Velocity Model Inversion Research Articles

Seismic Monitoring near Ithaca, New York, Reveals Nonuniform Distribution of Microseismicity in an Intraplate Region

Abstract Cornell University intends to use a deep direct-use geothermal system to heat its Ithaca, New York, campus. In preparation for this project, the Cornell Seismic Network has been monitoring the background seismicity in this intraplate region since 2019. From January 2020 to June 2023, 95 events were detected within 20 km of the proposed geothermal well site, with local magnitudes ranging from −1.02 to 0.56. None of these events appear in regional or national catalogs. Events locate in a narrow geographic band, with one-fourth exhibiting multimodal hypocentral probability peaks both near the surface and at 1–4 km depth. We relocate events with a joint hypocenter and 1D velocity model inversion, in addition to a fully nonlinear method, and then compare observations with synthetic waveforms. Together, these approaches provide strong evidence for >95% of events locating at the surface or within the 3-km-thick sedimentary sequence. We explore how anthropogenic activity and regional topographic stress may contribute to frequent surficial events. This information is critical for characterizing the background microseismicity for comparison during future geothermal operations. Ithaca’s geology of Paleozoic sediments overlying Precambrian crystalline basement is typical of many continental interiors, so these results also provide insight into intraplate microseismicity patterns.

Seismic Velocity Inversion via Physical Embedding Recurrent Neural Networks (RNN)

Seismic velocity inversion is one of the most critical issues in the field of seismic exploration and has long been the focus of numerous experts and scholars. In recent years, the advancement of machine learning technologies has infused new vitality into the research of seismic velocity inversion and yielded a wealth of research outcomes. Typically, seismic velocity inversion based on machine learning lacks control over physical processes and interpretability. Starting from wave theory and the physical processes of seismic data acquisition, this paper proposes a method for seismic velocity model inversion based on Physical Embedding Recurrent Neural Networks. Firstly, the wave equation is a mathematical representation of the physical process of acoustic waves propagating through a medium, and the finite difference method is an effective approach to solving the wave equation. With this in mind, we introduce the architecture of recurrent neural networks to describe the finite difference solution of the wave equation, realizing the embedding of physical processes into machine learning. Secondly, in seismic data acquisition, the propagation of acoustic waves from multiple sources through the medium represents a high-dimensional causal time series (wavefield snapshots), where the influential variable is the velocity model, and the received signals are the observations of the wavefield. This forms a forward modeling process as the forward simulation of the wavefield equation, and the use of error back-propagation between observations and calculations as the velocity inversion process. Through time-lapse inversion and by incorporating the causal information of wavefield propagation, the non-uniqueness issue in velocity inversion is mitigated. Through mathematical derivations and theoretical model analyses, the effectiveness and rationality of the method are demonstrated. In conjunction with simulation results for complex models, the method proposed in this paper can achieve velocity inversion in complex geological structures.

Walkaway vertical seismic profiling first-arrival traveltime tomography with velocity structure constraints

Abstract Walkaway vertical seismic profiling (WVSP) is known for its high level of credibility in obtaining the relationship between first-arrival traveltime and detector depth through first-arrival picking. This relationship can be utilized for seismic velocity model inversion to improve velocity model accuracy and rationality. Here, we present a WVSP first-arrival velocity model with velocity structure constraints, by utilizing layer and fault data interpreted by ground seismic structure technique. We constructed a geological structure and layer sequence models based on sedimentary patterns to obtain complex velocity structures. Furthermore, we introduced a smooth regularization term based on the velocity structure into the inversion model to enhance its consistency with geological laws and compensate for the reduced inversion accuracy owing to the regularization term based on flat structures. This approach addressed the limitations of the regularization term based on flat structures, resulting in more accurate and reliable inversion results. Through simulation analysis, the proposed method realized the WVSP first-arrival velocity inversion, with results being closer to those of the real velocity model.

Seismic velocity inversion transformer

Velocity model inversion is one of the most challenging tasks in seismic exploration, and an accurate velocity model is essential for high-resolution seismic imaging. Recently, velocity inversion methods based on deep learning (DL), particularly convolutional neural networks (CNNs), have attracted considerable attention from the seismic exploration community. These researchers aim to directly estimate the velocity model from raw seismograms using a well-trained model. Although CNN-based velocity inversion methods have demonstrated remarkable performance in terms of intelligence and automation, their inversion performance is often constrained by a limited long-range dependence. Specifically, when conducting a convolutional operation on raw seismic data using small kernels (i.e., 1 × 1, 3 × 3, 5 × 5, and 7 × 7), CNN-based methods extract only the local features and neglect the weak spatial correlation between different local features that reflect the information of the same interface. This correlation could assist CNN in providing an overview of the seismic data and promote inversion performance when using DL. Furthermore, the time-varying properties of seismic data pose a challenge to the weight sharing of CNNs. Here, we have developed a new DL framework based on a transformer, called the seismic velocity inversion transformer (SVIT), to address the problem of velocity inversion. SVIT uses a self-attention mechanism to capture the long-range dependence of seismic data, rather than stacking multiple convolutional layers as in CNNs. Thus, SVIT can provide more informative remote features for building velocity models. The validity and reliability of the proposed method are demonstrated through numerical experiments using synthetic models. Compared with the conventional full-waveform inversion method and an existing CNN-based velocity inversion method, our SVIT indicates greater consistency with the target in terms of the velocity value, subsurface structures, and geologic interfaces and is expected to provide a new DL-based solution to resolve inversion problems.

Dynamic Time Warping as an Alternative to Windowed Cross Correlation in Seismological Applications

Abstract We investigate the feasibility of using the dynamic time warping (DTW) technique as an alternative to windowed cross correlation (WCC) for an indirect measure to quantify both the similarity and relationship between two seismic time series. We first examine the sensitivity and performance of the DTW technique by analyzing both synthetic and real seismic time series in geophysical applications. Results show that DTW efficiently retrieves useful information from seismic data and has a high sensitivity to minor variations in time series that WCC fails to detect. We further propose four potential applications of DTW to routine seismic data interpretation—earthquake detection, template matching, clustering of waveforms, and full-waveform inversion for 1D velocity models. The earthquake detection scheme employing DTW is proposed in this study as an alternative to traditional methods. The accuracy of DTW in estimating similarity is explored for template matching and clustering of seismic traces. Finally, we discuss a realistic example of 1D Earth velocity model inversion using DTW and explore its feasibility in full-waveform inversion.

Global characteristics of ambient seismic noise

Ambient seismic noise becomes more and more important and helpful on assisting velocity model inversion, earthquake detection, and ground motion prediction. Based on the analysis of continuous seismic data and ocean wave height, we find that the ocean wave height and winter storms have a controlling factor on the DF microseismic energy level and its frequency extent in time scale. It shows that high and low DF microseismic energy accompanied with wide and narrow frequency range consistent with the high wave height period (when the ocean is stormier) and low wave height period, respectively. Since DF microseism is dominated by Rayleigh waves, its energy attenuates very quickly when it travels through shoreline to the continent crust. Our observations give a quality factor Q of about 83 for DF energy traveling from the middle of the Atlantic to the central of Europe. We observe a lower energy level of SPDF (short period DF) than that of LPDF (long period DF) for the continent stations, however a reversed situation for the island stations. It suggests that short period DF energy decays faster than the long period one. High-frequency ambient noise is called microtremor. The microtremor for the island station with low elevation has a semidiurnal modulation in phase with ocean tide. The microtremor for the station at other locations are from the anthropogenic activities which have diurnal, weekly, and annually variations.

Deep Neural Networks for Detection and Location of Microseismic Events and Velocity Model Inversion from Microseismic Data Acquired by Distributed Acoustic Sensing Array.

Fiber-optic cables have recently gained popularity for use as Distributed Acoustic Sensing (DAS) arrays for borehole microseismic monitoring due to their physical robustness as well as high spatial and temporal resolutions. As a result, the sensors record large amounts of data, making it very difficult to process in real-/semi-real-time using the conventional processing routines. We present a novel approach, based on deep learning, for handling the large amounts of DAS data in real-/semi-real-time. The proposed neural network was trained on synthetic microseismic data contaminated with real-ambient noise from field data and was validated using field DAS microseismic data obtained from a hydraulic fracturing operation. The results indicate that the trained network is capable of detecting and locating microseismic events from DAS data and simultaneously update the velocity model to a high degree of precision. The mean absolute errors in the event locations and the velocity model parameters are 2.04, 0.72, 2.76, 4.19 and 0.97 percent for distance (x), depth (z), P-wave velocity, S-wave velocity and density, respectively. In addition to automation and computational efficiency, deep learning reduces human expert data handling during processing, thus preserving data integrity leading to more accurate and reproducible results.

Low-rank representation of omnidirectional subsurface extended image volumes

Subsurface-offset gathers play an increasingly important role in seismic imaging. These gathers are used during velocity model building and inversion of rock properties from amplitude variations. Although powerful, these gathers come with high computational and storage demands to form and manipulate these high-dimensional objects. This explains why only limited numbers of image gathers are computed over a limited offset range. We avoid these high costs by working with highly compressed low-rank factorizations. These factorizations are obtained via a combination of probings with the double two-way wave equation and randomized singular-value decompositions. In turn, the resulting factorizations give us access to all subsurface offsets without having to form the full extended image volumes (EIVs) that are at best quadratic in image size. As a result, we can easily handle situations in which conventional horizontal offset gathers are no longer focused. More importantly, the factorization also provides a mechanism to use the invariance relation of EIVs for velocity continuation. With this technique, EIVs for one background velocity model can be directly mapped to those of another background velocity model. Our low-rank factorization inherits this invariance property, so that factorization costs arise only once when examining different imaging scenarios. Because all imaging experiments only involve the factors, they are computationally efficient with costs that scale with the rank of the factorization. Examples using 2D synthetics, including a challenging imaging example with salt, validate the methodology. Instead of brute-force explicit crosscorrelations between shifted source and receiver wavefields, our approach relies on the underlying linear-algebra structure that enables us to work with these objects without incurring unfeasible demands on computation and storage.

Deep-learning seismic full-waveform inversion for realistic structural models

Velocity model inversion is one of the most important tasks in seismic exploration. Full-waveform inversion (FWI) can obtain the highest resolution in traditional velocity inversion methods, but it heavily depends on initial models and is computationally expensive. In recent years, a large number of deep-learning (DL)-based velocity model inversion methods have been proposed. One critical component in those DL-based methods is a large training set containing different velocity models. We have developed a method to construct a realistic structural model for the DL network. Our compressional-wave velocity model building method for creating dense-layer/fault/salt body models can automatically construct a large number of models without much human effort, which is very meaningful for DL networks. Moreover, to improve the inversion result on these realistic structural models, instead of only using the common-shot gather, we also extract features from the common-receiver gather as well. Through a large number of realistic structural models, reasonable data acquisition methods, and appropriate network setups, a more generalized result can be obtained through our proposed inversion framework, which has been demonstrated to be effective on the independent testing data set. The results of dense-layer models, fault models, and salt body models that we compared and analyzed demonstrate the reliability of our method and also provide practical guidelines for choosing optimal inversion strategies in realistic situations.

Study on transmitted channel wave-based, horizontal multilayer 3-D velocity model inversion and quantitative coalbed thickness detection method

Most methods using transmitted channel wave (TCW) prospecting to quantitatively detect the thickness of coal seams based on the statistic relationship of group velocity in certain wave bands to the thickness of coal seams cannot be applied universally. To establish a universal applicable method, we first obtained the theoretical dispersion curve of TCW using the generalized reflection–transmission coefficient method and the 1-D horizontal multilayer velocity model, performed iteratively match calculation using the inversion model and the genetic algorithm and analyzed the distributive characteristics of shear wave velocity of coal and rock formations at a certain depth. We then obtained the 3-D velocity images of the coal seam working face based on TCW data using the 3-D back-projection technology. According to the changes of shear wave velocity at the coal–rock interface and the rate of inversion velocity change, we further proposed the quantitative discriminant model for coalbed thickness. Based on the model, we quantitatively interpreted the thickness of the coal seam by computing the depths corresponding to the extremes of the positive and negative rate of the shear wave velocity change and obtained the distribution characteristics of the coal thickness in the working surface. To verify the feasibility and validity of the proposed model for coalbed thickness, we conducted a 3-D physical similarity model experiment and subjected the collected two-component TCW data to inversion calculation and compared the obtained coal seam thickness with the known model parameters. Overall, our study achieved the universal 3-D quantitative detection of coalbed thickness and provided technical supports for intelligentized coalbed mining.

An automated quantitative multi-stage approach to invert velocity models for microseismic event locations

Complexity in hydraulic fracturing programmes has motivated microseismic service providers to innovate and propose creative methods to monitor drilling, completion and field development. Although microseismic analysis and interpretation have moved beyond the ‘dots-in-a-box’ solution, velocity model (VM) calibration using inversion plays a critical role in the initial phase of accurate microseismic event (event) locations to ensure the accuracy of subsequent higher-order microseismic attributes given data quality and monitoring geometry. Knowing that business decisions are, at times, required in real time, it is imperative to provide confident event locations efficiently through the construction of well-constrained VMs based on quantitative and objective methodologies. The most time-consuming aspects of microseismic data processing are optimal VM construction and inversion. In this paper, we demonstrate improved efficiency in microseismic data processing by developing and implementing an automated approach to perforation shot (perf) detection and VM inversion using Particle Swarm Optimization (PSO). These primary tasks (perf detection and VM inversion) are critical in the event location workflow and can benefit significantly from increased efficiency. Although more advanced Greens functions can provide more accurate solutions to the source location problem (e.g., Angus et al., 2014), we focus on ray-based approaches due to their high computational efficiency, especially for anisotropic media and hydraulic fracture monitoring where large volumes of microseismic data (commonly in excess of 100,000 events) must be processed.

Velocity analysis and subsurface source location improvement using moveout-corrected gathers

The location of subsurface seismic events is important for various geophysical applications. For example, it can be used for underground intrusion detection, monitoring precursors of natural hazards (e.g., sinkholes, rock-falls, landslides, etc.), tracking the structural integrity of mines, locating trapped personnel, and microseismic reservoir monitoring. For a useful analysis, it is imperative that located events be as close as possible to their true spatial position. Although a variety of location methods have been developed, most assume that the correct velocity model is known and are very sensitive to errors in its estimation. Velocity is often estimated at recording borehole locations and calibrated if possible. However, calibration requires manual picking that may induce errors. We use moveout-corrected gathers, whose flatness serves as an objective function, for picking-free velocity model inversion using known source locations. These gathers can be constructed using any implementation of seismic wave propagation. To limit computational costs, we use an eikonal traveltimes solver. The inverse problem is solved using a global optimization approach with an adequate borehole-driven model parameterization. The method performs well in constructing an effective velocity model for location with or without knowledge of the source origin time. We show its application on reservoir-scale synthetic examples as well as a 3D shallow subsurface field one and show the significant final improvement in location accuracy. A single known source is used for calibration of the velocity model. The updated model is not necessarily correct, but it can be effectively used to improve location.

VSP data inversion for vertical velocity gradient and elliptical anisotropy model

Inversion of velocity parameters for the walkaway VSP data in a multilayered medium can be impeded by velocity gradients and anisotropy in some layers. A problem occurs if we compare velocities obtained from borehole seismic profiling which are equal to their vertical components with the velocities calculated with paths coming from far offsets where the horizontal component plays an important role, especially when the vertical gradient exists and the ray paths are curve-shaped. In this contribution we present the results of velocity model inversion for VSP data considering velocity gradient and elliptical anisotropy. The algorithm consists of two steps, optimization of velocity parameters and optimization of ray paths for the given model. Both procedures use the Nelder-Mead simplex method which finds local minima. Due to the character of optimization we performed also multistart analysis which can provide information about possible equivalences between parameters. Analysis was conducted for different parameterizations, in some cases allowing introduction of additional parameters: vertical gradient and elliptical anisotropy coefficient. The optimal model for a specific set of data is chosen with the help of Bayesian Information Criterion to balance complexity of model with quality of approximation of traveltimes.

Coal mine microseismic velocity model inversion based on first arrival time difference

The formation velocity is an important factor affecting the precise location of microseismic source. The establishment of elastic wave velocity model in the monitoring area to satisfy the requirements for precise location of seismic source has been a technical problem for the mine microseismic monitoring. Based on the assumption of horizontal layered medium condition, a new velocity model inversion method has been proposed. According to the concept of equal difference time surface, the first arrival travel time difference between the measured points and datum points is investigated on the basis of the observation point of first arrival travel time duration placed in the middle in the observational network. The minimal difference (double time difference) between the measured first arrival time difference and the calculated first arrival time difference is taken as the constraint condition, and the objective function is constructed to solve the velocity model. The DIRECT fast search algorithm with global optimization characteristics is applied to solve the objective function. This method is used to carry out the trial treatment for the mine microseismic model data and the measured data. The results show that the stratified velocity model under the horizontal layered medium can be obtained by his method using the microseismic data of known seismic source, with a better adaptability to different monitoring systems. Through the test for the actual data of “well-ground” joint microseismic monitoring, the velocity model obtained by the method in this paper can get more accurate location of the seismic source.

Results of downhole microseismic monitoring at a pilot hydraulic fracturing site in Poland — Part 2: S-wave splitting analysis

Observations of azimuthal seismic anisotropy provide useful information, notably on stress orientation and the presence of preexisting natural fracture systems, during hydraulic fracturing operations. Seismic anisotropy can be observed through the measurement of S-wave splitting (SWS) on waveforms generated by microseismic events and recorded on downhole geophone arrays. We have developed measurements of azimuthal anisotropy from a Lower Paleozoic shale play in northern Poland. The observed orthorhombic anisotropic symmetry system is dominated by a vertically transverse isotropy (VTI) fabric, produced by the alignment of anisotropic platy clay minerals and by thin horizontal layering and overprinted by a weak azimuthal anisotropy. Despite the dominating VTI fabric, we successfully identified a weaker horizontal-transverse isotropy fabric striking east–southeast. We do this by constraining the rock-physics model inversion with VTI background parameters incorporated from other geophysical methods: microseismic velocity model inversion, 3D reflection seismic, and borehole cross-dipole sonic logs. The obtained orientation is consistent with a preexisting natural fracture set that has been observed using X-ray micro-imaging (XRMI) image logs from a nearby vertical well. The present-day regional maximum horizontal stress direction differs from the observed fracture strike by approximately 45°. This implies that the SWS measurements recorded during hydraulic stimulation of a shale-gas reservoir are imaging the preexisting natural fracture set, which influences the treatment efficiency, instead of the present-day stress.

Microseismic velocity model inversion and source location: The use of neighborhood algorithm and master station method

The accuracy of the velocity model strongly affects the accuracy of microseismic source location and hence the reliability of fracture imaging. We have developed a systematic methodology for microseismic velocity model inversion and source location. A new misfit function is used for both problems, which yields more reliable result than the conventional ones. Using the same measure of misfit, the location errors resulting from the use of different misfit functions are eliminated. The neighborhood algorithm and master station method (MSM) are adopted for calculating the velocity model and source location, respectively. The reason for using the neighborhood algorithm is that it has fewer tuning parameters and is easy to be tuned, whereas the advantage of the MSM is that it can automatically remove the mispicks. The performance of the proposed methods is illustrated using the ball-hit events with known locations, and the validity of the inversion results is verified by the relocations of these events. We also used the inverted velocity models to locate the microseismic events detected from the monitoring data. The location result indicates that the fractures have an average half-length of 280 m and height of 55 m and the fracture azimuth is approximately N77°W.

Velocity-model estimation with NIP-wave tomography inversion – A real data example

The common-reflection-surface (CRS) stack in addition to high signal-to-noise ratio stacked sections creates the curvature and local dip of a reflector. With this information, so-called kinematic wavefield attributes, it is possible to obtain a subsurface velocity model for laterally inhomogeneous media using normal-incidence-point (NIP) wave inversion. The result of CRS provides some location points on the stacked section as input for the inversion. In each iteration, dynamic ray tracing is applied along the central ray according to an input data point. With this technique, the parameter needed for forward modeling will be obtained. By updating the velocity model and minimizing the misfit between input data and the forward model parameter, it is possible to achieve a final velocity model consistent with input data. In this paper, we applied the CRS method on complex structure in the northeast of Iran, and then we performed the NIP-wave tomography inversion on this data set by means of CRS attributes. The result clearly shows the ability of NIP-wave tomography in velocity-model inversion.

An Automatic Phase Picker for Local Earthquakes with Predetermined Locations: Combining a Signal‐to‐Noise Ratio Detector with 1D Velocity Model Inversion

We present a simple method to pick additional P and S phases for local earthquakes with predetermined locations. Different from conventional characteristic function techniques, our method incorporates 1D velocity inversion into phase picking. It first predicts phase arrivals using initial velocity models and available event locations and then applies a detector function to search genuine phase arrivals around the initial predictions. Using the newest searched phase arrivals (picks), the velocity models are updated accordingly and then used to predict more accurate arrival times. Such a procedure can be iterated multiple times, during which both phase picking and velocity model are improved. We perform a synthetic test with a 1D velocity model. The resulting phase picks are consistent with true arrivals, and true velocity models can be well recovered. Another test with real data recorded by the Anza Seismic Network in southern California shows that the resulting velocity models agree with the average Southern California Earthquake Center community models in this region. Out of 23,932 event–station pairs, 23,770 P picks and 21,935 S picks are obtained from this method. After four iterations, 90% of our P picks and 80% of our S picks have differences within 0.15 s from the phase picks of the Southern California Earthquake catalog. Given its simplicity and efficiency and ability to produce robust P and S picks and 1D velocity models, the technique is particularly suitable for a wide range of seismological research in which phase picks at additional stations and/or refined 1D velocity models are needed.

Full‐waveform inversion for macro velocity model reconstruction in look‐ahead offset vertical seismic profile: numerical singular value decomposition‐based analysis

ABSTRACTFull‐waveform inversion is currently considered as a potential tool for improving depth‐velocity models for areas with complex geology. It is well‐known that success of the inversion is very sensitive to the available low‐frequency content of the data. In the paper we investigate this issue considering a look‐ahead offset vertical seismic profile survey and applying singular value decomposition analysis of a linearized forward map as the main tool. We demonstrate with this technique the difference between the sequential full‐waveform inversion strategy and the original time‐domain approach proposed in the early 1980s. We emphasize the role of the lowest frequency in the data, which is necessary for reliable velocity model inversion in particular cases. Finally we show the existence of a trade‐off between the lowest frequency and a regularization parameter of the inversion procedure. The presented approach may be adapted to answer general questions regarding the quality of data and acquisition system parameters required for feasible full‐waveform inversion.

Feasibility of joint 1D velocity model and event location inversion by the Neighbourhood algorithm

ABSTRACTUsing a set of synthetic P‐ and S‐wave onsets, computed in a 1D medium model from sources that mimic a distribution of microseismic events induced by hydrofrac treatment to a monitoring geophone array(s), we test the possibility to invert back jointly the model and events location. We use the Neighbourhood algorithm for data inversion to account for non‐linear effects of velocity model and grid search for event location. The velocity model used is composed of homogeneous layers, derived from sonic logging. Results for the case of one and two monitoring wells are compared. These results show that the velocity model can be obtained in the case of two monitoring wells, if they have optimal relative position. The use of one monitoring well fails due to the trade‐off between the velocity model and event locations.