Anelastic Absorption Research Articles

A workflow for processing mono‐channel Chirp and Boomer surveys

AbstractAcquiring seismic data with multichannel, multiple‐streamer and even multi‐componentsystems at sea provides excellent images of the Earth. However, the cost and complexity of operations prevent their use in busy areas such as ports or in sensitive environments such as lagoons. In the latter cases, mono‐channel Chirp or Boomer systems are the most viable instruments for marine surveys. The lack of multiple offsets prevents the use of standard tools for amplitude‐versus‐offset and velocity analysis, which are necessary for the lithological characterization of rocks, especially for the shallow sediments in offshore engineering. In this paper, we present a few recent techniques that exploit the traveltime and amplitude of multiple reflections to compensate for the offset limitation, including a new algorithm for the joint tomographic inversion of direct arrivals, primaries and multiples. We have developed a cost‐effective workflow for mono‐channel surveys based on a data‐driven, physically consistent philosophy that attempts to approximately extract lithological parameters, such as P velocity, anelastic absorption, acoustic impedance and even density. We applied the proposed workflow to a real field experiment and obtained a semi‐quantitative estimate for shallow sediments that can be used by offshore engineers.

Broadband Q-Factor Imaging for Geofluid Detection in the Gulf of Trieste (Northern Adriatic Sea)

Seismic surveys allow estimating lithological parameters, as P-wave velocity and anelastic absorption, which can detect the presence of fracture and fluids in the geological formations. Recently, a new method has been proposed for high-resolution imaging of anelastic absorption, which combines a macro-model from seismic tomography with a micro-model obtained by the pre-stack depth migration of a seismic attribute, i.e., the instantaneous frequency. As a result, we can get a broadband image that provides clues about the presence of saturating fluids. When the saturation changes sharply, as for gas reservoirs with an impermeable caprock, the acoustic impedance contrast produces “bright spots” because of the resulting high reflectivity at its top. When the fluid content changes smoothly, the anelastic absorption becomes a good detector, as fluid-filled formations absorb more seismic energy than hard rocks. We apply this method for imaging the anelastic absorption in a regional seismic survey acquired by OGS in the Gulf of Trieste (northern Adriatic Sea, Italy).

Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

ABSTRACTThe subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q‐compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non‐stationary sparse reflectivity inversion, we evaluate a series of methods for Q‐compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q‐compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two‐phase Q‐compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q‐filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over‐determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion‐based Q estimation method handles the wave‐interference effects better than conventional spectral‐ratio‐based methods. For Q‐compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q‐compensation without knowing Q but with wavelet given.

Broadband Q-factor tomography for reservoir monitoring

Time-lapse analysis of seismic surveys to monitor hydrocarbon production has been based so far mainly on amplitude and traveltime changes of seismic signals. However, lab measurements of rock properties show that we can also expect observable changes in the anelastic absorption, when the originally saturating fluids are replaced by others, or even when compaction or fractures are induced. These changes can be detected by Q-factor reflection tomography and used for time-lapse analysis, as a complement to traveltime inversion. Indeed, the seismic signal change due to fluid substitution is observable both in P velocity and Q factor estimates, and from case to case one can be stronger than the other. Their coupled inversion reduces the uncertainties for interpreters involved in reservoir characterization, providing them more information for detecting different lithotypes. The time-lapse tomography we adopted limits the variations of P velocity and Q factor away from the reservoir, and imposes that the interfaces' structure is the same in those external areas. The mismatch between actual and estimated models decreases significantly when these mutual constraints are applied, with respect to an uncoupled inversion where both rock parameters and interfaces' structures are inverted in a totally independent way.The resolution needed for reservoir monitoring is high, so a macro-model analysis, as provided by traveltime inversion or the frequency shift method for the Q factor, is not sufficient. However, those estimates may be complemented with a high-frequency component obtained by the instantaneous frequency. The resulting broadband image in depth for the anelastic absorption may approximate results typical of full-waveform inversion, but at a much cheaper computational cost.

Grain size‐sensitive viscoelastic relaxation and seismic properties of polycrystalline MgO

AbstractTorsional forced‐oscillation experiments on a suite of synthetic MgO polycrystals, of high‐purity and average grain sizes of 1–100 µm, reveal strongly viscoelastic behavior at temperatures of 800–1300°C and periods between 1 and 1000 s. The measured shear modulus and associated strain energy dissipation both display monotonic variations with oscillation period, temperature, and grain size. The data for the specimens of intermediate grain size have been fitted to a generalized Burgers creep function model that is also broadly consistent with the results for the most coarse‐grained specimen. The mild grain size sensitivity for the relaxation time τL, defining the lower end of the anelastic absorption band, is consistent with the onset of elastically accommodated grain boundary sliding. The upper end of the anelastic absorption band, evident in the highest‐temperature data for one specimen only, is associated with the Maxwell relaxation time τM marking the transition toward viscous behavior, conventionally ascribed a stronger grain size sensitivity. Similarly pronounced viscoelastic behavior was observed in complementary torsional microcreep tests, which confirm that the nonelastic strains are mainly recoverable, i.e., anelastic. With an estimated activation volume for the viscoelastic relaxation, the experimentally constrained Burgers model has been extrapolated to the conditions of pressure and temperature prevailing in the Earth's uppermost lower mantle. For a plausible grain size of 10 mm, the predicted dissipation Q−1 ranges from ~10−3 to ~10−2 for periods of 3–3000 s. Broad consistency with seismological observations suggests that the lower mantle ferropericlase phase might account for much of its observed attenuation.

A novel nonstationary deconvolution method based on spectral modeling and variable-step sampling hyperbolic smoothing

Abstract Deconvolution is an important part of seismic processing tool for improving the resolution. One of the key assumptions made in most deconvolutional methods is that the seismic data is stationary. However, due to the anelastic absorption, the seismic data is usually nonstationary. In this paper, a novel nonstationary deconvolution approach is proposed based on spectral modeling and variable-step sampling (VSS) hyperbolic smoothing. To facilitate our method, firstly, we apply the Gabor transform to perform a time-frequency decomposition of the nonstationary seismic trace. Secondly, we estimate the source wavelet amplitude spectrum by spectral modeling. Thirdly, smoothing the Gabor magnitude spectrum of seismic data along hyperbolic paths with VSS can obtain the magnitude of the attenuation function, and can also eliminate the effect of source wavelet. Fourthly, by assuming that the source wavelet and attenuation function are minimum phase, their phases can be determined by Hilbert transform. Finally, the estimated two factors are removed by dividing them into the Gabor spectrum of the trace to estimate the Gabor spectrum of the reflectivity. An inverse Gabor transform gives the time-domain reflectivity estimate. Tests on synthetic and field data show that the presented method is an effective tool that not only has the advantages of stationary deconvolution, but also can compensate for the energy absorption, without knowing or estimating the quality factor Q.

Physical mechanism of seismic attenuation in a two-phase medium

High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results from the interference of elastic microscopic multiple scattering waves. First, I propose a new theory on wave propagation in a two-phase medium which is based on the concept that the basic unit for wave propagation is a nano-mass point. As a result of the elasticity variations of pore fluid and rock framework, micro multiple scattering waves would emerge at the wavelength of the seismic waves passing through the two-phase medium and their interference and overlap would generate high-frequency seismic attenuation. Second, I present a study of the frequency response of seismic transmitted waves by modeling thin-layers with thicknesses no larger than pore diameters. Results indicate that high-frequency seismic waves attenuate slightly in a near-surface water zone but decay significantly in a near-surface gas zone. Third, I analyze the seismic attenuation characteristics in near-surface water and gas zones using dual-well shots in the Songliao Basin, and demonstrate that the high-frequency seismic waves attenuate slightly in water zones but in gas zones the 160–1600 Hz propagating waves decay significantly. The seismic attenuation characteristics from field observations coincide with the modeling results. Conclusions drawn from these studies theoretically support seismic attenuation recovery.

Observations of scattering attenuation in the Earth and implications for Q

Seismologists often attribute the attenuation of a transmitted seismic pulse to anelastic absorption or Q. Real data suggests a different dominant mechanism. The earth, particularly in sedimentary basins, is heterogeneous on all scales. This heterogeneity results in a transmitted pulse being attenuated by scattering at every boundary it encounters. Theoretical models proposed by Zien and Shapiro (1994) suggest that scattering attenuation is angle dependent, but not necessarily frequency dependent, at least for short propagation distances. In this paper we review the mechanisms for transmitted pulse attenuation both scattering- and absorption-based. We then analyze real data and compare the contributions of these mechanisms to the observed attenuation.

Numerical modeling for design of viscoelastic coatings with favorable sound absorbing properties

A thin rubber layer with cavities can be used to redistribute normally incident sound in the transverse direction, where it suffers losses by anelastic absorption. This is the basis for an old idea for anechoic submarine coatings. In this paper, modern techniques for electron scattering and band gap computations for photonic and phononic crystals are adapted to model the anechoic effect numerically. Reflection and transmission matrices are computed recursively, from basic ones for layers containing periodic arrays of cavities. The shear and viscoelastic properties of the rubber material turn out to be crucial, and multiple scattering among the cavities cannot be ignored. The reflectivity of a multilayered fluid–solid structure will depend in a nonlinear way on the geometry and the material parameters. Two different techniques are used to design coatings with favorable sound absorbing properties. The first one is based on analyticity of the reflectivity as a function of the complex shear wave velocity of the rubber material, and winding-number methods are applied. With appropriately implemented error control, the existence of thin coatings with zero reflectivity at a specified frequency is actually proved. To achieve low reflectivity within a broad frequency band, however, different techniques are needed, and genetic algorithms are applied.

Strong crustal heterogeneity in the Bolivian Altiplano as suggested by attenuation of Lg waves

Using the seismological data of four temporary networks installed across the Andes of Bolivia and Chile between 1990 and 1995, we study the amplitudes of the Lg phase for 45 regional events located at crustal depths. This analysis reveals that Lg is strongly attenuated for most of the ray paths crossing the Altiplano independent of the azimuth of propagation. To map the anomalies and evaluate their frequency dependence, we conduct a regionalization of the crustal average Qs factor using a damped least squares inversion technique in the frequency range 0.6–5 Hz. The resulting maps delineate regions with contrasting values of apparent attenuation. The Altiplano is characterized by strong attenuation with an average Qs of 100 at 1 Hz, whereas the Cordilleras are regions of weaker attenuation. The frequency dependence of Qs is investigated in an attempt to separate the source of the apparent attenuation into scattering and anelastic absorption. Within the hypothesis of a weak frequency dependence of the intrinsic Q, we show that at 1 Hz, scattering plays a major part in the attenuation of Lg waves whereas at 4 Hz, both mechanisms are of equal importance. These results indicate that the attenuation of Lg waves in the Altiplano is due more to scattering by small‐scale heterogeneities than to a high percentage (>1%) of partial melt involving a large part of the crust.

Physical description ofLgwaves in inhomogeneous continental crust

The view of Lg waves as a superposition of seismic surface waves is very useful for explaining the amplitudes of the late parts of seismograms from regional earthquakes. We have recently made computations for Rayleigh waves, interpreting the special attenuation of Lg waves in the North Sea as being caused by (1) the distribution of energy over longer time intervals, combined with (2) the upwards or downwards pumping of wave energy in the different crustal structures, combined with (3) anelastic absorption. No special discussion is necessary of the claim that anelastic absorption in a particular area gives a reduction in wave amplitude, whilst a physical description of the geometrical effect is warranted. A physical description of the wave propagation phenomena involved is given in the present paper by classifying the mode conversion that is involved in the propagation from one crustal structure into another. The physics is described via relations between the phase velocities, group velocities and energy dependences on depths of the various surface wave modes that exist in the different crustal structures. We introduce the concept of energy-depth similarity, a parameter that is almost as easily computed as the ratios of phase velocities or group velocities, but is a far better measure of the transition character. The crustal structures in question are representative of (1) the North Sea and its surroundings in general, and (2) the Viking and Central grabens in the middle of the North Sea. Wave propagation is fundamentally different for different wave frequencies; it is coherent for long-period waves and incoherent for short-period waves. The propagation may generally be termed well-behaved for wave periods longer than several seconds; that is, energy cross-coupling between incoming and outgoing modes follows some regular pattern. This regularity is highly dependent on the similarity of the two modes on either side of a discontinuity, and also on the similarity of their neighbouring modes. A characteristic of the regularity is that there is no mode conversion for very long-period modes. In contrast, a pattern cannot be recognized for waves of shorter period, and one may use the term ill-behaved. The Lg waves in the continental crust are in the short-period range because their wavelengths are short compared to thickness changes as well as to the thicknesses of crustal structures. This leads to the view that Lg waves are superpositions of many modes, changing into even more modes at any discontinuity. Since Rayleigh and Love waves are coupled at non-perpendicular incidence and the Earth has many discontinuities, the superposition of modes is constantly changing in relative proportions, Rayleigh and Love modes being intermingled.

Verification and refinement of spectral magnitude calibrating functions for P-waves

Calibrating functions for determination of P-wave spectral magnitudes calculated by Duda and Yanovskaya (1994) on the basis of the IASP91 velocity model and the PREM Q-model are verified empirically. For this purpose IRIS broadband records for 120 earthquakes are used, each earthquake having been recorded at about 100 stations. The discrepancies indicate that anelastic absorption assumed in PREM is too high. New calibrating functions are calculated on the basis of the AK135 velocity and anelasticity models (Kennet et al., 1995; Montagner and Kennet, 1996), in which Q in the mantle is higher than in PREM. The verification of the new calibrating functions based on the same observations yields magnitude figures less depending on the epicentral distance. In addition the parameter τ2in the Liu-Anderson Q(T) model is estimated, proceeding from the assumption that on the average the radiated spectra comply with the ω2-model. The value of τ2 was assumed to be 0.1 s in the analysis and its use resulted in the verification of the ω2-model for the source spectrum.

Seismic energies of earthquakes and relationships to other source parameters

An advanced method is presented to calculate the energy of teleseismic events by integrating the power spectra of P-and S-waves. The algorithm takes into account proper corrections for radiation pattern and anelastic absorption in the mantle. From theoretical considerations, near-field source spectra and the partitioning of P-and S-wave energy a frequency-dependent Q(ω)-model was derived. It is a combination of a global frequency-independent Q( z)-model developed by Anderson and Hart (1978a, 1978b) and a power law for frequency with exponent γ = 0.23 at a reference frequency f 0 = 0.1 Hz. The method was applied to shallow and deep earthquakes in Tonga-Fiji, Vanatu and the New Britain region, recorded by broadband stations of the GEOSCOPE network. The resulting energies are compared with m b, M s and the seismic moments M 0 of each event. In addition, 9 events at the Honshu and Kuriles subduction zone, recorded at the Gräfenberg array, were investigated and apparent stresses were computed from energy and seismic moment. The results suggest a systematic increase of apparent stress with depth of the subducted lithosphere, starting from approximately 20 bars for shallow events to 250 bars for depths of 200–300 km. The two lowermost events (500–600 km) show a decrease of apparent stress down to 2–15 bar.

Rayleigh waves in Quaternary alluvium from explosive sources: Determination of shear-wave velocity and Q structure

Surface-wave propagation in unconsolidated Quaternary alluvium has been investigated within the valley of the Chiusi Lake tributary (Central Italy). The seismic experiment was originally designed to determine the structural response of an Etruscan tomb to a 200-kg dynamite shot, planned as part of a refraction survey within the CROP-DSS (an Italian project for the investigation of deep crustal structures). The availability of many recording instruments allowed us to design a more complete experiment, and we decided to use surface waves generated by a small explosion (10 kg dynamite) to infer the shear-wave-velocity-attenuation model in the alluvium layer. We deployed a linear array aligned with the shot point on the river sediments. Sixteen digital, three-component recording stations were used; the minimum distance from the source was 1.9 km, and we chose an interstation separation of 50 m, for a total array length of 750 m. Clear Rayleigh waves were recorded along the array, and we were able to recognize two propagating modes in the waveforms. We calculated the dispersion curves of group velocities using a multiple filter technique. Dispersion curves of phase velocities were calculated using a p -ω stacking technique. The whole procedure was run as follows: (1) the inversion of the group-velocity dispersion; (2) the use of synthetic seismograms for mode recognition; (3) the extraction and the inversion of phase-velocity values from the p -ω stack performed on the observed waveforms; (4) the use of a trial-and-error approach for Qβ to obtain “good” synthetic waveforms; and (5) the application of a conjugate gradient inversion technique to the anelastic absorption model (no inversion was run on γ dispersion curves). Values of Qβ of ranging from 2 to 20, and a shear-wave velocity in the range 280 < β < 400 m/sec were found in the Holocene alluvium. Moreover, in our modeling we used the relation Qα = Qβ for unconsolidated, water-saturated sediments. Our results suggest that surface waves generated by explosions can be successfully used to determine shear-wave-velocity and attenuation models in soft sediment coverages.

Tidal variations in the rotation rate of an anelastic Earth

Based on the principles of numerical perturbation of Love and loading Love numbers and using the theoretical Chandler wobble period as a constraint in estimating the parameters of the anelastic absorption band model, the direct effect of anelasticity of the mantle on the effective Love number k and the indirect perturbation generated by the response of anelastic Earth to the equilibrium tides are discussed and their effect on the zonal harmonic tide scale factor k C , analysed. A tidal variation series in the universal time UT1 is accordingly defined for an Earth with dynamical tides, an anelastic mantle and a liquid core. When compared to the results of the new astronomical techniques, a good agreement is found for the higher frequencies. There is a notable effect of dispersion in the low-frequency terms, but it cannot be reliably detected with present observational data.

Thin crustal layering in Northern France: observations and modelling of thePMPspectral content

SUMMARY variations in spectral content of the P,P seismic phase (the P-wave reflected on the Moho) are investigated using refraction data collected along the North of France ECORS profile for offsets ranging from 60 to 110 km. The low-frequency component of the PMP (10-15 Hz) shows the usual increase in amplitude beyond the critical distance (90 km). An anomalous attenuation of post-critical amplitudes, however, occurs in the high-frequency part of the reflection. This frequency-selective attenuation characterizes the transmission through the reflective deep crust since it does not affect waves reflected from above. Synthetic seismograms are computed to investigate the influence on the spectral content of the Moho reflection of both thin lamellae and anelastic dissipation within the lower crust. They show that a cyclic repetition of thin low- and high-velocity layers efficiently removes high frequencies from the post-critical part of the PMP. A good fit to the observed rapid decrease in amplitude between 15 and 20 Hz requires: (i) sufficient impedance contrasts between highand low-velocity layers (>0.10), (ii) velocities alternating rapidly from high to low values, (iii) low velocities in the range 5.8-6.7 km s-l and high velocities in the range 7.0-7.6 km s-l (iv) thicknesses in the range 80-200 m. The observed frequency-selective attenuation supports the hypothesis of a layered structure of the lower crust. The constraint placed upon impedance contrasts favours a magmatic origin of the lamellae rather than a purely tectonic origin. The frequency-selective attenuation can also be accounted for by anelastic absorption. The required intrinsic Q is found to be 200 for the whole lower crust. Such a low value would imply the presence of pore fluids. However scattering due to thin layering is believed to play a great part in the observed attenuation since it also explains the high reflectivity of the lower crust pointed out by vertical seismics in the southern part of the profile.

Statistical Modelling of Lower-Crustal Reflections

For a geological feature to be resolved in a seismic reflection profile its size must be comparable with the dimensions of the Fresnel zone for its depth and the frequency-content of the seismic wavefield. Since the diameter of the Fresnel zone is over 5 km for lower-crustal reflections, the effects of variations of the crust on smaller length scales must be considered when interpreting deep reflection, profiles. Modelling the seismic wavefield using first-order scattering theory shows how the reflections observed in a small-offset profile are affected by the statistical distribution of elastic variations within the crust. Crustal heterogeneities on length-scales smaller than the seismic wavelength cause frequency-dependent attenuation which can be comparable with the losses due to anelastic absorption. Larger scale elastic variations cause rapid loss of coherence in the seismic field. The observation of deep seismic reflections can thus be used to constrain the degree to which the crustal elasticity varies on small length scales. Coherent seismic reflections from the lower crust limit the fractional variation of elasticity averaged over the entire crust to a few percent on a wide range of length-scales.

Dephasing of Seismic Sections

A perennial problem in the processing and interpretation of seismic data from the Cooper?Eromanga Basin is the estimation and subsequent removal of the wavelet phase. There are many non-geological factors such as vibrator coupling, geophone characteristics, anelastic absorption, instrument response and processing sequence which affect the wavelet phase.

Coda wave analysis for distinguishing attenuation due to isotropic scattering from attenuation due to absorption

When the quality factorQ is taken into account in attenuation studies, it is necessary to know the relative losses of wave energy due to scattering and to anelastic absorption. The coda is the most important phenomenon now known which is related to elastic scattering of seismic waves. Utilizing coda, this study presents relationships which give theQ factors of the medium around the recording station and discriminate between attenuations arising from elastic scattering (under the assumption of isotropic scattering) and those arising from anelastic absorption. This work proposes a technique for separately determining the attenuation due to isotropic scattering and that due to absorption from the observed envelope of coda waves.

Optical and Anelastic Absorptions and Resonator Frequency of Electron-Irradiated Quartz

For quartz resonators, optical (infrared, visible and ultra-violet) absorptions, anelastic absorptions and resonant frequencies were measured as functions of electron fluence. The data obtained nearly support King's equation of the frequency change and anelastic absorption, and also support a proposal by King et al. that the color center raises anelastic absorption at 100 K. It is very likely that, in the case of natural quartz, increase of anelastic absorption at 100 K, increase of the coloration intensity and decrease of infrared absorptions originating from Li+ and H+ ions are introduced by the detachment of Li+ and H+ ions from [AlO4]- centers, while in the coloration the synthetic quartz results from the detachment of alkali ions from [AlO4]- centers. The infrared absorption data show that complicated trapping and detrapping of H+ and alkali ions are occurring among various defects in both kinds of quartz during irradiation.