expressions, along with the regression relations, should prove useful for assessing the probable magnitude of breach-type outburst floods.     

The spatial and temporal changes inV p /V s before strong earthquakes in Kamchatka

A method was developed to obtain from a signal station the spatial and temporal distribution ofV _p /V _s ratios before earthquakes of magnitude>6. It was shown thatV _p /V _s values strongly depend upon the relative positions of the stations, the future large earthquake and the foci of the smaller earthquakes used forV _p /V _s determination. The appearance of a zone of anomalousV _p /V _s values with linear dimensions of the order of 100 km was noted at least 4 years before a deep earthquake of magnitude 7. Similar size anomalous zones were detected one year before some magnitude 6 earthquakes. V _p /V _s values decreased by a small but distinct amount during this time. Additionally, local short term minima inV _p /V _s ratios were observed some months before the major event. The epicenters of the large earthquakes were located within the 100 km size zone where the gradients of theV _p /V _s field were largest.     

Vp/Vs ratios in the Yellowstone National Park region, Wyoming

In this paper we study the variation of V_p/V_s and Poisson's ratio (δ) in the Yellowstone National Park region, using earthquakes which were well recorded by a local seismic network. We find that the average V_p/V_s value within the geothermally active Yellowstone caldera is about 7% lower than in the area outside the caldera. Within the caldera itself there may be a further 2–7% reduction of V_p/V_s in the hydrothermally active Norris Geyser Basin, the Upper and Lower Geyser Basins, and the Yellowstone Lake and Mud Volcano regions. After considering various possible causes for V_p/V_s changes, such as geologic and structural differences, thermal effects, partial melting, and hydrothermal activity, we conclude that the most plausible explanation for the observed V_p/V_s reduction is the presence of hot-water at temperatures and pore-pressures near the water steam transition in the caldera geothermal reservoirs.