Seismic Frequency Band Research Articles

Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory. The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges. The brine and four different density oils were used as pore fluids, which provided a good chance to investigate fluid viscosity-induced velocity dispersion. The analysis of experimental observations of velocity dispersion indicates that (1) the Biot model can explain most of the small discrepancy (about 2–3%) between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids (less than approximately 3 mP·S) and (2) the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model, above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

In‐situ permeability from integrated poroelastic reflection coefficients

A reliable estimate of the in‐situ permeability of a porous layer in the subsurface is extremely difficult to obtain. We have observed that at the field seismic frequency band the poroelastic behavior for different seismic wavetypes can differ in such a way that their combination gives unique estimates of in‐situ permeability and porosity simultaneously. This is utilized in the integration of angle‐ and frequency‐dependent poroelastic reflection coefficients in a cost function. Realistic numerical simulations show that the estimated values of permeability and porosity are robust against uncertainties in the employed poroelastic mechanism and in the data. Potential applications of this approach exist in hydrocarbon exploration, hydrogeology, and geotechnical engineering.

Accurate poststack acoustic-impedance inversion by well-log calibration

The seismic-impedance inversion problem is underconstrained inherently and does not allow the use of rigorous joint inversion. In the absence of a true inverse, a reliable solution free from subjective parameters can be obtained by defining a set of physical constraints that should be satisfied by the resulting images. A method for constructing synthetic logs is proposed that explicitly and accurately satisfies (1) the convolutional equation, (2) time-depth constraints of the seismic data, (3) a background low-frequency model from logs or seismic/geologic interpretation, and (4) spectral amplitudes and geostatistical information from spatially interpolated well logs. The resulting synthetic log sections or volumes are interpretable in standard ways. Unlike broadly used joint-inversion algorithms, the method contains no subjectively selected user parameters, utilizes the log data more completely, and assesses intermediate results. The procedure is simple and tolerant to noise, and it leads to higher-resolution images. Separating the seismic and subseismic frequency bands also simplifies data processing for acoustic-impedance (AI) inversion. For example, zero-phase deconvolution and true-amplitude processing of seismic data are not required and are included automatically in this method. The approach is applicable to 2D and 3D data sets and to multiple pre- and poststack seismic attributes. It has been tested on inversions for AI and true-amplitude reflectivity using 2D synthetic and real-data examples.

Measuring velocity dispersion and attenuation in the exploration seismic frequency band

No perfectly elastic medium exists in the earth. In an anelastic medium, seismic waves are distorted by attenuation and velocity dispersion. Velocity dispersion depends on the petrophysical properties of reservoir rocks, such as porosity, fractures, fluid mobility, and the scale of heterogeneities. However, velocity dispersion usually is neglected in seismic data processing partly because of the insufficiency of observations in the exploration seismic frequency band (∼5 through [Formula: see text]). The feasibility of determining velocity dispersion in this band is investigated. Four methods are used in measuring velocity dispersion from uncorrelated vibrator vertical seismic profile (VSP) data: the moving window crosscorrelation (MWCC) method, instantaneous phase method, time-frequency spectral decomposition method, and cross-spectrum method. The MWCC method is a new method that is satisfactorily robust, accurate, and efficient in measuring the frequency-dependent traveltime in uncorrelated vibrator records. The MWCC method is applied to the uncorrelated vibrator VSP data acquired in the Mallik gas hydrate research well. For the first time, continuous velocity dispersion is observed in the exploration seismic frequency band using uncorrelated vibrator VSP data. The observed velocity dispersion is fitted to a straight line with respect to log frequency to calculate [Formula: see text]. This provides an alternative method for [Formula: see text] measurement.

Transient solution for viscoacoustic wave propagation in a double porosity medium, and its limitations

It is well known that Biot theory (Biot, 1956;1962) of porous-media acoustics ignores all wave-induced flow at mesoscopic scales, i.e. scales greater than the grain size but less that the wavelength. Biot?s theory can not explain high level attenuation observed in natural porous media such as fluid-filled sands or sandstone over the seismic frequency range ( 10- 200 Hz). This attenuation is successfully described by the mesoscopic heterogeneity models (e.g., Gurevich and Lopatnikov, 1995; Gelinksy and Shapiro, 1997; Johnson, 2001). By applying the volume averaging theory to the local Biot poroelastic law, Pride an Berryman (2003a,b) developed the double-porosity, dual permeability (DPDP) model It gives a theoretical framework, including the field equations governing the linear acoustics of composites with two isotropic porous constituents (phase 1 and phase 2), to model acoustic wave propagation through heterogeneous porous structures. Under the assumption that phase 2 is entirely embedded in phase 1, the double-porosity theory is reduced to the effective Biot theory with the complex frequency-dependent elastic moduli in which the internal mesoscopic flow is incorporated. This theory provides good agreement with measurements of attenuation over the seismic and ultrasonic frequency bands (Pride et al., 2004). In this paper, the analytical transient solution and dispersion characteristics for the double-porosity model are obtained over the whole frequency range for a homogeneous medium. A homogeneous poro-viscoacoustic model is constructed and analytically solved to approximate the double porosity model. The comparison between the results of the two models shows the likely validity and limitations of numerical solutions using a poro-viscoacoustic model to represent a double porosity medium in the heterogeneous case. Our calculations show that the dissipation by local mesoscopic flow of the double porosity model is very hard to fit over the entire frequency range by a single Zener element. We choose the relaxation function which just approximates the dispersion behaviour of the double porosity model around the source centre frequency. It is shown that if the frequency is much lower than the peak attenuation frequency of the double porosity model, then wave propagation can be well described by the poro-viscoacoustic model with a single Zener element. For most water-filled sandstones having a double porosity structure, this holds true across the seismic frequency range.

Heavy oils: Their shear story

Heavy oils are important unconventional hydrocarbon resources with huge reserves and are usually exploited through thermal recovery processes. These thermal recovery processes can be monitored using seismic techniques. Shear-wave properties, in particular, are expected to be most sensitive to the changes in the heavy-oil reservoir because heavy oils change from being solid-like at low temperatures to fluid-like at higher temperatures. To understand their behavior, we measure the complex shear modulus (and thus also the attenuation) of a heavy-oil-saturated rock and the oil extracted from it within the seismic frequency band in the laboratory. The modulus and quality factor [Formula: see text] of the heavy-oil-saturated rock show a moderate dependence on frequency, but are strongly influenced by temperature. The shear-wave velocity dispersion in these rocks is significant at steam-flooding temperatures as the oil inside the reservoir losesviscosity. At room temperatures, the extracted heavy oil supports a shear wave, but with increasing temperature, its shear modulus decreases rapidly, which translates to a rapid drop in the shear modulus of the heavy-oil-saturated rock as well. At these low to intermediate temperatures [Formula: see text], an attenuation peak corresponding to the viscous relaxation of the heavy oil is encountered (also resulting in significant shear-wave velocity dispersion, well described by the Cole-Cole model). Thus, shear-wave attenuation in heavy-oil rocks can be significantly large and is caused by both the melting and viscous relaxation of the heavy oil. At yet higher temperatures, the lighter components of the heavy oil are lost, making the oil stiffer and less attenuative. The dramatic changes in shear velocities and attenuation in heavy oils should be clearly visible in multicomponent seismic data, and suggest that these measurements can be qualitatively and quantitatively used in seismic monitoring of thermal recovery processes.

Seismic imaging for seismic geomorphology beyond the seabed: potentials and challenges

Abstract A successful study of seismic geomorphology depends not only on knowledge of sedimentological, geomorphological principles and the local geological setting, but also on quality of the seismic geomorphological imaging. A thorough understanding of how seismic waves respond to geomorphology of depositional sequences and facies is essential prior to developing strategies and selecting tools for field seismic data interpretation. This is especially important in data that are of variable quality or lack marked amplitude anomalies. Studies presented in this paper show that it is more desirable to use stratal slices to display seismic information on geological time surfaces. Multi-slice or movie display of stratal slices is effective for the study of depositional process and is a good quality-control tool for avoiding seismic artifacts. Seismic wavelets adjusted to 90° phase help tie seismic traces to lithofacies with higher stratigraphic resolution. Seismic frequency bands of stratal slices should match the lithofacies thickness of interest for optimal facies imaging. Seismic facies analysis can be improved by automated geomorphological classification.

Wavelet filter analysis of splitting and coupling of seismic normal modes below 1.5 mHz with superconducting gravimeter records after the December 26, 2004 Sumatra earthquake

New generation superconducting gravimeters (SGs), which have been demonstrated to be better than the best seismometers STS-1 at frequencies below 1 mHz, can be accepted as the quietest vertical seismometers for observation of long-period earth free oscillations. Wavelet filtering with narrow band-pass frequency response as shown in this paper is very helpful in removing atmospheric pressure effects from on gravity records in long-period seismic mode frequency bands. The processing of high quality SG records after the great Sumatra earthquake (Dec. 26, 2004) with wavelet filtering leads to clear observations of all coupled toroidal modes below 1.5 mHz except these for 0 T 5, 0 T 7 and 1 T 1 ; moreover 1 T 2 and 1 T 3 are, for the first time, unambiguously revealed in the vertical components of the free oscillations. The three well-resolved splitting singlets of overtones 2 S 1 are observed from a single SG record for the first time.

Numerical Simulation of the Effect of a DC Electric Field on Seismic Wave Propagation with the Pseudospectral Time Domain Method

We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations for the seismic waves and the Maxwell's equations for the electromagnetic waves; the magnitude of the seismoelectric coupling effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave propagation and electric field variation with an existing background DC electric field are compared with the results of a physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band.

Prestack inversion of a Gulf of Thailand (OBC) data set

Seismic waveform inversion can be an important tool for reservoir characterization because high-resolution (within the seismic-frequency band) images of elastic parameters are obtainable from good quality seismic data. A detailed description of the velocity field with both high- and low-frequency variations is essential for delineating elastic properties of the medium for direct detection of hydrocarbon, lithologic discrimination, and estimation of fluid contents. Conventionally, amplitude-variation-with-offset (AVO) analysis determines fractional changes in P-impedance and Poisson's ratio from a linear fit of normal-moveout (NMO) corrected P-reflection amplitude to a two- or three-term approximation of reflection coefficients. Although, AVO analysis gives a useful estimation of elastic properties of the subsurface from AVO attributes, its limitation is well recognized; for example, it deals with “primaries only” models and is inadequate to account for mode-converted waves and internal multiples. In spite of several sources of error (such as random and coherent noise and a 1D earth-model assumption), a prestack seismic waveform inversion is generally desirable for more accurate mapping of the variation of the elastic properties of the subsurface. However, practical implementation of such an inversion scheme on a routine basis becomes discouragingly difficult as (1) the inverse problem is highly nonlinear, (2) the error function (a measure of data misfit in general) possesses multimodality, (3) the inverse problem is extremely computer intensive, and (4) inversion needs better data acquisition systems and data processing steps to preserve true amplitude in order to get precise estimates of elastic properties of the medium. Recently, Sen and Roy (2003) developed a regularized gradient-descent–based waveform inversion algorithm that is highly robust and addresses many of the problems encountered in wavefrom inversion. This paper is a sequel to that paper in that we demonstrate the applicability of the technique to a field data set from a gas field in the Gulf …

The search for the Slichter mode: comparison of noise levels of superconducting gravimeters and investigation of a stacking method

A worldwide network of superconducting gravimeters (SGs) is presently running under the coordination of the Global Geodynamics Project (GGP). SGs have proved in the past to be suited for the study of the long-period seismic and sub-seismic modes. The present paper provides some evidence of these results through the analysis of the noise levels at GGP stations in the seismic and sub-seismic frequency bands and the study of the 2001 M w=8.4 Peru earthquake. The knowledge of the noise level at each station is important in a number of studies that combine the data of several stations to determine global Earth parameters. One example is the stacking of the data in the search for the gravity variations associated with the translational mode of the solid inner core (Slichter mode). Synthetic signals are first used to estimate the possible detection of this degree-one mode with SGs and a stacking method is tested. This method is then applied to the gravity residuals from the GGP records after the Peruvian earthquake.

Frequency‐dependent anisotropy due to meso‐scale fractures in the presence of equant porosity

ABSTRACTFractured 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.

Reflection and transmission responses of a layered isotropic viscoelastic medium

Transmission effects in the overburden are important for amplitude versus offset (AVO) studies and for true‐amplitude imaging of seismic data. Thin layers produce transmission effects which depend on frequency and slowness. We consider an inhomogeneous viscoelastic layered isotropic medium where the parameters depend on depth only. This takes into account both the effects of intrinsic attenuation and the effects of the layering (including changes in attenuation). The seismic wavefield is decomposed into up‐ and downgoing waves scaled with respect to the vertical energy flux. This gives important symmetry relations for the reflection and transmission responses. For a stack of homogeneous layers, the exact reflection response can be computed in a numerically stable way by a simple layer‐recursive algorithm.The reflection and transmission coefficients at a plane interface are functions of the complex medium parameters (depending on frequency) and the real horizontal slowness parameter. Approximations for weak contrast and weak attenuation are derived and compared to the exact values in two numerical examples.We derive first‐order approximations of the PP and SS transmission responses which are direct extensions of the well‐known O'Doherty‐Anstey formula. They consist of a phase shift and attenuation term from direct transmission through the layers and two attenuation terms from backscattered P‐ and S‐waves. The average of these transmission responses may be used for overburden corrections in AVO analysis. The first‐order PP and PS reflection responses have been computed for a stack of very thin layers corresponding to about 2800 m thickness. Because of a lack of data, the intrinsic attenuation was assumed to be constant in the layers. In the seismic frequency band, the intrinsic attenuation dominates the thin‐layer effects. Approximate and exact layer‐recursive modeling of the reflection responses for this layered medium are in good agreement.

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.

Teleseismic travel time residuals in North America and anelasticity of the asthenosphere

The slope a of the relation δ t S= aδ t P+ b for the teleseismic S and P travel time residuals δ t s and δ t p is practically the only robust observational value that is equally sensitive to the lateral S and P velocity variations in the upper mantle. Published estimates of a for North America are about twice higher than those at ultrasonic frequencies in olivine at comparable pressures and temperatures. In our study, lateral variations of the S residuals in North America are found not from the S wave readings, which can be easily biased, but from accurately determined delays relative to P of the Ps phases converted from `410 km' and `660 km' discontinuities. Nevertheless, the estimates of a thus derived are close to the values obtained with the standard technique. The discrepancy between the ultrasonic and seismic estimates of a can be explained by physical velocity dispersion. On the assumption of a single absorption band, our value of a is consistent with the published values of Q in the seismic frequency band and velocities in the ultrasonic range, if the high-frequency cutoff of the absorption band in the upper mantle beneath western North America is on the order of several hundred Hertz. However, in the literature there are indications of a cutoff at around 1 Hz. Then our data imply the presence of another absorption band at high frequencies outside the seismic frequency band. This band may correspond to the viscous dissipation in the Walsh [Walsh, J.B., 1969. A new analysis of attenuation in partially melted rock. J. Geophys. Res., 74, 4333–4337] model of penny-shaped inclusions of melt.

Measuring seismic normal modes with the GWR C021 superconducting gravimeter

In the framework of the global geodynamic project (CGP) that plans to study Earth's normal modes with superconducting gravimeters (SG), we present a study of the C021 SG located in Membach, Belgium, in the seismic normal modes band (periods shorter than 1 h). Our results are based on the spectra associated with the Irian Jaya (February 17, 1996, M W=7.9) and the Baleny Island (March 25, 1998, M W=8.1) earthquakes. We demonstrate that the signal to noise ratio (SNR) of the SG can be improved by a factor of 4 below 1.2 mHz using local barometric records [Zürn, W., Widmer, R., 1995. On noise reduction in vertical seismic records below 2 mHz using local barometric pressure. Geophys. Res. Lett. 22, 3537–3540]. A side-by-side comparison of a long period STS-1 V seismometer with the SG C021 confirms the low noise level of this latter instrument and demonstrates its ability to measure seismic normal modes. Several suggestions are given about the noise sources that could affect SGs in the seismic frequency band.

Imaging complex geologic structure with single‐arrival Kirchhoff prestack depth migration

We compare various forms of single‐arrival Kirchhoff prestack depth migration to a full‐waveform, finite‐difference migration image, using synthetic seismic data generated from the structurally complex 2-D Marmousi velocity model. First‐arrival‐traveltime Kirchhoff migration produces severe artifacts and image contamination in regions of the depth model where significant reflection energy propagates as late or multiple arrivals in the total reflection wavefield. Kirchhoff migrations using maximum‐energy‐arrival traveltime trajectories significantly improve the image in the complex zone of the Marmousi model, but are not as coherent as the finite‐difference migration image. By carefully incorporating continuous phase estimates with the associated maximum‐energy arrival traveltimes, we obtain single‐arrival Kirchhoff images that are similar in quality to the finite‐difference migration image. Furthermore, maximum‐energy Green's function traveltime and phase values calculated within the seismic frequency band give a Kirchhoff image that is (1) far superior to a first‐arrival—based image, (2) much better than the analogous high‐frequency paraxial‐ray Green's function image, and (3) closely matched in quality to the full‐waveform finite‐difference migration image.

Comparative study of superconducting gravimeters and broadband seismometers STS-1 / Z in seismic and subseismic frequency bands

Superconducting gravimeters and broadband seismometers (vertical component) both measure gravity, but whereas the former are most sensitive to very long period signals (gravity tides with periods longer than 6 h), the latter are designed for recording the seismic band (elastic normal modes with periods shorter than 1 h). We investigate here the behaviour of each type of instrument in the spectral band where it is not generally used. More precisely, we compare the French superconducting gravimeter, located at Station J9 near Strasbourg, and the vertical component of an STS-1 seismometer located in a mine at Echery (ECH) in the Vosges, about 70 km away. Two different frequency bands are considered: the seismic band (frequencies between 0.2 and 1.667 mHz), for the study of normal modes after the Bolivian earthquake of 9 June 1994, and the subseismic band (frequencies lower than 0.2 mHz), including the study of gravity tides. The analysis of Fourier amplitude spectra and power spectral densities shows the obvious result that the broadband seismometer is more sensitive than the superconducting gravimeter in the seismic band because of a lower noise level, whereas the reverse is true in the subseismic band. The poorer quality of the gravimeter record in the seismic band is probably due to site effects (sediments vs. bedrock) rather than of instrumental origin. In contrast, the higher noise level of the seismometer in the subseimic band is probably due to the temperature response of the instrument. It is expected that operating the STS-1 isothermally, or recording on-site temperature changes for correction will considerably improve its signal-to-noise ratio in the subseimic band. In comparison with recent mean models of high and low seismic background noise levels, both instruments nevertheless indicate low noise levels at all frequencies.

Changes in attenuation with depth in an ocean carbonate section: Ocean Drilling Program sites 806 and 807, Ontong Java Plateau

Changes of in situ seismic attenuation with depth are estimated from full waveform acoustic logs in a soft formation (rock with shear velocity less than borehole fluid velocity). The relative attenuation Qp−1 is computed from the variation with depth of the P wave amplitude spectrum of a single source receiver pair. The method is applicable when unknown source and receiver responses of the sonic tool make other methods difficult to apply. Tests with synthetic data generated by a full waveform method verify that in a soft formation the decay of the P wave amplitude spectrum depends mainly on attenuation. The method is applied to Ocean Drilling Program data from holes 806B and 807A on the Ontong Java Plateau in the western Pacific Ocean. Four attenuation logs were computed independently using data from four source receiver pairs. Agreement of the four logs at each site and agreement of results from the two sites suggest that the method is robust and practical. The attenuation logs show a maximum attenuation between 300 and 500 m below the seafloor. They agree well with compilations of high‐frequency attenuation versus porosity and frequency in marine sediments but are somewhat greater than results from seismic experiments, possibly owing to the presence of sedimentary microbeds and the three‐decade difference between the seismic and sonic frequency bands.

Maximum energy traveltimes calculated in the seismic frequency band

Prestack Kirchhoff migration using first‐arrival traveltimes has been shown to produce poor images in areas of complex structure. To avoid this problem, I propose a new method for calculating traveltimes that estimates the traveltime of the maximum energy arrival, rather than the first arrival. This method estimates a traveltime that is valid in the seismic frequency band, not the usual high‐frequency approximation. Instead of solving the eikonal equation for the traveltime, I solve the Helmholtz equation to estimate the wavefield for a few frequencies. I then perform a parametric fit to the wavefield to estimate a traveltime, amplitude, and phase. The images created by using these parameters in a Kirchhoff imaging algorithm are comparable in quality to those created using full‐wavefield, finite‐difference, shot‐profile migration.