Amplitudes Of Seismic Waves Research Articles

Combining physical model with neural networks for earthquake site response prediction

The amplitude of seismic waves will be significantly amplified near the Earth's surface, and this phenomenon is known as the seismic site response. Site response prediction is of paramount importance for the seismic-resistant building design and seismic risk assessment. However, accurately predicting site response has always been a challenge due to the incomplete physical knowledge and insufficient dataset volumes. Here, we propose an approach that combines the neural networks with classical homogeneous layered model for site response prediction. This approach exploits the potential for improving the accuracy of site response prediction from both the physical and data perspectives, which reduces the requirements for the model complexity and the training data volume. Compared to the physics-driven method, this approach reduces the estimation errors by approximately 50 % on average, and corrects the correlation between the observed and predicted results. This approach firstly reproduces the four-stage characteristics of the site response in the entire seismic band, and provides a new framework for site response prediction.

A Study on the Dynamic Response and Deformation of Slopes Supported by Anti-Slide Piles Subjected to Seismic Waves with Different Spectral Characteristics

The long-term stability of slopes in areas with strong earthquakes not only is very important for people’s lives and the safety of property, but also it enables restoration of the ecological environment in the landslide areas, which is very important for sustainable development. The most commonly used seismic-support method, anti-slide piles, provides outstanding seismic performance. However, piles still deform and fail during earthquakes, which can lead to instability of the slope. The dynamic response of a slope reinforced with anti-slide piles is crucial for maintaining the long-term stability of the slope in a strong-earthquake area and, thus, for promoting its sustainable development. However, current research is focused mainly on the stability of the slope, and there have been few studies on the dynamic response of anti-slide piles. For this reason, we have undertaken the present study of a bedding-rock slope supported by a single row of anti-slide piles. By changing the frequency, amplitude, and duration of the input seismic waves, we have systematically explored the influence of their spectral characteristics on the dynamic response of the anti-slide piles and the slope using numerical simulations combined with the wavelet-transform method. Our results show that the spectral characteristics of the seismic waves significantly affect the deformations of the anti-slide piles. Low-frequency and high-amplitude seismic waves have stronger destructive effects on slopes, and high-amplitude seismic waves can generate multi-level sliding surfaces that extend to deeper levels. The low-frequency component of the seismic wave controls the overall deformation of the slope, and the high-frequency component controls the local deformations. An increase in the proportion and duration of low frequencies in seismic waves is the main cause of slope deformation and failure. The present work, thus, provides a useful reference for the design of a slope supported by anti-slide piles in an area with strong earthquakes, as well as for the maintenance of the long-term stability of such a slope, therefore, encouraging the sustainable development of related areas.

Shaking table study on the seismic dynamic behavior of high-speed railway subgrade with pile network composite-reinforced soil

Pile network composite structures are used in the construction of high-speed railway subgrades. There have been few studies on their seismic dynamic response, however, which has restricted the accurate evaluation of their seismic performance. In this study, a series of shaking table tests on a pile network composite-reinforced soil high-speed railway subgrade were conducted. Particle image velocimetry was used to analyze the slope motion and sensor data to evaluate the overall dynamic response characteristics of the subgrade. Findings indicate that seismic activity causes subsidence throughout the subgrade, with deformations occurring in three distinct phases depending on the input seismic amplitude from 0.1 to 0.4 g (slow increasing), 0.4 to 0.6 g (faster increasing), and 0.6 to 1.0 g (rapidly increasing). The inclusion of geogrids aids in dissipating seismic energy, thereby reducing the peak acceleration amplification along the elevation. The increased dynamic soil pressure of the subgrade is mitigated by the geogrid reinforcement, which improves local stability. Moreover, the geogrid strain escalated with greater seismic wave amplitudes, resulting in the progressive expansion of the unstable zone from the slope towards the center of the subgrade as the elevation increased.

Mechanism Design of Seafloor Current Meter (SCM) with Broadband OBS and Data Analysis in the Northeastern offshore Taiwan

To achieve precise measurements of near seabed water current velocities, this study designed a mechanical device for the Aquadopp-6000m Current meter that can be paired with the Yardbird-BB Ocean Bottom Seismometer (OBS). To ensure it does not affect the sinking rate during deployment or the buoyancy during recovery at sea, the overall ballasting of the OBS with the integrated water current meter needed to be recalibrated. The Aquadopp-6000m can record multiple physical data parameters simultaneously. During instrument deployment tests, we recorded the orientation of the entire OBS, time of seabed contact, time of seismic sensor detachment from the A-frame and falling onto the seabed, as well as profiles of sound speed, temperature, and pressure during the instrument sinking process. In deployment planning, it was determined that the original battery capacity inside the Aquadopp-6000m was insufficient to sustain the power consumption required for sampling rates of one sample per second for more than three months. This paper also provides detailed calculations for battery power and methods for modifying battery packs. Data from deployments in the Okinawa Trough in 2019 and 2020 indicated that seabed water current velocities and seismic activity share similar frequency characteristics over long periods. For seismic wave amplitudes greater than 0.006 m/s, there were intermittent decreases in water flow velocity following the arrival of radial S-waves, while the tangent component remained unaffected. Before the formation of typhoons thousands of kilometers away, atmospheric pressure variations were observed to influence minor changes in seabed temperature, seabed flow velocities, and seawater pressure, thereby affecting oceanic sound speed.

Characterization of Seismic Dynamic Response of Uranium Tailings Dams Based on Discrete Element Method

Tailings dams play a critical role in ensuring the safety of mining operations. However, earthquakes can cause breaches in these dams, resulting in significant casualties and property damage. This study investigates the dynamic response characteristics of uranium tailings dams subjected to seismic loading, employing the discrete element method. It specifically analyzes how seismic wave amplitude, frequency, and the friction angle of tailings sand affect the dams’ dynamic response. The results reveal that the peak ground acceleration ratio (PGAR) exhibits an increasing–decreasing–increasing pattern with elevation. When the friction angle of the tailings sand exceeds 35°, the overall stability of the dam improves. Conversely, a friction angle below 25° significantly increases the risk of dam failure. Additionally, the dam shows a reduced dynamic response to seismic waves with frequencies exceeding 15 Hz. At lower frequencies, deformation and damage are primarily concentrated on the slope face, while at higher frequencies, damage is predominantly located at the bottom of the model. These findings provide a theoretical foundation and reference for the safe operation of tailings dams, highlighting their practical significance.

Imaging Attenuation From Array Analysis of Surface Waves

AbstractAnelastic attenuation provides key insight in our understanding of thermal and rheological structures and the associated deformation and dynamic mechanisms of the Earth's deep interior. Unfortunately, attenuation tomography is advanced far behind wave‐speed tomography due to the challenge in properly excluding the complex effects of elastic heterogeneities on seismic wave amplitude. By taking advantage of phase tracking in seismic array analysis, here we derive a new theory of Helmholtz tomography that well accounts for attenuation, source radiation, and scattering, etc., and present a technique called Helmholtz Multi‐Event Tomography (HelMET) to retrieve the attenuation properly. The effectiveness of this method is then validated by synthetic inversions. Our synthetic seismograms are calculated using a newly developed three‐dimensional finite‐difference algorithm that accounts for physical dispersion and dissipation in anelastic media and remains accurate and stable even if strong attenuation exists. Compared to the traditional method poorly performed in the synthetic inversion, the HelMET well recovers the input attenuation anomalies, suggesting that this method can be used to successfully isolate attenuation from the complicated effects of elastic heterogeneities. Our results underline the implication of the new theory and method in accurately imaging high‐resolution attenuation structures and unambiguously interpreting the anelastic heterogeneities of the Earth by array‐based earthquake and ambient noise data with inexpensive computation.

Dynamic responses of steep bedding slope-tunnel system under coupled rainfall-seismicity: Shaking table test

The coupling effects of rainfall, earthquake, and complex topographic and geological conditions complicate the dynamic responses and disasters of slope-tunnel systems. For this, the large-scale shaking table tests were carried out to explore the dynamic responses of steep bedding slope-tunnel system under the coupling effect of rainfall and earthquake. Results show that the slope surface and elevation amplification effect exhibit pronounced nonlinear change caused by the tunnel and weak interlayers. When seismic wave propagates to tunnels, the weak interlayers and rock intersecting areas present complex wave field distribution characteristics. The dynamic responses of the slope are influenced by the frequency, amplitude, and direction of seismic waves. The acceleration amplification coefficient initially rises and then falls as increasing seismic frequency, peaking at 20 Hz. Additionally, the seismic damage process of slope is categorized into elastic (2-3 m/s2), elastoplastic (4-5 m/s2) and plastic damage stages (≥ 6.5m/s2). In elastic stage, ΔMPGA (ratio of acceleration amplification factor) increases with increasing seismic intensity, without obvious strain distribution change. In plastic stage, ΔMPGA begins to gradually plummet, and the strain is mainly distributed in the damaged area. The modes of seismic damage in the slope-tunnel system are mainly of tensile failure of the weak interlayer, cracking failure of tunnel lining, formation of persistent cracks on the slope crest and waist, development and outward shearing of the sliding mass, and buckling failure at the slope foot under extrusion of the upper rock body. This study can serve as a reference for predicting the failure modes of tunnel-slope system in strong seismic regions.

The role of mining-induced seismicity amplitude and frequency in gob-side roadway rib spalling

During underground coal mining, Mining-induced seismicity is a crucial factor leading to roadway deformation. Based on a case study of rib spalling caused by mining-induced seismicity in China, this paper utilizes the Universal Distinct Element Code to investigate the mechanism of rib spalling. It analyzes the stress evolution process of roadway surrounding rock and the damage process under the influence of mining-induced seismicity. Additionally, it examines the relationship between seismic wave amplitude, frequency and the damage characteristics of roadway surrounding rock. Findings show that seismic waves induce stress concentration zones in the deeper surrounding rock, causing shear failure, while stress concentration zones emerge in the top, bottom and shoulders of roadway, leading to tensile failure in the shallower surrounding rock. With increasing seismic wave amplitude, the critical crack length of surrounding rock decreases, resulting in a linear increase in crack count and distribution area. The roadway exhibits a ‘n'-shaped damage profile primarily driven by shear failure. With increasing seismic wave frequency, the crack count in the surrounding rock of the roadway exhibits a trend of initially increasing and then decreasing. This trend becomes more pronounced with larger amplitudes. Rib spalling damage is influenced by seismic wave frequency and amplitude: frequencies of 20–25 Hz and 80–100 Hz require amplitudes exceeding 3 m for damage, while 25–30 Hz and 55–80 Hz require amplitudes over 2 m, and 30–55 Hz necessitate amplitudes exceeding 1.5 m.

Asymptotic Series of the Associated Legendre Function with Respect to Seismic Surface Waves

The asymptotic series of the associated Legendre function is investigated for the angular degrees n=2-13 in the context of the amplitude and wavelength of seismic surface waves. The approximate formula for the associated Legendre function is used to determine the wavelength and phase velocity of free oscillations of the Earth and long-period surface waves. The approximate formula is derived from the first term of the asymptotic series and its error increases with decreasing n. In the present study, the effect of higher terms on the approximate formula is studied with respect to the amplitudes of the 1st term (a1), the 2nd term (a2), and the 3rd term (a3). For the colatitude angle θ of π/3≦θ≦2π/3, the amplitude ratios a2/a1 are approximately 3.5％-1.0％ for n=2-11 and are less than 1.0％ for n ≧ 12, while the amplitude ratios a3/a1 are approximately 0.4％ - 0.03％ for n=2-13. The effect of amplitudes of higher terms on the 1st term increases as the colatitude angle approaches the pole or the antipode. The wavelengths of the 1st term (λ1) , the 2nd term (λ2) , and the 3rd term (λ3) are in the sequence λ1 >λ2 >λ3. The wavelength ratiosλ2 /λ1 and λ3 >λ1 for n=2-13 are 0.71%-0.93% and 0.55%-0.87%, respectively. The relationship of the wavelengths between the different angular degrees may be expressed as λ n k =λn-1k+1, where n and k are respectively the angular degree and the ordinal number of the asymptotic series.

1300-m-High gas plume from pockmarks in the north Nansha waters, South China sea

The northeastern region of Nansha Waters, located in the southern margin of the South China Sea, is abundant in gas resources. However, it remains unclear if the central and northern areas of Nansha Waters possess gas resources and if there are any associated leaks. The Jiuzhang Basin is located in the northern Nansha Waters. Pre-stack depth migration, analysis of seismic attributes and multibeam data processing were conducted to image the seabed topography and backscatter intensity, as well as the seismic structure of the water and sedimentary layers in the Jiuzhang Basin. The result reveals a presence of large plumes, approximately 1500 m in width and up to 1300 m in height, from a pockmark. The plume is characterized by a strong seismic amplitude featuring chaotic reflections, a high instantaneous frequency (100–150 Hz), and a strong instantaneous amplitude. These seismic features commonly appear in hydrocarbon-bearing seawater, indicating that the plume is composed of gas. The relationship between the volume fraction of bubbles in the gas plumes and the amplitude of multi-channel seismic waves suggests that the volume fraction of bubbles within the gas plume can reach up to 5.0 × 10−3. Meanwhile, a new pockmark with a length of 248 m, a width of 90 m, and a depth of 20.4 m, and an abrupt 22 m drop in water depth of an existing pockmark are observed in the gas plume area. These observations, combined with the gas plume revealed by the multi-channel seismic collected in 2013 and multibeam collected in 2020, suggest a very strong and recently active gas leaks in the pockmark area of the northern Jiuzhang Basin. Furthermore, in the pockmark area, there are gas-bearing formations with weak reflections, and mud diapirs charactered by low seismic velocity, low amplitude chaotic reflections, and pulled up reflections on both sides, and faults extend to the seabed. These observations suggest that gas plume originate from deep strata of the northern Jiuzhang Basin. Large gas plumes and mud diapirs are often indicative of the existence of deep gas reservoirs. Therefore, the presence of such active gas plumes and mud diapirs in the northern region of the Jiuzhang Basin signifies the presence of abundant gas resources.

Preliminary Implications of Viscoelastic Ray Theory for Anelastic Seismic Tomography Models

ABSTRACT The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed-form solutions of forward ray-tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray-tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide-angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray-tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near-critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre-near-critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray-tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.

Can the seismic wave attenuation characteristics of various soils be identified using distributed acoustic sensing?

Seismic waves exhibit distinct attenuation characteristics that are contingent upon the medium they traverse. The attenuation characteristics can be employed to monitor engineering activities, such as detecting gas pipeline leaks and third-party intrusions, by the utilization of Distributed Acoustic Sensing (DAS) technology. This study aims to explore the feasibility of identifying the seismic wave attenuation characteristics of different soils using DAS. A circular experimental pit with a diameter of 1 m was designed to measure the responses of various soils. Seismic waves were recorded while propagating through sand and clay under different overlying pressure conditions, encompassing both dry and wet states. The waveform data, collected at various distance from the point of excitation, were analyzed using Power Spectral Density (PSD), Continuous Wavelet Transform (CWT), and quality factor analysis. The energy attenuation amplitude of seismic waves shows an opposite pattern in sand and clay as water content increased. By utilizing the seismic wave attenuation characteristics, it is possible to issue timely warnings for identifying third-party intrusions around urban underground tunnels and pipelines to mitigate potential damage to underground infrastructure.

Seismic Beacon-A New Instrument for Detection of Changes in Rock Massif.

The seismic beacon is a new instrument that allows for the measurement of changes in a rock massif with high sensitivity. It is based on effects, which affect the propagation of harmonic seismic waves generated continuously with stable and precise frequency and amplitude. These seismic waves are registered by a system of seismic stations. The amplitude of the seismic signal is very small, and it is normally hidden in a seismic noise. Special techniques are applied to increase the signal-to-noise ratio. In 2020, the first prototype of the seismic beacon was constructed in a laboratory, and field tests were performed in 2022 and 2023. During the tests, the changes in spectral amplitude and phase of seismic waves were detected, which is interpreted as the changes in material properties. These measurements testified the basic functionality of the device. The seismic beacon has been developed primarily for the detection of critical stress before an earthquake, which is manifested by non-linear effects such as higher harmonics generation. In addition, it could be used, for example, in the detection of magma movements, groundwater level changes, changes in hydrocarbon saturation in rocks during the extraction of oil and natural gas, or the penetration of gases and liquids into the earth's crust.

Fiber bundle model applied to slope stability assessment: co-detection multi-threshold analysis for early warning

Forecasting the imminent failure of natural slopes is crucial for effective Disaster Risk Reduction. However, the nonlinear nature of geological material failure makes predictability challenging. Recent advancements in seismic wave monitoring and analysis offer promising solutions. In this study, we investigated the co-detection method, which involves real-time processing of micro-seismic events detected concurrently by multiple sensors, to provide easy access to their initial magnitude and approximate location. By studying the Fiber Bundle Model and considering the attenuation of seismic waves, we demonstrated disparities in the statistical behavior of various rupture types before global catastrophic failure. Comparing avalanches with attenuated seismic wave amplitudes directly measured at sensor locations, we observed differences in their evolution towards catastrophic rupture. Leveraging a network of seismic wave sensors, we showed that the co-detection method was effective in detecting precursory seismic events, even with weak signals, making it a valuable tool for monitoring and predicting unstable slopes. Additionally, we demonstrated that a multi-threshold analysis of co-detection activity allowed for instantaneous capture of the seismic activity structure on unstable slopes. These findings contribute to our understanding of slope stability and offer insights for improved hazard assessment and risk management.

Dynamic response characteristics of shaking table model tests on the gabion reinforced retaining wall slope under seismic action

In the present study, a series of shaking table model tests were performed on a slope with a gabion reinforced retaining wall. Transfer functions were employed to compute the inherent frequencies of the slope. Furthermore, the investigation examined various aspects of the slope, including the peak acceleration amplification factor, incremental dynamic stresses, displacements, and tensile forces. Additionally, the study employed the Hilbert Huang transform (HHT) to analyze the slope's time-frequency characteristics and energy distribution. The findings of the study revealed that there is an inverse relationship between the amplitude of the input seismic wave and the natural frequency of the top of the gabion reinforced retaining wall slope. As the amplitude of the seismic wave increases, the natural frequency of the slope decreases. The amplification factors for peak acceleration were all found to be less than 1.9, suggesting a notable dissipation of seismic energy in comparison to typical slopes. The response of incremental dynamic stress was most pronounced in the middle section of the slope, followed by the top of the slope. The magnitude of the incremental displacement was found to be highest at layer 4, whereas the incremental tensile force exhibited its maximum value at layer 5. The dynamic response exhibited the least pronounced characteristics at the lower portion of the slope, demonstrating the most stable behavior. The peak frequencies observed in the Hilbert marginal spectrum displayed comparable characteristics to the natural frequencies.

Physics-Informed Deep Learning-Based Real-Time Structural Response Prediction Method

High-precision and efficient structural response prediction is essential for intelligent disaster prevention and mitigation in building structures, including post-earthquake damage assessment, structural health monitoring, and seismic resilience assessment of buildings. To improve the accuracy and efficiency of structural response prediction, this study proposes a novel physics-informed deep-learning-based real-time structural response prediction method that can predict a large number of nodes in a structure through a data-driven training method and an autoregressive training strategy. The proposed method includes a Phy-Seisformer model that incorporates the physical information of the structure into the model, thereby enabling higher-precision predictions. Experiments were conducted on a four-story masonry structure, an eleven-story reinforced concrete irregular structure, and a twenty-one-story reinforced concrete frame structure to verify the accuracy and efficiency of the proposed method. In addition, the effectiveness of the structure in the Phy-Seisformer model was verified using an ablation study. Furthermore, by conducting a comparative experiment, the impact of the range of seismic wave amplitudes on the prediction accuracy was studied. The experimental results show that the method proposed in this paper can achieve very high accuracy and at least 5000 times faster calculation speed than finite element calculations for different types of building structures.

Numerical Analysis of the Dynamic Response Law of Counter-Tilt Layered Rock Slopes

Counter-tilt layered rock slopes are common types of slopes that are susceptible to destabilizing damage under seismic action. Therefore, the dynamic response law of counter-tilt layered rock slopes under seismic action is of great significance for the study of slope stability. This study utilizes UDEC (Universal Distinct Element Code) numerical simulation software to vary slope geometry and seismic wave parameters, such as joint thickness, joint inclination angle, slope angle, seismic wave frequency, amplitude, and duration. The maximum displacements of the monitoring points of a slope were obtained, and the dynamic response law of counter-tilt layered rock slopes under seismic action was investigated. The results yielded the following insights: (1) The thickness of the joints of a slope is an important factor affecting the dynamic response of a slope, and with the increase in the thickness of the joints, the maximum displacement of each monitoring point of the slope will decrease. (2) The maximum displacement of a slope increases with the increase in the joint inclination angle and the slope angle. When the joint inclination angle is less than 50°, the change in the joint inclination angle has less of an effect on the maximum displacement of the slope in the x and y directions. When the joint inclination angle is more than 50°, the maximum displacement of the slope in the x and y directions increases faster with the change in the joint inclination angle, and a similar pattern is observed for the slope angle. (3) Slopes are less susceptible to damage when both the joint inclination angle and the slope angle are less than 50°, and the probability of slope damage increases significantly when both are greater than 50°. (4) The maximum displacement at each monitoring point of a slope increases with the frequency, amplitude, and duration of a seismic wave. (5) Seismic wave amplitude has the greatest effect on the dynamic response of a slope, followed by duration, and frequency has the weakest effect on the dynamic response of a slope. The conclusions drawn in this paper can be useful for the control of counter-tilt layered rock slopes.

Coda wave attenuation in Northern Aceh, Indonesia from a single station measurement: preliminary results

Sumatra-Andaman subduction zone is one of the most active tectonic areas in the world. Understanding seismic risk in this region is important for hazard mitigation. One of the crustal physical properties is attenuation. Attenuation structure may affect the seismic propagation through the medium. It expresses the seismic wave amplitude decay when wave propagates through a medium. In this preliminary result, we report the seismic attenuation characteristics in Northern Aceh, Indonesia. We estimate coda waves attenuation from a single station from GE network. using a single back-scattering model. We analyze about 123 waveforms from local earthquakes (less than 3°) with magnitudes between 3 and 6 using a single back-scattering model. The depth of the events is selected to be shallower than 40 km depth. We estimate coda quality factor (Qc ) for each event at frequencies 1 – 8 Hz. The coda window is estimated from two times of S-wave arrival time with different window length ranging from 20 to 80 s. Reference coda quality factor (Q0 ) is selected at frequency of 1 Hz. We obtain that Q0 varies from 74.34 ± 10.04 to 160.2 ± 5.96 at 20 s and 80 s window lengths, respectively. The frequency dependence factor (η) decreases from 1.12 ± 0.06 to 1.05 ± 0.03 at 20 s and 80 s window length, respectively. An increase of Q0 with window length may suggest the depth dependent of seismic wave attenuation at reference frequency of 1 Hz. Low Q0 and high η are also consistent with this region’s high tectonic activity.

Elastic and anelastic adjoint tomography with and full Hessian kernels

SUMMARYThe elastic and anelastic structures of the Earth offer fundamental constraints for understanding its physical and chemical properties. Deciphering small variations in the velocity and amplitude of seismic waves can be challenging. Advanced approaches such as full-waveform inversion (FWI) can be useful. We rewrite the anelastic Fréchet kernel expression of Fichtner & van Driel using the displacement–stress formulation. We then derive the full Hessian kernel expression for viscoelastic properties. In these formulations, the anelastic Fréchet kernels are computed by the forward strain and a shift of the adjoint strain. This is complementary to the quality factor Q (i.e., inverse attenuation) Fréchet kernel expressions of Fichtner & van Driel that are explicit for the velocity–stress formulation. To reduce disk space and I/O requirements for computing the full Hessian kernels, the elastic full Hessian kernels are computed on the fly, while the full Hessian kernels for Q are computed by a combination of the on-the-fly approach with the parsimonious storage method. Applications of the Fréchet and full Hessian kernels for adjoint tomography are presented for two synthetic 2-D models, including an idealized model with rectangular anomalies and a model that approximates a subduction zone, and one synthetic 3-D model with an idealized geometry. The calculation of the full Hessian kernel approximately doubles the computationally cost per iteration of the inversion; however, the reduced number of iterations and fewer frequency stages required to achieve the same level of convergence make it overall computationally less expensive than the classical Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) FWI for the 2-D elastic tested models. We find that the use of full Hessian kernels provides comparable results to the L-BFGS inversion using the improved anelastic Fréchet kernels for the 2-D anelastic models tested for the frequency stage up to 0.5 Hz. Given the computational expense of the Q full Hessian kernel calculation, it is not advantageous to use it in Q inversions at this time until further improvements are made. For the 3-D elastic inversion of the tested model, the full Hessian kernel provides similar image quality to the L-BFGS inversion for the frequency stage up to 0.1 Hz. We observe an improved convergence rate for the full Hessian kernel inversion in comparison to L-BFGS at a higher frequency stage, 0.1–0.2 Hz, and we speculate that at higher frequency stages the use of full Hessian kernels may be more computationally advantageous than the classical L-BFGS for the tested models. Finally, we perform 3-D elastic and Q L-BFGS inversions simultaneously using the rederived Q kernels, which can reduce the computational cost of the inversion by about 1/3 when compared to the classical anelastic adjoint tomography using the additionally defined adjoint source. The recovered Q model is smeared when compared to the recovered elastic model at the investigation frequencies up to 0.5 Hz. Q inversion remains challenging and requires further work. The 2-D and 3-D full Hessian kernels may be used for other purposes for instance resolution analysis in addition to the inversions.

CBM reservoir thickness prediction using the seismic nonlinear stochastic inversion method

Due to the complex reservoir conditions and rapid changes in lithological facies in seismic exploration, predicting coalbed methane (CBM) reservoirs is quite challenging. Conventional inversion methods are not highly effective at predicting reservoir thickness, and cannot keep up with current demands. Our aim is to demonstrate how seismic data can be used to forecast coal thickness, as well as the distribution and orientation of subtle structures that may be linked to enhanced permeability zones. In this study, we used a nonlinear stochastic inversion method based on making full use of seismic data and constraining it with known information, such as drilling and logging analysis. This method has been successfully applied in a mining area in Wuxiang County in the southeastern part of Shanxi Province. Compared with the actual geological data, it is found that the prediction accuracy is consistent with the drilling results, and the distribution of the predicted CBM reservoir thickness is consistent with the geological information. Furthermore, due to the randomness of the subsurface medium, the accuracy of reservoir prediction can be increased by observing the target layer seismic reflection wave amplitude, frequency, and other properties.