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The Imperial Valley is a seismically active basin occupying the southern end of the Salton trough, an area of rapid extension, high heat flow, and abundant geothermal resources. This report describes an ongoing large-scale distributed acoustic sensing (DAS) recording study acquiring high-density seismic data on an array between Calipatria and Imperial, California. This 27 km array, operating on dark fiber since 9 November 2020, has recorded a wealth of local seismic events as well as ambient noise. The goal of the broader Imperial Valley Dark Fiber project is to evaluate passive DAS as a tool for geothermal exploration and monitoring. This report is intended to provide installation information, noise characteristics, and metadata for future studies utilizing the data set. Because of the relatively small number of basin-scale DAS studies that have been conducted to date, we also provide a range of lessons learned during the deployment to assist future researchers exploring this acquisition strategy.

The study of seismic sources and wave propagation in ice plate is helpful to understand the structure, migration, fracture mechanics, mass balance and other processes. However, due to extreme environment, in-situ dense seismic observations are rare and the dynamic changes of the ice plate remain poorly understood. We conduct a seismic experiment with distributed acoustic sensing array on a frozen lake. We excite water vibrations by under-water airgun shots. With an artificial intelligence method, we detected seismic signals including high frequency icequakes and low frequency events. Icequakes cluster along the fractures and correlate with the local temperature variation. The flexural-gravity wave reveals the property of the ice plate. Our study demonstrates the utility of DAS array as an in-situ dense seismic network in illuminating the internal failure process and dynamic deformation of ice plate such as ice shelf, which contributes to understanding and prediction of disintegrations of ice shelves.

Elastic-wave imaging using multicomponent data can provide more useful subsurface information than acoustic-wave imaging, but it is usually algorithmically challenging. We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media. Our new method uses a vector deconvolution imaging condition based on dual wavefield decomposition, including an explicit directional wavefield separation using the Hilbert transform and a P/S vector wavefield decomposition using the low-rank decomposition method. Using three elastic models, we numerically determine that our new method produces notably higher resolution and more amplitude-balanced elastic images compared with a crosscorrelation-based vector elastic reverse time migration method.

The effective monitoring of hydraulic fracturing in unconventional oil and gas production requires tools to quantify elastic property variations even in the absence of microseismic activity. To track the subtle time-lapse variations in reservoir properties during such activities, monitoring techniques with high repeatability and high resolution, spatially and temporally, are required. Distributed acoustic sensing (DAS) is a rapidly maturing fiber-optic technology for low-cost, permanent, high density, in-well monitoring. Surface orbital vibrators (SOVs) are inexpensive fixed rotary seismic sources that offer the opportunity to frequently interrogate the subsurface with energies comparable to vibroseis sources. We have evaluated a field vertical seismic profile test, conducted in the Eagle Ford play, pairing an SOV source recorded by DAS behind casing in a deviated well to better evaluate the potential of the technology set for unconventional reservoir monitoring. We determine the data processing workflow for reservoir monitoring using the SOV-DAS system. We analyze the data characteristics of the SOV-DAS system, including the signal-to-noise ratio characteristics and source repeatability. High-quality P- and S-wave reflections, as well as mode conversions, are visible in the vertical section. In addition, clear P-P reflections are also observable along the horizontal well sections. Time shifts with a mean value of 10 μs between different data sets demonstrate the high repeatability for the semipermanent SOV source, which is crucial for time-lapse analysis. We also apply reflection imaging on P and S to reveal reflection depths. In a first-of-its-kind deployment, we implemented a rotating SOV with a slewing bearing and discuss the possibility to optimize S-wave construction along the horizontal well with specific SOV orientation directions. Our preliminary results indicate that the combination of repeatable surface sources such as SOVs with DAS has significant potential for providing a low-cost approach for high-resolution seismic monitoring of unconventional reservoirs.

The sparsity of permanent seismic instrumentation in marine environments often limits the availability of subsea information on geohazards, including active fault systems, in both time and space. One sensing resource that provides observational access to the seafloor environment are existing networks of ocean bottom fiber optic cables; these cables, coupled to modern distributed acoustic sensing (DAS) systems, can provide dense arrays of broadband seismic observations capable of recording both seismic events and the ambient noise wavefield. Here, we report a marine DAS application which demonstrates the strength and limitation of this new technique on submarine structural characterization. Based on ambient noise DAS records on a 20 km section of a fiber optic cable offshore of Moss Landing, CA, in Monterey Bay, we extract Scholte waves from DAS ambient noise records using interferometry techniques and invert the resulting multimodal dispersion curves to recover a high resolution 2D shear-wave velocity image of the near seafloor sediments. We show for the first time that the migration of coherently scattered Scholte waves observed on DAS records can provide an approach for resolving sharp lateral contrasts in subsurface properties, particularly shallow faults and depositional features near the seafloor. Our results provide improved constraints on shallow submarine features in Monterey Bay, including fault zones and paleo-channel deposits, thus highlighting one of many possible geophysical uses of the marine cable network.

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two-way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation-based reflection waveform inversion using one-way wave equations to retrieve the background velocity. In this method, one-way wave equations are used for the seismic wave forward modelling, migration/de-migration and the gradient computation of objective function in frequency domain. Compared with the method using two-way wave equation, the proposed method benefits from the lower computational cost of one-way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two-way wave equation both for two- and three-dimensional situations. Through numerical analysis, we also find that one-way wave equations can better construct the low wavenumber reflection wavepath without producing high-amplitude short-wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.

A vertical seismic profiling (VSP) survey conducted in 2010 in the original RRG-9 well at the Raft River geothermal field is to understand the subsurface geologic structures for geothermal reservoir characterization. This survey consists of 40 three-component (3C) geophones deployed in the upper 600 m of the well and 255 vibroseis sources positioned along eight walkaway lines at the surface. We perform elastic-waveform inversion and reserve-time migration of the VSP data to obtain high-resolution subsurface images. We first process the raw walkaway 3C VSP data and separate the upgoing compressional-to-compressional (PP) and compressional-to-shear (PS) wavefields. We then build an initial velocity model based on sonic logging and zero-offset VSP data, update the initial model with first-arrival traveltime tomography, and refine the model using elastic-waveform inversion to reveal high-resolution velocity variations. We finally apply reverse-time migration to the upgoing wavefields to obtain high-resolution PP and PS migration images of the lithologies encountered in the well. The refined velocity models obtained using elastic-waveform inversion improve the subsurface migration imaging results. Our elastic-waveform inversion and reverse-time migration confirm the lithology interfaces revealed from well logs and provide images of subsurface geologic layers away from well RRG-9 at the Raft River geothermal field.

The absence of low-frequency information in seismic data is one of the most difficult problems in elastic full waveform inversion. Without low-frequency data, it is difficult to recover the long-wavelength components of subsurface models and the inversion converges to local minima. To solve this problem, the elastic envelope inversion method is introduced. Based on the elastic envelope operator that is capable of retrieving lowfrequency signals hidden in multicomponent data, the proposed method uses the envelope of multicomponent seismic signals to construct a misfit function and then recover the longwavelength components of the subsurface model. Numerical tests verify that the elastic envelope method reduces the inversion nonlinearity and provides better starting models for the subsequent conventional elastic full waveform inversion and elastic depth migration, even when low frequencies are missing in multicomponent data and the starting model is far from the true model. Numerical tests also suggest that the proposed method is more effective in reconstructing the long-wavelength components of the S-wave velocity model. The inversion of synthetic data based on the Marmousi-2 model shows that the resolution of conventional elastic full waveform inversion improves after using the starting model obtained using the elastic envelope method. Finally, the limitations of the elastic envelope inversion method are discussed.

Because modeling for full-waveform inversion (FWI) cannot produce reflections unless the velocity model has the scattering potential (high wavenumbers), using a migration/demigration process to generate modeling data, which is a key step in what is now known as reflection FWI (RFWI), is a credible alternative to tackle the reflection nonlinearity associated with FWI. However, because RFWI depends on a conventional data residual or zero-lag correlation objective function, high nonlinearity can still exist when the true amplitude migration is not used, as well as at far offsets due to cycle skipping. To avoid the cycle skipping and the need for a true amplitude migration, we have developed a correlation-based reflection full-waveform inversion method to update the low-wavenumber components of the velocity model. The success of this method relies on a sensitivity kernel decomposition and a correlation-based objective function. The sensitivity kernel decomposition makes it possible to separate out the contributions of different subkernels and to smear the reflected wave residuals along the “rabbit-ear” wavepath to obtain middle and deep background model estimates. The correlation-based objective function measures differences in kinematic information and behaves in a more linear way than the traditional waveform residual misfit. Moreover, our approach is less sensitive to the frequency content and amplitude information of the seismic data, enabling reliable background velocity estimates to be obtained without the need for low frequencies and full-physics modeling. Because the kinematic features of reflected waves are described correctly, the inversion result of the proposed method can be used as a migration model or an initial model for conventional FWI to achieve a correct high-wavenumber model update.

Full waveform inversion (FWI) has been a successful tool to build high resolution velocity models, but it is affected by a local minima problem. The conventional multi-scale strategy to tackle this severe problem may not work for real seismic data without long offsets and low frequency data. We use an envelope-based objective function FWI method to provide the long wavelength components of the velocity model for the traditional FWI. The gradient can be computed efficiently with the adjoint state method without any additional computational cost. Simple models are used to prove that the envelope-based objective function is more convex than the traditional misfit function, thus the cycle-skipping problem can be mitigated. Due to the envelope demodulation effect, the adjoint source of the envelope-based FWI contains abundant low frequency information, therefore the gradient tends to sense the low wavenumber model update. A Marmousi synthetic data example illustrates that the envelope-based FWI method can provide an adequately accurate initial model for the traditional FWI approach even when the initial model is far from the true model and low-frequency data are missing.

In this paper, based on the acoustic Born kernel, we propose a flexible method to calculate the gradient and the approximate Hessian in frequency-domain full waveform inversion (FWI) by matrix decomposition. In this method, neither the kernel nor the approximate Hessian is necessarily stored in memory. We name FWI using this method as matrix decomposition FWI (MDFWI). Most of the calculation in MDFWI depends on the forward modeling from sources and unrepeated receivers in frequency domain. For the first order direction, this method is a good replacement of adjoint-state FWI (ADFWI) when the source number ns is more than half of number of the receiver stations nr, such as in controlled source exploration, OBS exploration, and natural seismology. For the second order direction, MDFWI is senior to commonly used ADFWI when source-station number is more than only a few percent of the receiver-station number. The effectiveness of MDFWI is proved through 2D numerical experiments.

A multi-scale approach is often applied to mitigate the nonlinearity of FWI. By using high precision variated-density acoustic wave equation, we analyze the variation of different objective function behaviors with media parameters (velocity, density, impedance and so on) perturbation in model space systematically. Through this analysis, some existing strategies are verified and the initial model building strategies are presented. Moreover, a series of numerical experiments are carried out to prove that the analysis of the objective function behaviors in FWI can provide effective strategies and theoretical guidance for FWI.

Full waveform inversion has been a successful tool to build high resolution velocity models, but it suffers from local minima problem. We propose an envelope based method allowing the updating of long wavelength components of the velocity model. The gradient of the misfit function can be efficiently computed through adjoint-state technique. We use simple models to prove that the envelope objective function is more convex than the traditional FWI objective function and is not as sensitive to the frequency components of the data as traditional FWI. Finally we compare the new approach to the traditional FWI through an application on a simple 2D synthetic data set to illustrate our method can be a supplement to traditional FWI approach when initial model is far from the true model and low-frequency data is missing.

Summary Full waveform inversion (FWI) is usually solved by local optimization methods. The Hessian or curvature information is of vital importance to improve the convergence rate and resolution of inversion. But it is difficult to compute directly because of high computational costs and large memory requirements. Quasi-Newton and Hessian-free inexact Newton (HFN) methods which do not need explicit Hessian matrix are popular to overcome these difficulties. This paper interlaces iteration of the limited memory BFGS method (L-BFGS) and a HFN method, designs a new scheme which adjusts the iteration type dynamically by the decrease ratio of the objective function, and then obtains a modified hybrid iteration optimization method. It uses curvature information about the objective function collected by one type of iteration to improve the performance of the other. Numerical experiments indicate that the hybrid method got better computation efficiency than L-BFGS method. It also performed faster than the HFN method and conjugate gradient (CG) method. Thus, it’s another effective method for FWI.

Summary A kind of hybrid scattering series combing both Born and Rytov approximations is presented in this paper. It contains a free variable which controls its behavior to continuously vary between the two approximations. The linearized hybrid approximation also has its own valid condition. Like Born or Rytov approximation, the hybrid series can also be applied to full waveform inversion (FWI). The calculation of the Frechet derivatives depends on the approximation chosen to linearly link data and parameter perturbations. We demonstrate this linearized hybrid approximation by simple numerical experiments on a spherical model. The inversion results show that the hybrid approximation achieves less error than either Born or Rytov approximation.