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During hydraulic fracturing (HF) stimulation for unconventional reservoir development, seismic attenuation has a significant influence on high-frequency microseismic data. Attenuation also provides important information for characterizing reservoir structure and changes to it due to HF injections. However, the attenuation effect is typically not considered in microseismic analysis. We have adopted the spectral ratio and centroid-frequency shift methods to estimate the subsurface attenuation (the factor [Formula: see text]) in a tight oil reservoir in the Ordos Basin, China. The P- and S-wave attenuations are calculated using the 3C waveform data recorded by a single-well downhole geophone array during a 12-stage HF stimulation. Both methods provide similar results (with differences in [Formula: see text] of absolute values less than 0.010 for P- and S-waves). For individual events, their median [Formula: see text] values calculated from different geophones are selected to represent the average attenuation. Spatiotemporal variations in attenuation are obtained by investigating [Formula: see text] values along propagating rays linking different source–receiver pairs. The [Formula: see text] values derived at different HF stages reveal significant attenuation in the targeted tight sandstone layer (0.030–0.062 for [Formula: see text] and 0.026−0.058 for [Formula: see text]), and the attenuation is apparently increased by fluid injection activities. We explain the sudden decrease in attenuation near the geophone array as a result of high shale content using log data from a horizontal treatment well. The consistency between the [Formula: see text] values and horizontal well-log data, as well as the HF process, indicates the reliability and robustness of the attenuation results. By studying spatiotemporal variations in attenuation, the changes in subsurface structures may be quantitatively characterized, thereby creating a reliable basis for microseismic modeling and data processing and providing additional information on monitoring the HF process.

SUMMARY On 2019 March 21, an explosion accidentally occurred at a chemical plant in Xiangshui, Yancheng City, Jiangsu Province, China. Using broad-band digital seismic data from East China, South Korea and Japan, we investigate properties of the Xiangshui explosion as well as two nearby chemical explosions and four nearby natural earthquakes in Jiangsu Province, East China. From Lg and Rayleigh waves recorded by regional networks, both body wave magnitude mb (Lg) and surface wave magnitude Ms (Rayleigh) are calculated for these events. The magnitudes of the Xiangshui explosion are mb (Lg) = 3.39 ± 0.24 and Ms = 1.95 ± 0.27, respectively. Both the empirical magnitude–yield relation for buried explosion and empirical yield–crater dimension relation for open-pit explosion are adopted for investigating the explosive yield. The result from the yield–crater dimension relation is approximately 492 ton, which is consistent with the ground truth and considerably larger than that from the buried source model. This also reveals that, for Xiangshui explosion, the explosion to seismic energy conversion rate is approximately one-third compared to a similar sized fully confined explosion. By comparing the body wave and surface wave magnitudes from explosions and nearby earthquakes, we find that the mb:Ms discriminant calculated at regional distances cannot properly distinguish explosions from natural earthquakes. However, the P/S spectral ratios Pg/Lg, Pn/Lg and Pn/Sn from the same data set can be good discriminants for identifying explosions from earthquakes.

SUMMARYThe crustal attenuation structure can effectively reveal the rheology and thermal properties of different geological blocks, and can provide seismological constraints on regional tectonic evolution. Based on 11 306 vertical-component Lg-wave seismograms recorded at 111 broad-band stations from 891 crustal earthquakes that occurred between 1994 and 2020, a broad-band Lg-wave attenuation model is obtained for Southeast Asia. This study demonstrates the capability of applying crustal Lg-wave attenuation inversion in a complex region mixed with continents, islands and marginal seas. The resolution approaches 2° in most parts in the study region. Lg blockages are observed at places with sharp Moho depth changes. The resultant Q models are consistent with regional geologic structures provided by previous studies. Prominent low-attenuation anomalies are located in the Sundaland Core containing stable ancient crust, including Indochina, Malay Peninsula, East Sumatra, Sunda Shelf and Borneo Core. Regions with strong attenuation are associated with complex tectonic conditions, such as the Indo–Australian subduction zone, sutures in Sarawak and Sabah. The observed Lg-wave attenuation characteristics provide constraints on the tectonic affinities and evolutions of the geological blocks. The results show that the Borneo Core remained stable since its accretion with the Sundaland Core. Ancient blocks are characterized by weak Lg attenuation, whereas geologically younger terranes are often characterized by strong Lg attenuation, which can be exploited to better understand the separation and convergence of plates during the tectonic evolution.

Through the study of microseismic focal mechanisms, information such as fracture orientation, event magnitude, and in situ stress status can be quantitatively obtained, thus providing a reliable basis for unconventional oil and gas exploration. Most source inversion methods assume that the medium is isotropic. However, hydraulic fracturing is usually conducted in sedimentary rocks, which often exhibit strong anisotropy. Neglecting this anisotropy may cause errors in focal mechanism inversion results. We have developed a microseismic focal mechanism inversion method that considers velocity anisotropy in a vertically transverse isotropic medium. To generate synthetic data, we adopt the moment-tensor model to represent microearthquake sources. We use a staggered-grid finite-difference method to calculate synthetic seismograms in anisotropic media. We perform seismic moment-tensor (SMT) inversion with only P-waves by matching the synthetic and observed waveforms. The synthetic and field data sets are used to test the inversion method. For the field data set, we investigate the inversion stability using randomly selected partial data sets in the calculation. We pay special attention to analyze the sensitivity of the inversion. We test and evaluate the impact of noise in the data and errors in the model parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) on the SMT inversion using synthetic data sets. The results indicate that, for a surface acquisition system, our method can tolerate moderate noise in the data and deviations in the anisotropy parameters can cause errors in the SMT inversion, especially for dip-slip events and the inverted percentages of non-double-couple (DC) components. According to our study, including anisotropy in the model is important to obtain reliable non-DC components of moment tensors for hydraulic fracturing-induced microearthquakes.

The applicability of the empirical magnitude–yield relations developed for northeast China and Korean Peninsula explosions was investigated for data from northwest China. We collected regional broadband digital seismic data from 13 chemical explosions (CEx) detonated between 6 September and 10 October 2018, on the eastern margin of the Junggar basin, northwest China, five nuclear tests at the Semipalatinsk nuclear test site, and eight natural earthquakes. Both Lg and Rayleigh-wave magnitudes (mb(Lg) and Ms, respectively) were estimated for these events. Similar to the North Korean test site, the mb(Lg)–Ms discriminant did not properly distinguish explosions from natural earthquakes at the Semipalatinsk test site. However, network-averaged P/S spectral ratios (Pg/Lg, Pn/Lg, and Pn/Sn) did successfully discriminate explosions from earthquakes at both the North Korean and the Semipalatinsk test sites at frequencies above 2.0 Hz. Based on 13 known-yield CEx, we selected an empirical magnitude–yield relation to constrain the explosive yields of five historical nuclear tests at the Semipalatinsk test site. The resulting yields are lower than those previously obtained from teleseismic observations.

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

The seismological characteristics of the 15 February 2013 Chelyabinsk bolide explosion are investigated based on seismograms recorded at 50 stations with epicentral distances ranging from 229 to 4324 km. By using 8–25 s vertical-component Rayleigh waveforms, we obtain a surface-wave magnitude of 4.17±0.31 for this event. According to the relationship among the Rayleigh-wave magnitude, burst height and explosive yield, the explosion yield is estimated to be 686 kt. Using a single-force source to fit the observed Rayleigh waveforms, we obtain a single force of 1.03×1012 N, which is equivalent to the impact from the shock wave generated by the bolide explosion.

We characterize the seismic events that occurred in North Korea on 9 September 2016 and South Korea on 12 September 2016. The 9 September 2016 event was identified as an explosion, and the two 12 September 2016 events were identified as natural earthquakes using the P/S (P-and S-wave) spectral ratios, Pg/Lg, Pn/Lg, and Pn/Sn as discriminants. The explosive event was relocated within the North Korean nuclear test site using a relative location method and the 2006 North Korea underground nuclear test as the master event, and the epicenter was identified at 41.2976 degrees N latitude and 129.0804 degrees E longitude. From the regional Lg and Rayleigh waves, the body-and surface-wave magnitudes for the 9 September 2016 event were calculated as m(b) (Lg) = 4: 8 +/- 0: 2 and M-s = 4: 2 +/- 0: 1. By adopting an empirical magnitude-yield relation for the body-wave magnitude, and assuming that the explosion was fully coupled and detonated at a normally scaled depth, we estimated that the seismic yield was similar to 6 kt, and the uncertainty range was between 3 and 11 kt. If an overburied depth range between 780 and 1200 m was applied, then the yield would be increased to 16-22 kt.

The Pn phase for crustal earthquakes refracts through the uppermost mantle to become the first seismic‐wave arrival at distances of ∼200 to ∼1500 km. The amplitude of Pn is particularly sensitive to the mantle lid radial velocity gradient, and the elastic geometric spreading is frequency dependent. Lateral variations in the radial velocity gradient and in the crustal thickness encountered by Pn phases that traverse boundaries of geological provinces further complicate the frequency‐dependent geometric spreading behavior. We use 2D finite‐difference (FD) calculations to explore the effects of smoothly varying lateral structures in the lid and crust on Pn phases in the 0.4–10 Hz frequency range. Pn geometric spreading for 1D structures with mantle lid gradients is calculated first to ensure that the FD calculations correctly capture the expected frequency dependence. Then, 2D models with smooth laterally varying radial lid gradients are computed to explore how the phase samples the structures to give the overall geometric spreading. The direction of propagation through the laterally varying structure affects the frequency dependence and the transition from source‐side to receiver‐side dominance in the spreading. Laterally varying crustal thickness is explored in the context of the North Korean nuclear test site, for which many observations of Pn are made by stations with paths either through continental structure or along paths with variation from continental to oceanic to arc structure (in Japan). Frequency‐dependent amplitude effects are observed on the paths through oceanic structure. 2D FD calculations for structures with a central region of thin oceanic crust reproduce the observed first‐order frequency dependence of Pn along corresponding paths, including rapid amplitude decay for frequencies above 6 Hz. These analyses demonstrate that even though Pn propagation is very complex, modeling approaches can guide interpretations of the behavior when constraints on the structure are available. Electronic Supplement: Figures of Pn ‐wave snapshots, first Pn arrival times, and frequency dependence of the Pn amplitudes.

Seismic migration moves reflections to their true subsurface positions and yields seismic images of subsurface areas. However, due to limited acquisition aperture, complex overburden structure and target dipping angle, the migration often generates a distorted image of the actual subsurface structure. Seismic illumination and resolution analyses provide a quantitative description of how the above-mentioned factors distort the image. The point spread function (PSF) gives the resolution of the depth image and carries full information about the factors affecting the quality of the image. The staining algorithm establishes a correspondence between a certain structure and its relevant wavefield and reflected data. In this paper, we use the staining algorithm to calculate the PSFs, then use these PSFs for extracting the acquisition dip response and correcting the original depth image by deconvolution. We present relevant results of the SEG salt model. The staining algorithm provides an efficient tool for calculating the PSF and for conducting broadband seismic illumination and resolution analyses.

Seismology plays an important role in characterizing potential underground nuclear tests. Using broad-band digital seismic data from Northeast China, South Korea and Japan, we investigated the properties of the recent seismic event occurred in North Korea on 2016 January 6. Using a relative location method and choosing the previous 2006 explosion as the master event, the 2016 event was located within the North Korean nuclear test site, with its epicentre at latitude 41.3003°N and longitude 129.0678°E, approximately 900 m north and 500 m west of the previous event on 2013 February 12. Based on the error ellipse, the relocation uncertainty was approximately 70 m. Using the P/S spectral ratios, including Pg/Lg, Pn/Lg and Pn/Sn, as the discriminants, we identify the 2016 event as an explosion rather than an earthquake. The body-wave magnitude calculated from regional wave Lg is mb(Lg) equal to 4.7 ± 0.2. Adopting an empirical magnitude–yield relation, and assuming that the explosion is fully coupled and detonated at a normally scaled depth, we find that the seismic yield is about 4 kt, with the uncertainties allowing a range from 2 to 8 kt.

We investigate the geometric spreading and attenuation of seismic Pn waves in Northeast China and the Korean Peninsula. A high-quality broadband Pn wave data set generated by North Korean nuclear tests is used to constrain the parameters of a frequency-dependent log-quadratic geometric spreading function and a power law Pn Q model. The geometric spreading function and apparent Pn wave Q are obtained for Northeast China and the Korean Peninsula between 2.0 and 10.0 Hz. Using the two-station amplitude ratios of the Pn spectra and correcting them with the known spreading function, we remove the contributions of the source and crust from the apparent Pn Q and retrieve the P wave attenuation information along the pure upper mantle path. We then use both Pn amplitudes and amplitude ratios in a tomographic approach to obtain the upper mantle P wave attenuation in the studied area. The Pn wave spectra observed in China are compared with those recorded in Japan, and the result reveals that the high-frequency Pn signal across the oceanic path attenuated faster compared with those through the continental path.

Internal multiple reflections have different propagation paths than primary reflections and surface-related multiples; thus, they can complement illumination where other waves are unavailable. Consequently, migration of internal multiples may provide vital images in the shadow zone of primary reflections. We have developed an approach to image structures with internal multiples. With this method, internal multiples can be separated and used as data for reverse time migration. Instead of applying the imaging condition directly to the source and receiver wavefields, we decomposed the extrapolated source and receiver waves into up- and downgoing waves. Then we applied the imaging condition to upgoing source and receiver waves to form an up-up (UU) image and also to downgoing source and receiver waves to form a down-down (DD) image. The image of the true reflector and the artifacts behave differently in the DD and UU images. A similarity analysis is conducted to the UU and DD images to separate true images from artifacts. Numerical examples with simple velocity models are used to demonstrate how to construct UU and DD imaging conditions and eliminate migration artifacts. Finally, we test the 2D SMAART JV model with salt structures for migration using internal multiples.

Online Material: Figures of Pn waveform comparisons and spectral ratios; tables of Pn differential times and parameters for events used in the study. On 12 February 2013, North Korea conducted its third and the largest nuclear test to date in the China–North Korea border area. According to local news, people living in nearby Chinese cities experienced shaking from this explosion. The U.S. Geological Survey (USGS) reported the explosion was located at (41.301° N, 129.066° E) and the magnitude was M 5.1. This event trigged abundant regional seismic phases in northeast China, Korea, and Japan. Because of its large magnitude, the seismic records from this event showed better signal‐to‐noise ratios than those from previous two nuclear explosions. Illustrated in Figure 1 are broadband regional seismograms at station MDJ for three North Korea nuclear tests. These waveforms are highly similar, all are featured with abrupt P ‐wave arrivals, weak Lg phases and well‐developed short‐period Rayleigh waves. We collect the regional waveforms recorded on China National Digital Seismic Network (CNDSN), Global Seismic Network (GSN), and Japan F‐net to investigate the 12 February 2013 North Korean nuclear test. Figure 1. Seismograms recorded on MDJ from three North Korean nuclear tests in 2013, 2009, and 2006. Illustrated are normalized vertical displacements. The event date, maximum amplitudes, and epicenter distances are listed on the left. Marks on the waveforms indicate apparent group velocities. Note that the waveforms show similar features and display clear impulsive P ‐wave onset, relatively weak Lg phases, and 3–5 s period Rayleigh waves. ### High‐Precision Location By adopting the relative location method (e.g., Schaff and Richards, 2004; Zhang et al. , 2005; Wen and Long, 2010; Murphy et al. , 2013), and using the first North Korean nuclear test on 9 October 2006 as the master event, we calculate the origin times and locations of the 25 May 2009 and …

As a prominent geophysical anomaly, unusually high seismic wave attenuation is observed in the crust and upper mantle of the Tibetan Plateau, particularly along its northern area. Theoretical and laboratory investigations show that the strong seismic attenuation can indicate high temperatures and partial melting, which may decrease the viscosity of the material and cause it to flow. Thus, seismic attenuation distribution may provide useful constraints to the crust flows if they exist. Using Lg-wave Q tomography, we construct a 0.05–10.0 Hz broadband high-resolution crust attenuation model for the Tibetan Plateau and its surrounding regions. The maximum spatial resolution is approximately 1.0 ° × 1.0 ° in well-covered areas and for frequencies between 0.05 and 1.5 Hz. This attenuation model reveals an apparent low-QLg belt stretching along the northern and eastern Tibetan plateau. Combining the Lg-wave Q model with other geophysical data, two possible crust flow channels are found in the Tibetan Plateau. The main flow channel is from north to east and then turns to southeastern Tibet along the western edge of the rigid Sichuan basin, while a second channel starts from southern Tibet and crosses the Eastern Himalayan syntaxis.

Lian-Feng Zhao,1,2 Xiao-Bi Xie,2 Wei-Min Wang,3 Jin-Hai Zhang1 and Zhen-Xing Yao1 1Key Laboratory of the Earth’s Deep Interior, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China. E-mail: zhaolf@mail.iggcas.ac.cn 2Institute of Geophysics and Planetary Physics, University of California, Santa Cruz, CA 95064, USA 3Key Laboratory of Continental Collision and Plateau Uplift, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China

We collect nine vertical component broadband seismograms from the 25 May 2009 North Korean nuclear explosion for a regional seismic network in which eight stations also recorded the 9 October 2006 North Korean nuclear test. Comparing the observed waveforms and spectra from the two events, we estimate that the amplitudes of the records from the second event are approximately five times those from the first one. Additionally, we use 599 vertical broadband seismograms from 82 regional events recorded on the regional network between December 1995 and May 2009 to calibrate the network Lg ‐wave magnitude. The calibrated network is used to calculate the Lg ‐wave body‐wave magnitude m b( Lg )=4.53 for the 25 May 2009 North Korean nuclear explosion. Based upon 15 first arrivals from the two North Korea nuclear explosions, the regional Pn velocity in the northeast China–North Korea region is calculated to be 8.0 km/s. This result, along with the regional geological structures, suggests that the North Korean test site (NKTS) is located at a relatively stable continental region. We thus use a modified fully coupled magnitude–yield relation to estimate the explosion yield, and the result shows that the yield of the 25 May 2009 North Korean nuclear test is approximately 2.35 kt under the minimum burial depth assumption. Online Material: Epicentral parameters, computed m b( Lg ), and corrected m b( Lg ) for 82 events used in the study.

The ability to model only primaries is very desirable in seismic exploration and can find broad applications in modeling, imaging, data processing, and interpretation. In this article, “primaries” mean the primary transmitted or reflected waves that involve only single interactions (transmission or reflection) at interfaces (sharp discontinuities) inside a heterogeneous medium. Primary-only modeling usually is much faster and more memory-efficient than full-wave methods, and, in addition, can provide “clean” seismograms free from multiples—a feature useful in testing certain features of migration/imaging or velocity analysis algorithms. This ability of modeling primary-only events also means the method can eliminate pure multiples from full-wave seismograms. The potential applications of primary-only modeling go beyond seismic modeling. For example, it can be applied as an extended one-way propagator to migration/imaging using unconventional waves (such as turning waves), reflected waves, or duplex waves ...

We investigate the regional seismic signature of the 9 October 2006 North Korean nuclear test. Broadband regional data for the nuclear test and a group of earthquakes close to the test site were obtained between December 2000 and No- vember 2006. Epicentral distances from the stations to the test site are between 371 and 1153 km. We first use these regional events to calibrate the Lg-wave magnitude in the network. Then the network is used to calculate mbLg �� 3:93 for the North Ko- rean nuclear explosion. Using a modified fully coupled magnitude-yield relation, the yield of the North Korean nuclear test is estimated to be 0.48 kt. Because of large uncertainties in the source depth, the estimate is preliminary. The P=S-type spectral ratios Pg=Lg, Pn=Lg, and Pn=Sn are calculated for the nuclear explosion and a group of earthquakes close to the test site. At frequencies above 2 Hz, the network-averaged P=S spectral ratios clearly separate the 9 October 2006 explosion from the regional earthquakes. Our result indicates that a single-blast explosion in the North Korea re- gion shows different seismic characteristics from an earthquake. Any well-coupled single-blast explosion detonated in this region with yield similar to that for the North Korean nuclear test has a large probability of being identified by a regional seismic network such as the one adopted in this study.

Summary We develop a slowness analysis method for investigating the seismic wave scattering in complex velocity models. The wavefield is decomposed into mixed space-time and slowness-frequency domains. The scattering process can be better investigated in these mixed domains. We conduct finite-difference simulations for velocity models with different random fluctuations and apply the slowness analysis to the synthetic wavefield. The results reveal that in random velocity models with different correlation lengths along different directions, the scattered waves show different radiation patterns. It is possible using this property to determine the dominant direction of subsurface heterogeneities such as the crack alignment in the

[1] We investigate regional variations in the Lg-wave quality factor (Q) in Northeast China and its vicinity with a tomographic method. Digital seismic data recorded at 20 broadband stations from 125 regional events are used to extract Lg-wave spectra. Tomographic inversions are independently conducted at 58 discrete frequencies distributed log evenly between 0.05 and 10.0 Hz. We simultaneously invert for the Lg-wave Q distribution and source spectra at individual frequencies without using any a priori assumption about the frequency dependence of the Q model and source function. The best spatial resolution is approximately 1° × 1° in well-covered areas for frequencies between 0.4 and 2.0 Hz. The Lg Q shows significant regional variations and an apparent relationship with regional geology. We use a statistical method to investigate the regional variations of Lg Q and their frequency dependence. The average Q0 (1 Hz Lg Q) in the entire investigated region is 414. Sedimentary basins are usually characterized by lower average Q0 values (from 155 to 391), while volcanic mountain areas have relatively high average Q0 values (from 630 to 675). Lg Q generally increases with increasing frequency. However, the frequency dependence has complex nonlinear features on a double-logarithmic scale, indicating that the commonly adopted power-law relationship may be oversimplified in a broad frequency band. The frequency dependence varies in different geological areas, with larger variations seen at lower frequencies.

We investigate the capability of inverting large scale velocity errors through wave equation migration velocity analysis using shot-indexed sensitivity kernels. We find that the global shift of the image (absolute residual moveout) is crucial for constraining the large-scale velocity errors in the model when the shift of the image is more than a number of wavelengths. We estimate the shift through fitting the curvature of RMOs on CIGs and add this information into the inversion system. Although the extraction of the shift information is based on a simple model, including this information into RMO data considerably improves the inversion result. We apply our method to Sigsbee benchmark model and demonstrate that the velocity analysis based on sensitivity kernels can handle both large-scale and small-scale velocity errors in a complex geological environment.

Summary Using a simple salt layer elastic model with both flat and steep faults at the subsalt area, we demonstrated the concepts and method of selected C-path (converted-wave path) imaging to improve the subsalt illumination and reduce migration artifacts. First we investigate the survey efficiency of different C-paths through energy budget evaluation for different incident and scattering paths. Then we test the image quality for different migration C-paths. By using C-paths with at least one S-segment inside the salt body, the blind area of pure P-wave imaging for steep subsalt faults having dip larger than the critical angle (37 0 ) was eliminated. Using different C-path combinations can also substantially reduce the elastic migration artifacts caused by path-mismatches between the data and migration. Further study for eliminating the conversion mismatch artifacts is needed.

We have used data from the 80-km-diameter NORSAR array and the 3-km-diameter NORESS array to determine the Transverse Coherence Function (TCF) of arrival time for spatial separations ranging from a few hundred meters to 80 km. To accomplish our objective, we have devised a method to combine data from arrays of different aperture. The procedure is based on information about rms fluctuations and rms tilts on each array. Synthetic fluctuation fields with different statistical properties were generated to test the combination method. Our results for the TCF from NORSAR and NORESS are in reasonable agreement with the predictions of the Flatte-Wu model of heterogeneities under NORSAR.

It is well known that for natural earthquakes the faulting processes are highly complicated. To study such processes, all of the different types of data that can be acquired should be incorporated into the investigations. In accordance with this consideration, the faulting process of the Tangshan earthquake ( M S = 7.8) on 27 July 1976 is investigated. First, the geometrical attitude of the fault is determined by analysing the geological structure, intensity distribution, locations of the aftershocks and geodesic data collectively. Then the faulting process is simultaneously inverted from 14 WWSSN long-period teleseismic waveforms and 70 horizontal geodesic static deformation data. The results show that the Tangshan earthquake is one of the strongest intraplate earthquakes with a complex faulting process. The dimension of the main fracture is approximately 100 km by 15 km with a change in direction at the central part of the fault; the southern segment strikes at about NE30°, becoming 50–60° for the northern segment. The total seismic moment inverted is 2.0 × 10 20 Nm and the dislocation was relatively concentrated near the central part of the fault, where the slip elapsed for a longer time. These results suggest that near the city of Tangshan there might be a strong unbroken block and the fault changes its trend there. Hence the fault system was locked before the earthquake. When the regional stress increased and exceeded the strength limit, the fracture initiated from this location and extended bilaterally.

We propose a full-wave equation based method for seismic illumination analysis. The full-wave finite-difference method is used to calculate the waves from the source and receiver to the subsurface target. A time domain local slowness analysis technique is used to decompose the wavefield into angle domain beams. Based on the angle domain information, we formulate the illumination matrix from which different illumination measurements can be derived. Unlike the one-way wave equation based method, the current approach does not have the angle limitation and the reflection/transmission energy can be accurately calculated. The new illumination method can handle turning waves which are crucial for imaging steep structures. Thus, this method is particularly useful for providing illumination analysis in reverse-time migration. A group of numerical examples are calculated to demonstrate the time-domain wavefield decomposition and the creation of different illumination measurements. The illumination in the 2D BP model is investigated. Our special attention is focused on the illumination of vertical and overhung structures.

We define and formulate the resolution of an imaging system based on the inverse theory and local angle domain decomposition of Green’s functions. The resolution defined in this way includes both the effects of acquisition system and imaging (migration) process. The theory and method are based on wave theory and no asymptotic approximation is made in the calculation. It represents and quantifies the actual resolution we observed in the migrated images. The resolution taking into account only the influence of the acquisition system (frequency band and spatial aperture) and neglecting the factors such as the errors in backpropagation (migration) can be considered as the resolution limit of the system, the best resolution an acquisition system can get. Theoretical analysis and numerical examples are given to show the importance of propagator accuracy in the evaluation of resolution in complex media.

The recent development of wave equation based migration methods provided accurate propagators for seismic wave extrapolation. These propagators brought the possibility that many analysis and inversion can be made at the depth using migrated wavefield. In this study, we propose an approach for extracting angle domain information from migrated wavefield. The method is based on localized plane wave analysis and can be used for almost any migration method. Then, using the concept of the local image matrix, useful information (angle domain image gathers, reflector dips, etc.) can be further extracted from this angle related information. Numerical examples are conducted to demonstrate the applications of this method.

In this paper. we first give a brief summary of the formulation for calculating reflections from a 3D elastic structure based on a complex-screen method. The incident wave and reflected wave are propagated by using a complexscreen propagator. The reflections are calculated based on local Born approximation. When using a small angle approximation, the backscattering can also be formulated into a screen reflection which has a high computation efficiency and needs relatively small computer memory. As expected from the scattering theory. the forward transmitted waves, like P to P or to are controlled by the Pand S-wave velocity perturbations, while the reflections are controlled by the impedance perturbations. The converted waves are mainly controlled by the density and shear module perturbations. Numerical examples are given to show the accuracy of the method. For two special cases, the synthetic seismograms obtained with this method are compared with that calculated by elastic finite-difference method. The results show general consistency.

Due to the limitation of sparse seismic observations on the earth’s surface, the deterministic picture of small‐scale heterogeneities in the earth is difficult to obtain in general. Statistical characterization is a viable alternative to study the distribution and properties of the small‐scale heterogeneities. The pioneering work of Aki in 1973 modeled the heterogeneities with a single‐layer uniform random medium having only three parameters: scale, perturbation strength, and layer thickness. This simple model is consistent with the observations which are limited to only the transversal coherence functions of seismic wave (phase and amplitude) across an array and it has no depth resolution. The following work in 1970s and early 1980s were based on similar models. Flatte introduced the key idea of angular coherence functions using different earthquakes at large epicentral distances in the late 1980s (Flatte and Wu, 1988), which opened a new area of earth heterogeneity characterization by extending the single, uniform layer model to a depth‐dependence model. Later, the angular coherence function was extended to the joint transverse‐angular coherence function, which significantly increases the depth resolution of the heterogeneity spectra. In this talk, we summarize the research results along this direction conducted by a group of scientists in the earth science at University of California, Santa Cruz, collaborated with Flatte in different stages.

Using Lg-wave Q tomography, we construct a broadband crustal attenuation model for the Middle East. The Q Lg images reveal a relationship between attenuation and geological structures. Strong attenuation is found in the continental collision orogenic belt that extends from the Turkish and Iranian plateau to the Pamir plateau. We investigate the frequency dependence of Q Lg in different geologic formations. The results illustrate that Q Lg values generally increase with increasing frequency but exhibit complex relationships both with frequency and between regions. An average Q Lg value between 0.2 and 2.0 Hz, Q Lg (0.2–2.0 Hz), may be a critical index for crustal attenuation and is used to infer the regional geology. Low-Q Lg anomalies are present in the eastern Turkish plateau and correlate well with low Pn-velocities and Cenozoic volcanic activity, thus indicating possible partial melting within the crust in this region. Very strong attenuation is also observed in central Iran, the Afghanistan block, and the southern Caspian Sea. This in line with the previously observed high crustal temperature, high-conductivity layers, and thick marine sediments in these areas, suggests the high Lg attenuation is caused by abnormally high tectonic and thermal activities.