Geophysics

Stolt’s frequency‐wavenumber (f-k) method is computationally efficient and has unlimited dip accuracy for constant‐velocity media. Although the f-k method can handle moderate vertical velocity variations, errors become unacceptable for steep dips when such variations are large. This paper describes an extension to the f-k method that removes its restrictions on vertical velocity variation, yielding accuracy comparable to phase‐shift migration at only a fraction of the computational time. This extension of the f-k method is based on partitioning the velocity field, just as in cascaded finite‐difference migration, and performing a number of stages of f-k migration. In each stage, the migration‐velocity field is closer to a constant—the ideal situation for the f-k migration method—than when the migration is done conventionally (i.e., in just one stage). Empirical results and error analyses show that, at most, four stages of the cascaded f-k algorithm are sufficient to migrate steep events as accurately as by the phase‐shift method for virtually any vertically inhomogeneous velocity field. Given its accuracy and efficiency, cascaded f-k migration can become the method of choice for 2-D, two‐pass 3-D, and single‐pass 3-D time migrations.

Assessing the effectiveness of elastic full-waveform-inversion (FWI) algorithms when applied to shallow 2D structures in the presence of a complex topography is critically important. By using FWI, we overcome inherent limitations of conventional seismic methods used for near-surface prospecting (acoustic tomography and multichannel spectral analysis of surface waves). The elastic forward problem, formulated in the frequency domain, is based on a mixed finite-element P0-P1 discontinuous Galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost. The inversion problem uses an FWI algorithm to minimize the misfit between observed and calculated data. Based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the Super-Sauze earthflow, we analyzed the effect of using a hierarchical preconditioning strategy, based on a simultaneous multifrequency inversion of damped data, to mitigate the strong nonlinearities coming from the surface waves. This strategy is a key point in alleviating the strong near-surface effects and avoiding convergence toward a local minimum. Using a limited-memory quasi-Newton method improved the convergence level. These findings are analogous to recent applications on large-scale domains, although limited source-receiver offset ranges, low-frequency content of the source, and domination of surface waves on the signal led to some difficulties. Regarding the impact of data decimation on the inversion results, we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution. In our investigations of the effect of increased source spacing, we found that a sampling of 4 m (less than three times the theoretical maximum of one half-wavelength) led to severe aliasing.

Passive seismic low-frequency (from approximately [Formula: see text]) data have been acquired at several locations around the world. Spectra calculated from these data, acquired over fields with known hydrocarbon accumulations, show common spectral anomalies. Verification of whether these anomalies are common to only a few, many, or all hydrocarbon reservoirs can be provided only if more and detailed results are reported. An extensive survey was carried out above a tight gas reservoir and an adjacent exploration area in Mexico. Data from several hundred stations with three-component broadband seismometers distributed over approximately [Formula: see text] were used for the analysis. Severalhydrocarbon reservoir-related microtremor attributes were calculated, and mapped attributes were compared with known gas intervals, with good agreement. Wells drilled after the survey confirm a predicted high hydrocarbon potential in the exploration area. A preliminary model was developed to explain the source mechanism of those microtremors. Poroelastic effects caused by wave-induced fluid flow and oscillations of different fluid phases are significant processes in the low-frequency range that can modify the omnipresent seismic background spectrum. These processes only occur in partially saturated rocks. We assume that hydrocarbon reservoirs are partially saturated, whereas the surrounding rocks are fully saturated. Our real data observations are consistent with this conceptual model.

Sinkhole collapse may result in significant property damage and even loss of life. Early detection of sinkhole attributes (buried voids, raveling zones) is critical to limit the cost of remediation. One of the most promising ways to obtain subsurface imaging is 3D seismic full-waveform inversion. For demonstration, a recently developed 3D Gauss-Newton full-waveform inversion (3D GN-FWI) method is used to detect buried voids, raveling soils, and characterize variable subsurface soil/rock layering. It is based on a finite-difference solution of 3D elastic wave equations and Gauss-Newton optimization. The method is tested first on a data set constructed from the numerical simulation of a challenging synthetic model and subsequently on field data collected from two separate test sites in Florida. For the field tests, receivers and sources are placed in uniform 2D surface grids to acquire the seismic wavefields, which then are inverted to extract the 3D subsurface velocity structures. The inverted synthetic results suggest that the approach is viable for detecting voids and characterizing layering. The field seismic results reveal that the 3D waveform analysis identified a known manmade void (plastic culvert), unknown natural voids, raveling, as well as laterally variable soil/rock layering including rock pinnacles. The results are confirmed later by standard penetration tests, including depth to bedrock, two buried voids, and a raveling soil zone. Our study provides insight into the application of the 3D seismic FWI technique as a powerful tool in detecting shallow voids and other localized subsurface features.

The hydrogeological properties and responses of a productive aquifer in northeastern Switzerland are investigated. For this purpose, 3D crosshole electrical resistivity tomography (ERT) is used to define the main lithological structures within the aquifer (through static inversion) and to monitor the water infiltration from an adjacent river. During precipitation events and subsequent river flooding, the river water resistivity increases. As a consequence, the electrical characteristics of the infiltrating water can be used as a natural tracer to delineate preferential flow paths and flow velocities. The focus is primarily on the experiment installation, data collection strategy, and the structural characterization of the site and a brief overview of the ERT monitoring results. The monitoring system comprises 18 boreholes each equipped with 10 electrodes straddling the entire thickness of the gravel aquifer. A multichannel resistivity system programmed to cycle through various four-point electrode configurations of the 180 electrodes in a rolling sequence allows for the measurement of approximately 15,500 apparent resistivity values every 7 h on a continuous basis. The 3D static ERT inversion of data acquired under stable hydrological conditions provides a base model for future time-lapse inversion studies and the means to investigate the resolving capability of our acquisition scheme. In particular, it enables definition of the main lithological structures within the aquifer. The final ERT static model delineates a relatively high-resistivity, low-porosity, intermediate-depth layer throughout the investigated aquifer volume that is consistent with results from well logging and seismic and radar tomography models. The next step will be to define and implement an appropriate time-lapse ERT inversion scheme using the river water as a natural tracer. The main challenge will be to separate the superposed time-varying effects of water table height, temperature, and salinity variations associated with the infiltrating water.

The inversion of fracture density from field measured P- and S-wave seismic velocities is performed using a neural network trained with an output from the modified displacement discontinuity fracture model. The basic idea is to use input‐output pairs generated by the fracture model to train the neural network. Once the neural network is trained, inversion of fracture density from field‐measured seismic velocities is performed very quickly. The overall performance of the neural network in the inversion process is assessed by means of a loss function. The results indicate that both sources of field information (P- and S-wave velocities) predict the field fracture density with reasonable accuracy. The performance of the neural network was compared to the prediction from least‐squares fitting. It is shown that the neural network out performs the least‐squares fitting in predicting the field‐fracture density values.

The question of uniqueness or otherwise of the various geophysical methods has been looked into from a general point of view. A method is theoretically determinate or indeterminate according as the totality of unknowns is smaller or greater than that of the independent measurables. While all natural field methods fall in the latter category, all applied field methods do not necessarily come under the former. Actual interpretations, however, cannot make any use of the theoretical uniqueness even where it exists and must depend on simplifying but permissible hypotheses based on extraneous information. These hypotheses are found to be surprisingly similar in all geophysical methods.

A few important issues for performing nonlinear refraction traveltime tomography have been identified. They include the accuracy of the traveltime and raypath calculations for refraction, the physical information in the refraction traveltime curves, and the characteristics of the refraction traveltime errors. Consequently, we develop a shortest path ray‐tracing method with an optimized node distribution that can calculate refraction traveltimes and raypaths accurately in any velocity model. We find that structure ambiguity caused by short and long rays in the seismic refraction method may influence the inversion solution significantly. Therefore, we pose a nonlinear inverse problem that explicitly minimizes the misfits of the average slownesses (ratios of traveltimes to the corresponding ray lengths) and the apparent slownesses (derivatives of traveltimes with respect to distance). As a result, we enhance the resolution as well as the convergence speed. To regularize our inverse problem, we use the Tikhonov method to avoid solving an ill‐posed inverse problem. Errors in refraction traveltimes are characterized in terms of a common‐shot error, a constant deviation for recordings from the same shot, and a relative traveltime‐gradient error with zero mean with respect to the true gradient of the traveltime curve. Therefore, we measure the uncertainty of our tomography solution using a nonlinear Monte Carlo approach and compute the posterior model covariance associated with two different types of random data vectors and one random model vector. The nonlinear uncertainty analysis indicates that the resolution of a tomography solution may not correspond to the ray coverage. We apply this tomography technique to image the shallow velocity structure at a coastal site near Boston, Massachusetts. The results are consistent with a subsequent drilling survey.

Describing hydraulic properties in the subsurface in at least two dimensions is one of the main objectives in hydrogeophysics. However, due to the limited resolution and ambiguity of the individual methods, those images are often blurry. We have developed a methodology to combine two measuring methods, magnetic resonance tomography (MRT) and electrical resistivity tomography (ERT). To this end, we extend a structurally coupled cooperative inversion scheme to three parameters. It results in clearer images of the three main parameters: water content, relaxation time, and electrical resistivity; thus, there is a less ambiguous hydrogeophysical interpretation. Synthetic models demonstrate its effectiveness and show how the parameters of the coupling equation affect the images and how they can be chosen. Furthermore, we examine the influence of resistivity structures on the MRT kernel function. We apply the method to a roll-along MRT data set and a detailed ERT profile. As a final result, a hydraulic conductivity image is produced. Known ground-penetrating radar reflectors act as the ground truth and demonstrate that the obtained images are improved by the structural coupling.

Geophysical methods can characterize aquifer systems noninvasively and are particularly helpful to image the complex depositional architecture of the subsurface. Among these, ground-penetrating radar (GPR) is an effective tool for detailed investigations of shallow subsurface geometry, but it provides only limited information on hydraulic properties. Magnetic resonance tomography (MRT) provides parameters such as water content (porosity) and relaxation time/hydraulic conductivity, but it suffers from resolution limits. Furthermore, it requires knowledge of subsurface electrical resistivity, which can be obtained by electrical resistivity tomography (ERT) also suffering from resolution limits. To overcome the limitations in resolution, we have incorporated GPR reflectors as structural information into the ERT and MRT data inversion. We test the methodology on a synthetic example and find improved imaging properties compared to standard inversion, particularly at greater depths, where the resolution is limited. We apply the methodology to a test site that is characterized by a complex depositional architecture. The Quaternary deposits consist of interbedded meltwater deposits (aquifers) and till (aquitards), overlain by aeolian deposits. To image the subsurface depositional architecture in three dimensions, a [Formula: see text] area was surveyed by GPR. The use of GPR constraints clearly improves the resolution and zonation of the subsurface image, which is validated by drill-core analyses. We develop a workflow to combine GPR, MRT, and ERT, leading the way to high-resolution hydrogeologic models that can be used for groundwater studies.