利用基于子波估计的频谱校正方法提高Q值估计精度(英文)

用Q值刻画的地震衰减在地震信号处理和解释中具有很广泛的应用。利用反射地震资料进行Q值估计需要解决地震子波和反射系数序列耦合的问题。从反射地震资料中去除反射系数序列的影响,这个过程称为频谱校正。本文提出了一种基于子波估计的求取Q值的方法,进而设计了一个反Q滤波器。该方法利用反射地震资料的高阶统计量进行子波估计,并利用所估计子波实现频谱校正。我们利用合成数据实验给出了质心频移法与频谱比法这两种常用的Q值估计方法在不同参数设置下的性能。人工合成数据和实际数据处理表明,利用本文提出的方法进行频谱校正后,可以得到可靠的Q值估计。经过反Q滤波,地震数据的高频部分得到了有效地恢复。     

Attenuative Dispersion of <Emphasis Type="Italic">P</Emphasis> Waves and Crustal <Emphasis Type="Italic">Q</Emphasis> in Turkey and Germany

We have measured group delays of the spectral components of high-frequency P-waves along two portions of the North Anatolian Fault Zone (NAFZ) in Turkey and in a region of southern Germany. Assuming that the observed dispersion is associated with attenuation in the crust and that it can be described by a continuous relaxation model, we obtained Q and the high-frequency relaxation times for those waves for each of the three regions. Individual P-wave Q values exhibit large scatter, but mean values in the NAFZ increase from about 25 to 60 over the distance range 5–90 km. Mean Q values are somewhat higher in the eastern portion of the NAFZ than in the western portion for measurements made at distances between 10 and 30 km. P-wave Q values in Germany range between about 50 and 300 over the hypocentral distance range 20–130 km. In that region we separated the effects of Q for basement rock (2–10 km depth) from that of the overlying sediment (0–2 km depth) using a least-squares method. Q varies between 100 and 500 in the upper 8–10 km of basement, with mean values for most of the distance range being about 250. Q in the overlying sediments ranges between 6 and 10. Because of large scatter in the Q determinations we investigated possible effects that variations of the source-time function of the earthquakes and truncation of the waveform may have on Q determinations. All of our studies indicate that measurement errors are relatively large and suggest that useful application of the method requires many observations, and that the method will be most useful in regions where the number of oscillations following the initial P pulse is minimized. Even though there is large scatter in our Q determinations, the mean values that we obtained in Turkey are consistent with those found in earlier studies. Our conclusions that Q is significantly higher in the basement rock of Germany than in the basement rock of Turkey and that Q is lower in western Turkey than in eastern Turkey are also consistent with results of Q studies using Lg coda.     

Borehole study of compressional and shear attenuation of basalt flows penetrated by the Brugdan and William wells on the Faroes shelf

We investigated the seismic attenuation of compressional (P‐) and converted shear (S‐) waves through stacked basalt flows using short‐offset vertical seismic profile (VSP) recordings from the Brugdan (6104/21–1) and William (6005/13–1A) wells in the Faroe‐Shetland Trough. The seismic quality factors (Q) were evaluated with the classical spectral ratio method and a root‐mean‐square time‐domain amplitude technique. We found the latter method showed more robust results when analysing signals within the basalt sequence. For the Brugdan well we calculated effective Q estimates of 22–26 and 13–17 for P‐ and S‐waves, respectively, and 25–33 for P‐waves in the William well. An effective Q_S/Q_P ratio of 0.50–0.77 was found from a depth interval in the basalt flow sequence where we expect fully saturated rocks. P‐wave quality factor estimates are consistent with results from other VSP experiments in the North Atlantic Margin, while the S‐wave quality factor is one of the first estimates from a stacked basalt formation using VSP data. Synthetic modelling demonstrates that seismic attenuation for P‐ and S‐waves in the stacked basalt flow sequence is mainly caused by one‐dimensional scattering, while intrinsic absorption is small.     

Attenuation of coda waves and Q c value beneath the Chengdu telemetered seismic network

Based on the single scattering model of coda power spectrum analysis, digital waveform data of 50 events recorded by the real-time processing system of the Chengdu telemetry network are analyzed to estimate the Q _c values of earth medium beneath the Chengdu telemetry network for several specified frequencies. It is found that the Q _c shows the frequency dependency in the form of Q _c = Q ₀ f ⁿ in the range of 1.0 to 20.0Hz. Estimated Q ₀ ranges from 60.83 to 178.05, and n is found to be 0.713 to 1.159. The average value of Q ₀ and n are 117 and 0.978 respectively. This result indicates the strong frequency dependency of the attenuation of coda waves beneath the Chengdu telemetry network. Comparing with the results obtained in other regions of the world, it is found that Q ₀ ⁻¹ value and its change with frequency are similar to those in regions with strong tectonic activity. This subject is supported by the Ministry of Personnel, China for partly sponsoring.     

The estimation of spectra from time‐frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.     

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

The 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.     

Causes of systematic over‐ or underestimation of low streamflows by use of index‐streamgage approaches in the United States

Low‐flow characteristics can be estimated by multiple linear regressions or the index‐streamgage approach. The latter transfers streamflow information from a hydrologically similar, continuously gaged basin (‘index streamgage’) to one with a very limited streamflow record, but often results in biased estimates. The application of the index‐streamgage approach can be generalized into three steps: (1) selection of streamflow information of interest, (2) definition of hydrologic similarity and selection of index streamgage, and (3) application of an information‐transfer approach. Here, we explore the effects of (1) the range of streamflow values, (2) the areal density of streamgages, and (3) index‐streamgage selection criteria on the bias of three information‐transfer approaches on estimates of the 7‐day, 10‐year minimum streamflow (Q_{7, 10}). The three information‐transfer approaches considered are maintenance of variance extension, base‐flow correlation, and ratio of measured to concurrent gaged streamflow (Q‐ratio invariance). Our results for 1120 streamgages throughout the United States suggest that only a small portion of the total bias in estimated streamflow values is explained by the areal density of the streamgages and the hydrologic similarity between the two basins. However, restricting the range of streamflow values used in the index‐streamgage approach reduces the bias of estimated Q_{7, 10} values substantially. Importantly, estimated Q_{7, 10} values are heavily biased when the observed Q_{7, 10} values are near zero. Results of the analysis also showed that Q_{7, 10} estimates from two of the three index‐streamgage approaches have lower root‐mean‐square error values than estimates derived from multiple regressions for the large regions considered in this study. Published in 2011 by John Wiley & Sons, Ltd.     

Building and Testing an <Emphasis Type="Italic">a priori</Emphasis> Geophysical Model for Western Eurasia and North Africa

We construct and evaluate a new three-dimensional model of crust and upper mantle structure in Western Eurasia and North Africa (WENA) extending to 700 km depth and having 1° parameterization. The model is compiled in an a priori fashion entirely from existing geophysical literature, specifically, combining two regionalized crustal models with a high-resolution global sediment model and a global upper mantle model. The resulting WENA1.0 model consists of 24 layers: water, three sediment layers, upper, middle, and lower crust, uppermost mantle, and 16 additional upper mantle layers. Each of the layers is specified by its depth, compressional and shear velocity, density, and attenuation (quality factors, Q _P and Q _S ). The model is tested by comparing the model predictions with geophysical observations including: crustal thickness, surface wave group and phase velocities, upper mantle _n velocities, receiver functions, P-wave travel times, waveform characteristics, regional 1-D velocities, and Bouguer gravity. We find generally good agreement between WENA1.0 model predictions and empirical observations for a wide variety of independent data sets. We believe this model is representative of our current knowledge of crust and upper mantle structure in the WENA region and can successfully be used to model the propagation characteristics of regional seismic waveform data. The WENA1.0 model will continue to evolve as new data are incorporated into future validations and any new deficiencies in the model are identified. Eventually this a priori model will serve as the initial starting model for a multiple data set tomographic inversion for structure of the Eurasian continent.     

Updating estimates of low-streamflow statistics to account for possible trends

ABSTRACT

Accurate estimators of streamflow statistics are critical to the design, planning, and management of water resources. Given increasing evidence of trends in low-streamflow, new approaches to estimating low-streamflow statistics are needed. Here we investigate simple approaches to select a recent subset of the low-flow record to update the commonly used statistic of 7Q10, the annual minimum 7-day streamflow exceeded in 9 out of 10 years on average. Informed by low-streamflow records at 174 US Geological Survey streamgages, Monte Carlo simulation experiments evaluate competing approaches. We find that a strategy which estimates 7Q10 using the most recent 30 years of record when a trend is detected, reduces error and bias in 7Q10 estimators compared to use of the full record. This simple rule-based approach has potential as the basis for a framework for updating frequency-based statistics in the context of possible trends.     

Multiwell study of seismic attenuation at the CO2CRC Otway project geosequestration site: Comparison of amplitude decay,centroid frequency shift and 1D waveform inversion methods

At the CO2CRC Otway geosequestration site, the abundance of borehole seismic and logging data provides a unique opportunity to compare techniques of Q (measure of attenuation) estimation and validate their reliability. Specifically, we test conventional time-domain amplitude decay and spectral-domain centroid frequency shift methods versus the 1D waveform inversion constrained by well logs on a set of zero-offset vertical seismic profiles. The amplitude decay and centroid frequency shift methods of Q estimation assume that a seismic pulse propagates in a homogeneous medium and ignore the interference of the propagating wave with short-period multiples. The waveform inversion explicitly models multiple scattering and interference on a stack of thin layers using high-resolution data from sonic and density logs. This allows for stable Q estimation in small depth windows (in this study, 150 m), and separation of the frequency-dependent layer-induced scattering from intrinsic absorption. Besides, the inversion takes into account band-limited nature of seismic data, and thus, it is less dependent on the operating frequency bandwidth than on the other methods. However, all considered methods of Q estimation are unreliable in the intervals where subsurface significantly deviates from 1D geometry. At the Otway site, the attenuation estimates are distorted by sub-vertical faults close to the boreholes. Analysis of repeated vertical seismic profiles reveals that 15 kt injection of the CO₂-rich fluid into a thin saline aquifer at 1.5 km depth does not induce detectable absorption of P-waves at generated frequencies 5–150 Hz, most likely because the CO₂ plume in the monitoring well is thin, <15 m. At the Otway research site, strong attenuation Q ≈ 30–50 is observed only in shaly formations (Skull Creek Mudstone, Belfast Mudstone). Layer-induced scattering attenuation is negligible except for a few intervals, namely 500–650 m from the surface, and near the injection interval, at around 1400–1550 m, where Q_scat ≈ 50–65.     

Inversion of source parameters and attenuation of the Tangshan aftershocks

Source parameters and characteristics of regional attenuation of Tangshan aftershocks are studied by using digital records of Tangshan aftershocks. An inversion method of P wave spectra to reduce influence on the ambiguity in the estimates of parameters by the usual spectrum analysis method is developed. By testing with digital simulation data and applying to actual data, it is confirmed that the method is usable. Source parameters of the Tangshan Luanxian area are obtained by using records of 35 earthquakes at 5 stations.Q values of P wave and high frequency decay rate γ of source spectrum at 5 stations are obtained. TheQ values range from 408 to 847, and the mean value is 520; whiley ranges from 1.54 to 3.22, and the mean value is 2.41. In the studies of spectra of the micro-earthquakes in the Luanxian area, that stress drop increases with increasing earthquake moment is found. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 430–441, 1991.     

Q estimation based on the centroid frequency and standard deviation of frequency-weighted-exponential function

The quality factor Q is a vital parameter for quantitatively describing the attenuation information of underground reservoirs, which is of great significance for hydrocarbon detection and reservoir characterization. A frequency-weighted-exponential (FWE) method utilizing the symmetry index and the characteristic frequency can obtain this parameter. Unfortunately, the constant symmetry index assumption of it reduces the accuracy of Q values under the non-standard FWE shape. Selecting an optimal symmetry index is also a problem for this method. Hence, the basic idea of a novel Q estimation method is to substitute the symmetry index with the standard deviation of the source and attenuated wavelet spectrums. The added standard deviation varies with the degree of attenuation under different wavelet shapes, which can reduce the effects of the constant assumption. Meanwhile, it is simple to calculate this parameter directly from the spectrums. In this way, the proposed method has wider applicability to various wavelets. The synthetic records show the better performance of the novel method in improving the accuracy of Q values and the resistance to random noise than the FWE method. Furthermore, the results of matching wavelets exhibit the applicability of the proposed method in real data, and the quadratic spectrum simulation method improves the stability of the spectrums. Finally, real data experiments indicate the effectiveness of the proposed method after the above two processing means.     

Construction of constant-Q viscoelastic mode with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor （Q） and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

Attenuation of short period seismic waves at Etna as compared to other volcanic areas

CodaQ for Etna volcano is frequency dependent and theQ frequency pattern and the numerical values ranging from about 100 at 1 Hz to about 300 at 18 Hz are similar to the values obtained for other volcanoes: Campi Flegrei, Aeolian Islands and Hawaii. Moreover the frequency pattern and the numerical values of coda quality factor, for most of the seismically active zones of Italy are very different from those of the volcanic zones.Several studies of the location of magma chambers show the presence of magma pockets beneath Lipari and Vulcano Islands of the Aeolian archipelago and an anomalous low velocity body beneath Etna. These evidences suggest that a possible interpretation of the characteristic frequency pattern ofQ on volcanic areas is that the presence of magma can modify the scattering environment and consequently the codaQ estimates.     

An efficient and self‐adaptive approach for Q value optimization

The time‐invariant gain‐limit‐constrained inverse Q‐filter can control the numerical instability of the inverse Q‐filter, but it often suppresses the high frequencies at later times and reduces the seismic resolution. To improve the seismic resolution and obtain high‐quality seismic data, we propose a self‐adaptive approach to optimize the Q value for the inverse Q‐filter amplitude compensation. The optimized Q value is self‐adaptive to the cutoff frequency of the effective frequency band for the seismic data, the gain limit of the inverse Q‐filter amplitude compensation, the inverse Q‐filter amplitude compensation function, and the medium quality factor. In the processing of the inverse Q‐filter amplitude compensation, the optimized Q value, corresponding gain limit, and amplitude compensation function are used simultaneously; then, the energy in the effective frequency band for the seismic data can be recovered, and the seismic resolution can be enhanced at all times. Furthermore, the small gain limit or time‐variant bandpass filter after the inverse Q‐filter amplitude compensation is considered to control the signal‐to‐noise ratio, and the time‐variant bandpass filter is based on the cutoff frequency of the effective frequency band for the seismic data. Synthetic and real data examples demonstrate that the self‐adaptive approach for Q value optimization is efficient, and the inverse Q‐filter amplitude compensation with the optimized Q value produces high‐resolution and low‐noise seismic data.     

Dispersion Measurements of <Emphasis Type="Italic">P</Emphasis> Waves and their Implications for Mantle <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We analyze the anelasticity of the earth using group delays of P-body waves of deep (>200 km) events in the period range 4–32 s for epicentral distances of 5–85 degrees. We show that Time Frequency Analysis (TFA), which is usually applied to very dispersive surface waves, can be applied to the much less dispersive P-body waves to measure frequency-dependent group delays with respect to arrival times predicted from the CMT centroid location and PREM reference model. We find that the measured dispersion is due to: (1) anelasticity (described by the P-wave quality factor Q _p ), (2) ambient noise, which results in randomly distributed noise in the dispersion measurements, (3) interference with other phases (triplications, crustal reverberations, conversions at deep mantle boundaries), for which the total dispersion depends on the amplitude and time separation between the different phases, and (4) the source time function, which is dispersive when the wavelet is asymmetrical or contains subevents. These mechanisms yield dispersion ranging in the order of one to 10 seconds with anelasticity responsible for the more modest dispersion. We select 150 seismograms which all have small coda amplitudes extending to ten percent of the main arrival, minimizing the effect of interference. The main P waves have short durations, minimizing effects of the source. We construct a two-layer model of Q _p with an interface at 660 km depth and take Q _p constant with period. Our data set is too small to solve for a possible frequency dependence of Q _p . The upper mantle Q ₁ is 476 [299–1176] and the lower mantle Q ₂ is 794 [633–1064] (the bracketed numbers indicate the 68 percent confidence range of Q _p ^–1). These values are in-between the AK135 model (Kennett et al., 1995) and the PREM model (Dziewonski and Anderson, 1981) for the lower mantle and confirm results of Warren and Shearer (2000) that the upper mantle is less attenuating than PREM and AK135.     

Near‐field seismic effects in a homogeneous medium and their removal in vertical seismic profile attenuation estimates

To better understand (and correct for) the factors affecting the estimation of attenuation (Q), we simulate subsurface wave propagation with the Weyl/Sommerfeld integral. The complete spherical wavefield emanating from a P‐wave point source surrounded by a homogeneous, isotropic and attenuative medium is thus computed. In a resulting synthetic vertical seismic profile, we observe near‐field and far‐field responses and a 90° phase rotation between them. Depth dependence of the magnitude spectra in these two depth regions is distinctly different. The logarithm of the magnitude spectra shows a linear dependence on frequency in the far‐field but not in those depth regions where the near‐field becomes significant. Near‐field effects are one possible explanation for large positive and even negative Q‐factors in the shallow section that may be estimated from real vertical seismic profile data when applying the spectral ratio method. We outline a near‐field compensation technique that can reduce errors in the resultant Q estimates.     

Construction of constant-<Emphasis Type="Italic">Q</Emphasis> viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

INSUFFICIENTLY SAMPLED Q: A CAUSE OF WAVELET DISTORTION IN THE GENERATION OF SYNTHETIC SEISMOGRAMS?*

The effect of sampling of Q-values on the generation of one dimensional synthetic seismograms including absorption and dispersion is investigated. For the well data considered, a decrease in the Q-sampling interval results in an elongation of the estimated reflection waveform. Two explanations are given. The first refers to the way multiple energy is absorbed in the stratified medium. The second is based on the general observation that geological media with high velocity (e.g. limestones) often have high Q-values, whereas media with low velocity (e.g. shales) often have low Q-values.     

Variation of Q value before and after the 1999 Xiuyan, Liaoning Province, M =5.4 earthquake on the basis of analysis on attenuation dispersion of P waves

A method for determining medium quality factor is developed on the basis of analyzing the attenuation dispersion of the arrived first period P wave. In order to enhance signal to noise ratio, improve the resolution in measurement and reduce systematic error we applied the data resampling technique. The group velocity delay of P wave was derived by using an improved multi-filtering method. Based on a linear viscoelastic relaxation model we deduced the medium quality factor Q _m, and associated error with 95% confidence level. Applying the method to the seismic record of the Xiuyan M=5.4 earthquake sequences we obtained the following result: (1) High Q _m started to appear from Nov. 9, 1999. The events giving the deduced high Q _m value clustered in a region with their epicenter distances being between 32 and 46 km to the Yingkou station. This Q _m versus distance observation obviously deviates from the normal trend of Q _m linearly increasing with distance. (2) The average Q _m before the 29 Dec. 1999 M=5.4 earthquake is 460, while the average Q _m between the M=5.4 event and the 12 Jan. 2000 M=5.1 earthquake is 391, and the average Q _m after the M=5.1 event is 204. Foundation item: State Key Project of Science and Technology during the Tenth Five-year Plan (2004BA601B01-03-01).