Homogeneous Velocity Model Research Articles

Numerical simulation of ultrasonic P-wave propagation in water-bearing coal based on gas-liquid homogeneous wave velocity model

This paper establishes the equivalent density and equivalent P-wave velocity models of coal bodies with different water saturation, and investigates the P-wave propagation evolution law of coal bodies with different water saturation from the perspective of numerical simulation. When the experimental coal samples continue to use high-pressure water after reaching the natural saturation state, the water saturation can be further increased, and the increase in water saturation is larger, and the corresponding P-wave velocity also appears to be increased more substantially, and this phenomenon also occurs in numerical simulation results, which indicates that the P-wave velocity will have an obvious increasing trend when the coal body is from nearly saturated to fully saturated. The experimental and numerical simulation results show that the P-wave velocity of coal samples increases with the water saturation degree in a similar exponential function, which further verifies the reasonableness and feasibility of the modelling based on the assumption of gas-liquid homogeneous medium. In addition, the propagation of P-wave in coal samples is affected by the pore and fracture structure, and the pore and fracture with small pore size has less influence on the P-wave, and vice versa.

Locating clustered seismicity using Distance Geometry Solvers: applications for sparse and single-borehole DAS networks

Summary The determination of seismic event locations with sparse networks or single-borehole systems remains a significant challenge in observational seismology. Leveraging the advantages of the location approach HADES (eartHquake locAtion via Distance gEometry Solvers), which was initially developed for locating clustered seismicity recorded at two stations, through the solution of a Distance Geometry Problem, we present here an improved version of the methodology: HADES-R (HADES-Relative). Where HADES previously needed a minimum of 4 absolutely located master events, HADES-R solves a least-squares problem to find the relative inter-event distances in the cluster, and uses only a single master event to find the locations of all events, and subsequently applies rotational optimizer to find the cluster orientation. It can leverage iterative station combinations if multiple receivers are available, to describe the cluster shape and orientation uncertainty with a bootstrap approach. The improved method requires P- and S-phase arrival picks, a homogeneous velocity model, a single master event with a known location, and an estimate of the cluster width. The approach is benchmarked on the 2019 Ridgecrest sequence recorded at two stations, and applied to two seismic clusters at the FORGE geothermal test site in Utah, USA, with a microseismic monitoring scenario with a DAS in a vertical borehole. Traditional procedures struggle in these settings due to the ill-posed network configuration. The azimuthal ambiguity in such a scenario is partially overcome by the assumption that all events belong to the same cluster around the master event and a cluster width estimate. We are able to find the cluster shape in both cases, although the orientation remains uncertain. HADES-R contributes to an efficient way to locate multiple events simultaneously with minimal prior information. The method’s ability to constrain the cluster shape and location with only one well-located event offers promising implications, especially for environments where limited or specialised instrumentation is in use.

Acoustic full waveform inversion for 2-D ambient noise source imaging

SUMMARYWe present a method for estimating seismic ambient noise sources by acoustic full waveform inversion (FWI) of interstation cross-correlations. The method is valid at local scales for laterally heterogeneous media, and ambient noise sources confined to the Earth’s surface. Synthetic tests performed using an actual field array geometry, are used to illustrate three unique aspects of our work. First: the method is able to recover noise sources of arbitrary spatial distribution, both within and outside the receiver array, with high fidelity. This holds true for complex velocity models and does not require a good initial guess for inversion, thereby addressing an outstanding issue in the existing research literature. Second: we analyse the extent of biases in source inversion that arise due to inaccurate velocity models. Our findings indicate that source inversion using simplified (e.g. homogeneous) velocity models may work reliably when lateral variations in velocity structure are limited to 5 or 10 per cent in magnitude, but is vitiated by strong variations of 20 per cent or higher, wherein the effect of strong scattering and/or phase distortions become significant. Finally, our technique is implemented without the adjoint method, which is usually inextricably linked to FWI. Inversions are performed using source kernels computed for each receiver pair, and this approach is computationally tractable for real-world problems with small aperture seismic arrays.

Sensitivity analysis to near-surface velocity errors of the Kirchhoff single-stack redatuming of multi-coverage seismic data

We present a study of a Kirchhoff-type redatuming approach for irregular multi-coverage land seismic data to remove the disturbing influence of rugged topography and a considerable near-surface velocity inhomogeneity, like a thick weathering layer, on the subsurface reflections. The redatuming method is physically more justified than the commonly used field-static correction methods that provide - in the indicated situation - non-physical temporal adjustments (field statics) by shifting traces in time, which lead to sub-optimal imaging and inversion of the reflections. The redatuming procedure studied here is different: It transforms the multi-coverage seismic reflection data on the irregular measurement surface to a regular measurement configuration on a pre-specified datum, below the inhomogeneous velocity overburden. This is done by stacking/summing the input traces with certain operators or traveltime curves which are calculated by ray tracing. In this way, incoherent subsurface reflections in the input data become coherent and thus recognizable in the output data. To have this happen, the redatuming operation requires a good approximation of the overburden velocity model and a reasonable one of the sub-burden homogeneous velocity model (below the datum). Then the multi-coverage output data on the new flat datum can be imaged and inverted much better than with standard data processing, i.e., with field-static correction. This work is dedicated to explaining the single-stack Kirchhoff-type redatuming approach kinematically using a synthetic model and data based on a real geological situation. However, our main aim is to study the sensitivity of this redatuming method to errors of the overburden velocity model, which is determined from multi-coverage seismic data using first arrivals traveltime tomography commonly used in the oil industry. We apply the redatuming process to a multi-coverage synthetic seismic dataset generated from the models that represent the real geological situation with irregular measurement surfaces and inhomogeneous overburden or near-surface velocity. To assess accuracy, the redatumed data was migrated in depth-domain and the results showed the correct positioning of the reflectors. The results revealed that this redatuming method produces reliable and accurate redatumed data even using approximate velocity models, which can be useful for prestack time and depth imaging.

Convolutional neural network-based moment tensor inversion using domain adaptation for microseismicity monitoring

Microseismic monitoring is widely used to analyze the locations and growth directions of fractures formed at sites of hydraulic fracturing treatment and CO2 geologic sequestration. Because moment tensors can provide focal mechanisms, moment tensor inversion has received considerable attention in microseismic monitoring; the real-time processing of moment tensor inversion is important for rapid decision-making. Pre-trained machine learning (ML) models can make nearly instantaneous predictions in the application stage and thus present an attractive alternative to real-time processing. However, prior information regarding the velocity model at the target site is a prerequisite for generating the dataset used to train the ML model that is applied in moment tensor inversion. In addition, it is difficult to create the training dataset because it requires three-dimensional numerical modelling when the velocity model is complex; numerous simulations must be executed for sources with various locations and moment tensors. To overcome these limitations, we applied the domain adaptation technique to the convolutional neural network (CNN)-based moment tensor inversion method, which uses peak amplitudes and arrival times of P- and S-waves as input features. The CNN model was pre-trained with the dataset generated from a homogeneous velocity model. Then, in the domain adaptation stage, the pre-trained model was fine-tuned along with the target dataset. To validate the performance of the domain adaptation, moment tensors from both horizontal and tilted three-layer models were predicted. In each case, the domain-adapted model performance was similar to the performances of the CNN-based models that had been trained using the dataset generated with the exact target velocity models.

Seismic source location using the shortest path method based on boundary discretisation scheme for microseismic monitoring in underground mines

In seismic monitoring at underground mines, the velocity models can be highly complex, particularly in presence of major geological structures . In practice, homogeneous velocity models have been widely used for the purposes of seismic event location in mine seismology . Although heterogeneous velocity models can be incorporated, ray tracing methods need be adopted in these velocity models to compute the travel times for accurately locating seismic events. These methods require each geological unit to be discretised to grids (corner-node or center-node discretisation scheme), which requires large computational capacity. In this research, the Shortest Path Method (SPM) (Moser, 1991) based on a novel Boundary Discretisation Scheme (BDS) is proposed to compute the travel times for seismic event location in heterogeneous velocity models. Only the boundaries of each geological unit are discretised to nodes. The graphical network is constructed by establishing ray paths between discretised nodes on the boundaries of geological units. Dijkstra’s algorithm (Dijkstra et al., 1959) using heap sorting method (Cao et al., 1993) is applied to search for the shortest ray paths with the first arrivals for seismic event location. The accuracy and efficiency of this method are validated using a 2D synthetic example. The seismic events recorded during the field monitoring of a dyke-roadway intersected area are located with the proposed BDS-SPM method. The results demonstrate that, compared with the conventional location method using homogeneous velocity models, the proposed method can provide more accurate seismic event locations for microseismic monitoring in underground mines.

Microseismic P-Wave Travel Time Computation and 3D Localization Based on a 3D High-Order Fast Marching Method.

The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.

Damped wave-equation-based first-arrival traveltime tomography using the embedded boundary method

First-arrival traveltime tomography (FATT) is used to delineate shallow velocity structures to identify static effects in oil exploration as well as to characterize the near surface for geotechnical purposes. Because FATT is generally used for land seismic data processing, it becomes necessary to consider irregular topography especially when performing wave-based tomography. However, the standard Cartesian finite-difference method cannot properly handle irregular topography. Hence, the embedded boundary method (EBM) is incorporated into the frequency-domain damped-wave equation to correctly describe irregular topography. The developed modeling algorithm is used to calculate first-arrival traveltimes and to perform FATT. The EBM-based modeling algorithm accurately describes the irregular surfaces of numerical velocity models on a regular mesh by exploiting the mirror image principle. The accuracy of the EBM-based traveltime calculation is validated by using two homogeneous velocity models with dipping and complex surfaces. The validation results demonstrate that our algorithm is unaffected by the staircase approximation. FATT is then applied to synthetic and real data to demonstrate the applicability of the developed algorithm to velocity models with complex topography. For the real data example, the inverted velocity model is used to apply static corrections. The processing results demonstrate an improvement in the continuity of seismic events, thus confirming the accuracy of the developed FATT method.

Locating Mine Microseismic Events in a 3D Velocity Model through the Gaussian Beam Reverse-Time Migration Technique.

Microseismic (MS) source location is a fundamental and critical task in mine MS monitoring. The traditional ray tracing-based location method can be easily affected by many factors, such as multi-ray path effects, waveform focusing and defocusing of wavefield propagation, and low picking precision of seismic phase arrival. By contrast, the Gaussian beam reverse-time migration (GBRTM) location method can effectively and correctly model the influences of multi-path effects and wavefield focusing and defocusing in complex 3D media, and it takes advantages of the maximum energy focusing point as the source location with the autocorrelation imaging condition, which drastically reduces the requirements of signal-to-noise ratio (SNR) and picking accuracy of P-wave arrival. The Gaussian beam technique has been successfully applied in locating natural earthquake events and hydraulic fracturing-induced MS events in one-dimensional (1D) or simple two-dimensional (2D) velocity models. The novelty of this study is that we attempted to introduce the GBRTM technique into a mine MS event location application and considered utilizing a high-resolution tomographic 3D velocity model for wavefield back propagation. Firstly, in the synthetic test, the GBRTM location results using the correct 2D velocity model and different homogeneous velocity models are compared to show the importance of velocity model accuracy. Then, it was applied and verified by eight location premeasured blasting events. The synthetic results show that the spectrum characteristics of the recorded blasting waveforms are more complicated than those generated by the ideal Ricker wavelet, which provides a pragmatic way to evaluate the effectiveness and robustness of the MS event location method. The GBRTM location method does not need a highly accurate picking of phase arrival, just a simple detection criterion that the first arrival waveform can meet the windowing requirements of wavefield back propagation, which is beneficial for highly accurate and automatic MS event location. The GBRTM location accuracy using an appropriate 3D velocity model is much higher than that of using a homogeneous or 1D velocity model, emphasizing that a high-resolution velocity model is very critical to the GBRTM location method. The average location error of the GBRTM location method for the eight blasting events is just 17.0 m, which is better than that of the ray tracing method using the same 3D velocity model (26.2 m).

Robust wavefield inversion via phase retrieval

SUMMARY Extended formulation of full waveform inversion (FWI), called wavefield reconstruction inversion (WRI), offers potential benefits of decreasing the non-linearity of the inverse problem by replacing the explicit inverse of the wave-equation operator of classical FWI (the oscillating Green functions) with a suitably defined data-driven regularized inverse. This regularization relaxes the wave-equation constraint to reconstruct wavefields that match the data, hence mitigating the risk of cycle skipping. The subsurface model parameters are then updated in a direction that reduces these constraint violations. However, in the case of a rough initial model, the phase errors in the reconstructed wavefields may trap the waveform inversion in a local minimum leading to inaccurate subsurface models. In this paper, in order to avoid matching such incorrect phase information during the early WRI iterations, we design a new cost function based upon phase retrieval, namely a process which seeks to reconstruct a signal from the amplitude of linear measurements. This new formulation, called wavefield inversion with phase retrieval (WIPR), further improves the robustness of the parameter estimation subproblem by a suitable phase correction. We implement the resulting WIPR problem with an alternating-direction approach, which combines the majorization-minimization (MM) algorithm to linearise the phase-retrieval term and a variable splitting technique based upon the alternating direction method of multipliers (ADMM). This new workflow equipped with Tikhonov-Total variation (TT) regularization, which is the combination of second-order Tikhonov and total variation regularizations and bound constraints, successfully reconstructs the 2004 BP salt model from a sparse fixed-spread acquisition using a 3 Hz starting frequency and a homogeneous initial velocity model.

Relocating Mining Microseismic Earthquakes in a 3-D Velocity Model Using a Windowed Cross-Correlation Technique

Microseismic source location is a fundamental research interest in real-time microseismic monitoring and hazard risk assessment, and it provides the basis for determining the fracture zones and calculating seismic source parameters of the microseismicity (e.g., the event magnitude, the focal mechanism). In the present work, we carefully relocate some microseismic earthquakes that occurred in the Yongshaba mine (China) using the shooting 3-D ray-tracing (3D-RT) method based on a high-resolution 3-D velocity model, which is determined by a large amount of seismic data. Furthermore, a semiautomatic waveform cut method based on the cross-correlation (CC) technique (WCC) is developed for a quick, robust and precise determination of the direct P-phase relative delay times. Compared with the full waveform cross-correlation (FWCC)-based method, the WCC-based method is free from the influence of complex later-phase waveform spectra. To verify the proposed method, we artificially generate the locations of 892 synthetic microseismic events, the P-phase travel times of which are calculated based on the given 3-D velocity model and the 3-D ray-tracing technique. The relocated hypocentres of these synthetic events obtained by the developed method are improved compared with those obtained by a homogeneous velocity model and the straight line-ray tracing based L1 norm time difference (TD) method (HV-SL-TD1), as well as those obtained by the 3-D velocity model and the straight line-ray tracing based L1 norm and L2 norm TD methods (3D-SL-TD1 and 3D-SL-TD2). Finally, we apply the proposed method to eight experimental blasts with pre-measured locations. The synthetic and application tests show that, despite some multi-path phenomena existing in the ray-tracing methods, the WCC-based method performs as well as the experienced manual picking method, and the results obtained by the 3D-RT location have smaller location errors (~30 m) than those of the homogeneous velocity model-based methods (>40 m). The TD-based method is slightly better than the trigger time (TT)-based method when using the same norm, and the location precision of the L1 norm-based methods have a better resilience to larger picking errors than that of the L2 norm-based methods. Further improvements can be obtained by improving the resolution of the 3-D velocity model and including spatial voids in the model (e.g., tunnels and cavities) for the inversion.

Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method

We propose a radial basis function collocation method (RBF method) to solve fractional Laplacian visco-acoustic wave equation for the Earth media having heterogeneous velocity model and complex geometry. Unlike the fractional Laplacian wave equation proposed in Zhu and Harris (2014), the wave equation we consider has a different definition for the fractional Laplacian. Specifically, spectral and Riesz fractional Laplacians are considered in Zhu and Harris (2014) and the present paper, respectively. Accordingly, the Fourier pseudospectral method (FPS method) and the RBF method are employed to solve the spectral and the Riesz fractional Laplacian wave equations. The two wave equations are observed to produce obviously different wavefields. We demonstrate the validity and flexibility of the proposed RBF method by considering five benchmarks of seismic forward modeling: (1) two-dimensional Earth media with four types of velocity models (homogeneous, two-layer, homogeneous but complex-geometry, and heterogeneous models) and (2) a spherical medium with homogeneous velocity model. We make a three-way comparison among numerical solutions to the Riesz fractional Laplacian, the spectral fractional Laplacian, and the integer-order visco-acoustic wave equations, and observe that when wave attenuation is weak the Riesz wave equation yields more similar wavefield to that of the integer-order wave equation than the spectral wave equation does. Furthermore, uniform and quasi-uniform layouts for collocation points of the RBF method are considered, and the latter layout turns out to be economical since it can preserve the solution accuracy with the minimum number of collocation points. The RBF method is truly mesh-free and dimension-free and can easily handle high-dimensional, irregular domains. Additionally, the method is easier to implement than element-based methods, such as finite element and spectral element methods, for discretizing the Riesz fractional Laplacian.

3-D fluid channel location from noise tremors using matched field processing

SUMMARY Presently ongoing geodynamic processes within the intracontinental lithospheric mantle give rise to different natural phenomena in the NW Bohemia/Vogtland region (Czech Republic, Germany), amongst others: earthquake swarms, mineral springs and degassing zones of mantle-derived fluids as well as highly concentrated CO2 (mofettes). Their interaction mechanisms and relations are not yet fully understood, but fluid pathways within the crust are assumed, that allow efficient fluid transport between the main hypocentral swarm quake region and the degassing areas at the surface. Here, we focus on the location of the presumed fluid channels as well as on the investigation of their near-surface spatio-temporal variability, targeting a depth of a few hundreds of metmetres. We applied a 3-D matched field processing (MFP) approach in the frequency band of 10–20 Hz considering the fluid flow as seismic noise source. Within three campaigns in 2015/2016, we recorded continuous seismic noise data on the Hartoušov Mofette Field within the Cheb Basin (NW Bohemia, CZ), which is a key site to study fluid flow as it is characterized by strong and continuous surface degassing of CO2. We used temporary arrays varying in extent (70-600 m aperture) and in the amount of stations (25–95 units). Assuming a homogeneous velocity model and applying conventional MFP phase-matching over a 3-D grid search, we located two channel-like structures beneath the test site, which could be traced down to a common source area down to 2000 m depth. We thereby evaluated the influence of amplitude normalization of the measured noise signal on the MFP location considering water-filled or dry mofette channels. Additionally, a spatio-temporal analysis using time windows with a length of 10 min during 5 hr of noise record shows variability of fluid flow activity in space and time and hence, its migration beneath the test site on a short timescale.

Trapezoid coordinate finite difference modeling of acoustic wave propagation using the CPML boundary condition

Due to compaction of clastic sedimentary rocks caused by gravitational forces, the wave propagation velocity tends to gradually increase with depth. Based on this observation, a trapezoid coordinate system is built to integrate the general velocity variation, and an acoustic wave equation is derived in the new coordinate system. Numerically, a conventional uniform rectangular grid FD scheme can be evoked to solve the new equation. Physically, a variable grid mesh is used: that is, fine grids for shallow areas with low velocity and coarse grids for deep areas with high velocity. This method is free of artificial reflections caused by the transition of different grid sizes. Furthermore, the Convolutional Perfectly Matched Layer (CPML) boundary condition is adapted to eliminate artificial boundary reflections. A homogeneous velocity model is used to verify the effectiveness of the CPML boundary. Tests using the Marmousi benchmark model show that with the demonstrated comparable accuracy, the proposed method is 2.9 times as fast as the conventional physical uniform grid FD algorithm while saving as much as 75% of the computer memory.

Prestack Depth Migration Using Seismic Virtual Source Gathers

Prestack depth migration is used to image for complex geological structure. In this case, the surface reflection data are used as an input data in general. However, the surface reflection data have some problems in imaging the subsalt and the salt flank due to the complex wavefields and multiples which come from overburden. To overcome the defect of the surface reflection data, we used the virtual source in terms of seismic interferometry to image the subsurface. Inhomogeneous velocity models were developed and virtual source gathers were generated ocean bottom seismic numerical modelling. Cross-correlation gathers were generated by the crosscorrelation between the reference trace and others. The virtual source gathers were made by the integration at the stationary phase interval. Numerical test showed that the virtual source gathers integrated at the stationary interval are superior to that of all sources. To verify the possibility of subsurface imaging, prestack depth migration was applied for the virtual source gathers. This prestack depth migrated section re-produced the velocity model below receivers.. Especially artificial interface by multiples were suppressed without any further data processing. The results of imaging obtained from inhomogeneous velocity model below receivers also showed that the artificial geological interfaces were significantly reduced comparing to the homogeneous velocity models case.

Finite-fault source inversion using adjoint methods in 3-D heterogeneous media

Accounting for lateral heterogeneities in the 3-D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1-D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3-D heterogeneity in source inversion involves pre-computing 3-D Green’s functions, which requires a number of 3-D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense data sets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green’s functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green’s functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3-D heterogeneous velocity model. The velocity model comprises a uniform background and a 3-D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3-D velocity model are performed for two different station configurations, a dense and a sparse network with 1 and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak-slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect, homogeneous velocity model. We find that, for velocity uncertainties that have standard deviation and correlation length typical of available 3-D crustal models, the inverted sources can be severely contaminated by spurious features even if the station density is high. When data from thousand or more receivers is used in source inversions in 3-D heterogeneous media, the computational cost of the method proposed in this work is at least two orders of magnitude lower than source inversion based on pre-computed Green’s functions.

Imaging Shallow Crustal Structure in the Upper Mississippi Embayment Using Local Earthquake Waveform Data

A 1D normal moveout (NMO)‐corrected and stacked pseudoprofiling method was applied to analyze the characteristic features shown on primary P ‐ and S ‐wave coda and on Sp waveforms from local microearthquakes in an attempt to image prominent reflectors and to resolve shallow crustal velocity structure (∼5 km) in the upper Mississippi embayment. Acoustic well log data were used to constrain the P ‐wave velocity in the upper 5 km. Events at close distances and with clear P and S arrivals were selected to ensure reliable NMO correction for reflections and transmissions. The observed reflections and transmissions are important controlling factors on modeling waveforms. We analyzed local earthquake data recorded at all broadband and one short‐period station of the Cooperative New Madrid Seismic Network. Despite polarity differences among P , S , and Sp waveforms, consistent reflectors in the sedimentary section can be imaged across the three wave types. Correlation with a basement‐penetrating well indicates that reflectors at the base of the Upper Cretaceous–Holocene Mississippi Embayment Supergroup, the base of the Cambrian–Ordovician Knox Group, and the high‐velocity lower Upper Cambrian Bonneterre Formation are shown in pseudoprofiles among stations in the upper Mississippi embayment. Our study finds that a one‐layer homogeneous velocity model of sediments in the ranges of 1.95–2.42 km/s for V P and 0.60–0.73 km/s for V S overlying a half‐space of Paleozoic rocks with velocities in the ranges of 6.0–6.2 km/s for V P and 3.26–3.6 km/s for V S can represent shallow crustal structure in the upper Mississippi embayment. Differential times of P – PpPhp and S – SsShs appear linearly proportional to sediment thicknesses, which best fits a one‐layer sediment structure with average V P 2.042±0.041 km/s and V S 0.709±0.051 km/s, in the least‐squares sense predicted by the wave propagation effects. Online Material: Figures illustrating seismograms, process procedure, imaged reflectors, and resolved velocity structure for six broadband stations and one short‐period station.

Source reverberations, near-surface resonances, or Q? Comment on “The peak frequency of direct waves for microseismic events” (Leo Eisner, Davide Gei, Miroslav Hallo, Ivo Opršal, and Mohammed Y. Ali, Geophysics, 78, no. 6, A45–A49)

In a recent Geophysics Letter, Eisner et al. (2013) measure peak frequencies in velocity spectra of direct waves from microseismic events. The authors interpret these peak frequencies as being caused by attenuation and use them for estimating the effective Q -factor of the medium. Nevertheless, I point out a significant problem with these results, namely, that the authors’ model for the earthquake source is not accurate enough to allow the determination of Q for the surrounding medium. This can be seen by considering the following question: Do the Q values reported in Eisner et al. (2013) characterize the medium, the source model, or the spectral data for direct arrivals? Eisner et al. (2013) assume the first of these answers to be correct; however, careful analysis shows that the correct answer is actually the last one. In answering the above question, note that the Q and t * values measured by this method are not unique physical properties of the medium because they change whenever a different source model is used. The flat plateau at f f c in the Eisner et al. (2013) source spectrum is unrealistic, and yet this plateau is the principal tool of the authors’ method for Q estimation. If we use, for example, Brune’s (1970) model as a more accurate one, then the Q would be much larger than the values reported by Eisner et al. (2013) (see the subsection “Meaning of Q ” below). Thus, the inferred Q s follow from the assumed source model. However, these Q values still cannot be viewed as corrections to the source model because even after these corrections, the model fits the observations very poorly (see the subsection “Data fit”). Therefore, the Q values proposed by Eisner et al. (2013) can only be interpreted as the observed spectral-peak frequencies heuristically multiplied by traveltimes: …

Kirchhoff prestack depth migration in 3-D simple models: comparison of triclinic anisotropy with simpler anisotropies

We use Kirchhoff prestack depth migration to calculate migrated sections in 3-D simple anisotropic homogeneous velocity models in order to demonstrate the impact of anisotropy on migrated images. The recorded wave field is generated in models composed of two homogeneous layers separated by one either non-inclined or inclined curved interface. The anisotropy in the upper layer is triclinic. We apply Kirchhoff prestack depth migration to velocity models with different types of anisotropy: a triclinic anisotropic medium, an isotropic medium, transversely isotropic media with a horizontal (HTI) and vertical (VTI) symmetry axis. We observe asymmetry in migration caused by triclinic anisotropy and we show the errors of the migrated interface caused by inaccurate velocity models used for migration. The study is limited to P-waves.

Seismo-volcano source localization with triaxial broad-band seismic array

Seismo-volcano source localization is essential to improve our understanding of eruptive dynamics and of magmatic systems. The lack of clear seismic wave phases prohibits the use of classical location methods. Seismic antennas composed of one-component (1C) seismometers provide a good estimate of the backazimuth of the wavefield. The depth estimation, on the other hand, is difficult or impossible to determine. As in classical seismology, the use of three-component (3C) seismometers is now common in volcano studies. To determine the source location parameters (backazimuth and depth), we extend the 1C seismic antenna approach to 3Cs. This paper discusses a high-resolution location method using a 3C array survey (3C-MUSIC algorithm) with data from two seismic antennas installed on an andesitic volcano in Peru (Ubinas volcano). One of the main scientific questions related to the eruptive process of Ubinas volcano is the relationship between the magmatic explosions and long-period (LP) swarms. After introducing the 3C array theory, we evaluate the robustness of the location method on a full wavefield 3-D synthetic data set generated using a digital elevation model of Ubinas volcano and an homogeneous velocity model. Results show that the backazimuth determined using the 3C array has a smaller error than a 1C array. Only the 3C method allows the recovery of the source depths. Finally, we applied the 3C approach to two seismic events recorded in 2009. Crossing the estimated backazimuth and incidence angles, we find sources located 1000 ± 660 m and 3000 ± 730 m below the bottom of the active crater for the explosion and the LP event, respectively. Therefore, extending 1C arrays to 3C arrays in volcano monitoring allows a more accurate determination of the source epicentre and now an estimate for the depth.