Boundary-refl ected waves and ultrasonic coda waves in rock physics experiments

Ultrasonic coda waves are widely usea to stuay hign-trequency scattering, however, ultrasonic coda waves are strongly affected by interference from by boundary-reflected waves. To understand the effect of boundary-reflected waves, we performed ultrasonic experiments using aluminum and shale samples, and the rotating staggered-mesh finite-difference method to simulate the wavefield. We analyzed the wavefield characteristics at the different receiving points and the interference characteristics of the boundary-reflected waves with the ultrasonic coda wave, and the effect of sample geometry on the ultrasonic coda waves. The increase in the aspect ratio of the samples delays the interference effect of the laterally reflected waves and reduces the effect on the ultrasonic coda waves. The main waves interfering with the ultrasonic coda waves are laterally reflected PP-, PS-, PPP-, and PPS-waves. The scattering and attenuation of the high-frequency energy in actual rocks can weaken the interference of laterally reflected waves with the ultrasonic coda waves.

Moment magnitudes of two large Turkish earthquakes on February 6,2023 from long-period coda

Two large earthquakes(an earthquake doublet)occurred in south-central Turkey on February 6,2023,causing massive damages and casualties.The magnitudes and the relative sizes of the two mainshocks are essential information for scientific research and public awareness.There are obvious discrepancies among the results that have been reported so far,which may be revised and updated later.Here we applied a novel and reliable long-period coda moment magnitude method to the two large earthquakes.The moment magnitudes(with one standard error)are 7.95±0.013 and 7.86±0.012,respectively,which are larger than all the previous reports.The first mainshock,which matches the largest recorded earthquakes in the Turkish history,is slightly larger than the second one by 0.11±0.035 in magnitude or by 0.04 to 0.18 at 95%confidence level.

Attenuation characteristics of coda waves and estimation of Qc values in eastern China

For short-period near-earthquake records in eastern China,from the empirical attenuation formula of coda ground motion amplitude A with timeτ:lgA=G-2.235lgτ,using the single scattering theory modified with epicentral distance,we obtain the curve family of corrected coda amplitude Ac(r,t),and w/2Qc values for each time interval of coda. From this,Qc(f,h) values, which correspond to each observational average frequency and sampling depth,are calculated.The results substantially agree with those observational Qc values in Yunnan,Beijing and central Asia.

On the generation and decay of the long-period coda energy of large earthquakes

Seismic coda wave is the tail portion of the earthquake record after main arrivals.Studies on the coda usually focus on high-frequency data within several hours after regional events and attribute them to the scattering effect of the heterogeneities inside the earth.Here,we use records of seven large earthquakes at globally distributed seismic stations to examine the decay of long-period(100 s to 300 s)coda in the time window of 10,000 s to 140,000 s after the origin time and fit it with a statistical model.The geometric spreading effect in the estimated initial energy and a locationindependent equivalent attenuation coefficient indicate that the long-period coda energy is less affected by the heterogeneity-induced scattering effect than that of shorterperiod coda.The coda energy can reach the earth’s inner core and can be explained by a 1D earth model,making it more effective for constraining the global attenuation model.It also has the potential to determine the magnitudes of large earthquakes and to explore the interior of planetary bodies.

Reservoir time-lapse variations and coda wave interferometry

Coda waves are multiply scattered waves that arrive much later than the major waves. Small seismic velocity variations are observed in reservoirs because of small variations in reservoir properties, which affect the first arrivals. Hence, first arrivals cannot be used to detect small seismic velocity variations. However, small variations can be reliably detected by the coda waves because of the amplification owing to multiple scattering. We investigate the ability of coda wave interferometry to detect seismic velocity variations and monitor time-lapse reservoir characteristics using numerical simulations and experimental data. We use the Marmousi II model and finite-difference methods to build model seismic data and introduce small seismic velocity variations in the target layer. We examine the model seismic data before and after the changes and observe the coda waves. We find that velocity changes can be detected by coda wave interferometry and demonstrate that coda wave interferometry can be used in monitoring time- lapse reservoir characteristics.

Research on coda Q distribution in Beijing and its surrounding regions

Based on the single scattering model of seismic coda waves, we have calculated the Q-factor in Beijing and its surrounding regions by means of calculating the power density spectrum in frequency domain with a fixed time window. The digital seismic data of 69 earthquakes from Beijing Telemetered Seismographic Network are used.These earthquakes were recorded from January 1, 1989 to December 31,1990 at 20 stations. This paper shows the variations of the coda Q-factors in the studied region with different sites, frequency and lapse time, and the temporal change of the coda Q-factors in these two years. The results indicate that coda Q-factor depends strongly on the lapse time and frequency. It is assumed that when Qc=Q0f″, for the three time windows of 15 -30 s, 30-60 s and 60-90 s, the average values of Q0 are 48, 115 and 217; and the average values of ηare 0.89, 0. 91 and 0. 74, respectively.

Theoretical researches on three-dimensional coda wave scattering problem

Based on the previous researches on scattering theory, a model of single and multiple scattering in a three-dimensional infinite medium with non-zero hypocentral distance is proposed in this paper. According to the assumptionof three-dimensional medium with numerous, statistically isotropic and uniformly distributed scatterers, we obtain the analytic form of power spectrum of coda waves for single scattering and the integral form of power spectrum of coda waves for multiple scattering.

Temporal variations of coda Q^（－1） associated with the dahaituoshan， Beijing， earthquake of 1990

emporal variation of coda Q-1 associated with the occurrence of Dahaituoshan earthquake (ML= 5. 4) and its variation with the seismicity in Beijing area were studied by using 90 local earthquakes from the China Digital Seismograph Network (CDSN). The results showed that there was a significant temporal change in coda Q-1 during the period from Jan. 1987 to Aug. 1991 and it was relative to the seismicity of this area. Coda Q-1 was determined for the lapse time window ranging from 10 to 60 s, frequency 1 to 16 Hz. By comparing the average values of Q-1 for different time periods, we found that in region near the mainshock area the coda Q-1 for earthquakes which occurred after the mainshock were higher than those earthquakes that occurred prior to the mainshock, while the coda Q-1 after the mainshock for the surrounding area were lower than before. We also found the temporal changes in η, the exponential in formula Q-1=Q0-1 (f/f0) -η, and Q0, the Q-factor at 1 Hz. Measurements of coda Q-1 from three components showed inconsistency in temporal variations for different frequencies.

Discussion on the Measurement Method for the Coda Wave Quality Factor

The Quality factor is the parameter that can be used to describe the energy attenuation on seismic wave. In theory, we can obtain the relationship between the change of the coda wave quality factor with time and the strong earthquake preparation process on the basis of the quality factor of a coda wave in a same ray path. However, in reality the coda wave quality factor measured by different seismic coda waves corresponds to different seismic wave ray paths. The change of the quality factor with time is related to non-elastic characteristics of the medium and the volume of scattering ellipsoid constrained by scattered wave phase fronts, besides the change of regional stress field. This paper discusses the relationship between quality factor, epicenter distance and different lapse time, and then discusses the relationship between quality factor and frequency. Furthermore the determination method of the coda wave quality factor is put forward. The improved determination method of the quality factor, which removes the influence of different earthquakes or propagation depth of scattered waves, may increase measurement precision, thus information pertaining to abnormal changes in quality factor and the relationship between the quality factor and earthquake preparation process can be acquired.

Precise Measurement of Subsurface Seismic Velocity Variation by Coda Wave Interferometry

A filed experiment was conducted continuously for three days,and the velocity variation was measured using coda wave interferometry.The measurement error is estimated to be around 10-4,which coincides well with the theoretical error.The velocity variation during this period is up to 10-3.The relationship between velocity variation and changes in air temperature,barometric pressure and solid earth tide was analyzed with linear least square fitting.The velocity has no dependence on air temperature,but displayed change of the order of 10-6～10-7 when the barometer or earth tide changed one Pa.

Monitoring Media Velocity Variations with Coda Wave Interferometry

Multiply scattered waves are sensitive to media changes owing to the effect of repeated sampling,superposition and amplification. Based on this characteristic,small-medium changes could be detected by using coda wave interferometry. In recent years,coda wave interferometry has been widely used in estimating velocity variation with high precision in areas such as seismology and non-destructive testing. This paper systematically presents the principle and research status of coda wave interferometry,and especial focus is placed on the research of media velocity variations by using repeating earthquakes,artificial sources,and ambient noise. Applications of coda wave interferometry can contribute to the more subtle understanding of dynamic evolution process in the medium.

High frequency S wave envelope synthesis using a multiple non-isotropic scattering model: application to aftershocks from the 2008 Wenchuan earthquake

Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the initial intensity spectral density of a seismic wave is incorporated into the integral equation of seismic wave energy density. And, a recursive formula of Green＇s function is derived to obtain the higher order Green＇s function, which is included to describe the stronger non-isotropic scattering process. Then, the effect of the scattering pattern on the energy density envelope is investigated by the modified scattering theory. Significant differences arc found in the decay of the energy density envelopes with distances using different scattering patterns. The envelope synthesized by the forward dominated scattering pattern is larger than the results obtained by the isotropic and backward dominated scattering pattern. Different scattering patterns are also used to fit the observation data from the aftershocks of the 2008 Wenchuan earthquake. It is concluded that the envelopes synthesized by the forward scattering pattern can match the data better than the isotropic and backward dominated scattering cases, and a new interpretation of the coda wave is given. Finally, using the forward dominated scattering pattern, the envelope broadening of the observed data is reproduced.

Monitoring the Modal Frequency and Velocity Variations of Bridges under Ambient Excitation

We conducted a long-term monitoring experiment on the Lutuanxilu Bridge located in Changping District of Beijing, employing our recently developed real-time bridge monitoring system based on the Guralp CMG-6TD broadband seismometer. We identified the modal parameters with the stochastic subspace identification( SSI) algorithm,and continuously monitored the temporal velocity variation with coda wave interferometry.The results show that:( 1) the highly sensitive Guralp CMG-6TD broadband seismometer,which records the three-component vibration signal within broad frequency range,is well suited for long-term bridge health monitoring.( 2) With the continuous vibration signal from ambient excitation,the stochastic subspace algorithm can robustly identify the low-order modal parameters and the coda wave interferometry can accurately monitor the tiny velocity variation.( 3) The elastic modulus of bridge materials changes significantly associated with varying temperature,leading to diurnal velocity variation with amplitude of approximately 1%. The velocity variation shows strong negative correlation with temperature fluctuation. Meanwhile,the modal frequencies remain quite stable,suggesting that the velocity variation may be a more sensitive quantitative damage index.( 4) While the modal frequencies reflect the integrated health status of the bridge,the velocity variation can be utilized to monitor the local elastic modulus. Therefore,it is crucial for bridge health monitoring to continuously monitor the two key damage indexes under ambient excitation.

The Q value variations in the preparing pro－cess of rock rupture

In this paper, the 'spectral amplitude ratio method'(SAR) , 'energy method'(EN) and 'coda wave method'(CW) are used to calculate the Q value variations of gneiss in the preparing rupture process. The obtained results show that the variation state of Q values by SAR features the shape of relative stability gradual increment to the maximum then decrement and final rupture.The variation state of Q values by EN is just contrary to that by SAR,i.e.with the shape of stability decrement increment and final rupture . The varation state of Q values by CW is similar to that by EN, its main frequency features the shape of relatively high value decrement to the minimum increment and final rupture.But to the high frequency (higher than the main frequency),the variation state of Q values features the shape of the stable value increment to the maximum decrement and final rupture.At the same time, the results by coda wave amplitude spectrum show that, when stress reaches 70% of rupture stress, the high frequency component of S wave rapidly reduces( Q c increasing); at the time of impending the main rupture, the main frequency component reduces with a large scale( Q c increasing again), this may be the reason which causes the different variation states of two coda Q values.The result of amplitude spectra of P, S(initial wave) waves also show that with the appearance of microcracks the frequency band of S wave turn to be narrow, the high frequency component is reduced quickly, i.e. the S wave spectra have different variation states with different frequeny components. That is why the Q s obtained by different methods have different variation characteristics.