Geophysics

Từ Định luật Ampere (với một trái đất đồng nhất) và từ phương trình Maxwell sử dụng khái niệm vectơ Hertz (cho một trái đất nhiều tầng), các giải pháp được tìm ra cho các thành phần ngang của trường điện và từ tại bề mặt do dòng điện đất (telluric currents) trong lòng đất. Tỷ lệ của các thành phần ngang này, cùng với pha tương đối của chúng, là chỉ báo về cấu trúc và điện trở suất thực của các lớp dưới mặt đất. Tỷ lệ của một số cặp yếu tố điện từ khác cũng có tính chỉ báo tương tự. Thông thường, một bảng đo quang điện-lừu từ được thể hiện bằng những đường cong điện trở suất biểu kiến và sự khác biệt pha tại một trạm cụ thể, được vẽ dưới dạng hàm của chu kỳ của các thành phần dòng điện đất khác nhau. Các công thức cụ thể được xây dựng cho điện trở suất, độ sâu tới các mặt phân cách, v.v. trong cả bài toán hai và ba lớp. Đối với hai vùng có hình dạng tương tự và điện trở suất tương ứng của chúng chỉ khác nhau bởi một hệ số tuyến tính, các mối quan hệ về pha là giống nhau và các điện trở suất biểu kiến khác nhau bởi cùng một hằng số tỷ lệ mà liên hệ với các điện trở suất thực tương ứng. Nguyên tắc "tính tương tự" này đơn giản hóa đáng kể việc biểu diễn một bộ đường cong chủ, như đã được đưa ra để sử dụng trong việc giải thích địa chất. Ngoài các lợi thế thông thường mang lại bởi việc sử dụng dòng điện đất (không cần các nguồn dòng điện hoặc cáp dài, độ sâu khảo sát lớn hơn, v.v.), phương pháp điện-lừu-từ trong thăm dò địa chất giải quyết các hiệu ứng của từng lớp đất tốt hơn so với các phương pháp điện trở thông thường. Nó dường như là một công cụ lý tưởng để điều tra ban đầu các lưu vực trầm tích lớn có tiềm năng dự trữ dầu mỏ.

We use high-resolution electrical resistivity imaging to delineate the geometry of complex landslides in the Lucanian Apennine chain of southern Italy, to identify the discontinuity between the landslide material and bedrock, and to locate possible surfaces of reactivation. The Lucanian Apennine chain is characterized by high hydrogeological hazard and shows a complete panorama of mass movements. In this area, all typologies of landslides markedly predisposed and tightly controlled by the geostructural characteristics, are found: rotational and translational slides, rototranslational slides, earth and mudflows, as well as deep-seated gravitational slope phenomena with a predominance of rototranslational slides evolving as earthflow slides. Three test sites, characterized by complex geology and a high hydrogeologic hazard, are studied. The Giarrossa and Varco Izzo earthflow slides are located to the west and east of the town of Potenza, whereas the Latronico slide is located close to the town of Latronico. Electrical images are produced from dipole-dipole geoelectric data acquired along arrays spanning selected profiles positioned perpendicular and parallel to the landslide bodies. High-resolution electrical resistivity images are attained through the use of geologic and borehole constraints in the interpretation phase. Integration and comparison of our results with other geophysical data delineate the geometries and hydrologic characteristics of the landslide structures.

One of the nagging problems which arises in application of discrete solution methods for wave‐propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh. These undesired events eventually override the actual seismic signals which propagate in the modeled region. The solution to avoiding boundary effects used to be to enlarge the numerical mesh, thus delaying the side reflections and wraparound longer than the range of times involved in the modeling. Obviously this solution considerably increases the expense of computation. More recently, nonreflecting boundary conditions were introduced for the finite‐difference method (Clayton and Enquist, 1977; Reynolds, 1978). These boundary conditions are based on replacing the wave equation in the boundary region by one‐way wave equations which do not permit energy to propagate from the boundaries into the numerical mesh. This approach has been relatively successful, except that its effectiveness degrades for events which impinge on the boundaries at shallow angles. It is also not clear how to apply this type of boundary condition to global discrete methods such as the Fourier method for which all grid points are coupled.

The second‐order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high‐order approximations for these derivatives. A one‐dimensional model is used to illustrate the relative accuracy of [Formula: see text] central‐difference schemes. For comparison, [Formula: see text] pseudospectral schemes are used as an additional measure of performance. The results indicate that [Formula: see text] differencing can achieve similar accuracy as the [Formula: see text] spectral scheme. For practical illustration, a two‐dimensional form of the [Formula: see text] algorithm is used to compute the exploding reflector response of a salt‐dome model and compared with a fine‐grid [Formula: see text] result. Transmissive sponge‐like boundary conditions are also examined and shown to be effective.

Most migration methods are based on a variety of one‐way approximations of the wave equation, one noticeable exception being the finite‐difference, reverse‐time, depth migration algorithm. Since this method requires enormous computer resources as compared to all other migration algorithms, its applications have been restricted primarily to 2-D synthetic data. Consequently, its potential for migrating poststack real data and imaging complex 3-D structures by constructive interference of wavefronts has not been exploited. Finite‐difference depth migration is subject to the same conditions for avoiding grid dispersion and numerical instability as are forward modeling techniques. For field data, this can necessitate interpolation both in space and time. One can, however, exploit the fact that in forward modeling one tries to generate accurate reflection signals; whereas in migration, the primary objective is to accomplish imaging from the prerecorded signals, which may be attainable under less stringent conditions. Indeed our investigations indicate that accurate imaging can be clone without making rigid provisions for grid dispersion in the lateral direction, which reduces or eliminates the use of interpolated traces. In the case of 3-D data, the elimination of an interpolation step reduces the computational task by a factor of 50 or more, with similar reductions in memory requirements. Further efficiency can be achieved by using a nonuniform grid in the vertical direction that adapts to the expansion and contraction of the downward propagating wavelet in response to variations in velocity and frequency content of the input data. These steps reduce the time required to do high‐resolution migration of large 3-D data volumes to several hours or less, depending on the machine and the size of the input data. Two applications on large, exploration‐scale, 3-D field data carried out on a massively‐parallel machine are presented. We compare our results with the results obtained by the Hale‐McClellan algorithm.

I present a finite‐difference method for modeling P-SV wave propagation in heterogeneous media. This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid. The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson’s ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson’s ratio. Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid‐solid interface. Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results. The weathered‐layer and corner‐edge models show in seismograms the same converted phases obtained by previous authors. This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half‐space. The head wave preserves the correct amplitude. Finally, the corner‐edge model illustrates a more complex geometry for the liquid‐solid interface. As the Poisson’s ratio v increases from 0.25 to 0.5, the shear converted phases are removed from seismograms and from the time section of the wave field.

We studied the elastic moduli, ductile creep behavior, and brittle strength of shale-gas reservoir rocks from Barnett, Haynesville, Eagle Ford, and Fort St. John shale in a series of triaxial laboratory experiments. We found a strong correlation between the shale compositions, in particular, the volume of clay plus kerogen and intact rock strength, frictional strength, and viscoplastic creep. Viscoplastic creep strain was approximately linear with the applied differential stress. The reduction in sample volume during creep suggested that the creep was accommodated by slight pore compaction. In a manner similar to instantaneous strain, there was more viscoplastic creep in samples deformed perpendicular to the bedding than parallel to the bedding. The tendency to creep also correlated well with the static Young’s modulus. We explained this apparent correlation between creep behavior and elastic modulus by appealing to the stress partitioning that occurs between the soft components of the shales (clay and kerogen) and the stiff components (quartz, feldspar, pyrite, and carbonates). Through a simple 1D analysis, we found that a unique relation between the creep compliance and elastic modulus, independent of composition and orientation, can be established by considering the individual creep behavior of the soft and stiff components that arises from the stress partitioning within the rock. This appears to provide a mechanical explanation for why long-term ductile deformational properties can appear to correlate with short-term elastic properties in shale-gas reservoir rocks.

Understanding the controls on the elastic properties of reservoir rocks is crucial for exploration and successful production from hydrocarbon reservoirs. We studied the static and dynamic elastic properties of shale gas reservoir rocks from Barnett, Haynesville, Eagle Ford, and Fort St. John shales through laboratory experiments. The elastic properties of these rocks vary significantly between reservoirs (and within a reservoir) due to the wide variety of material composition and microstructures exhibited by these organic-rich shales. The static (Young’s modulus) and dynamic (P- and S-wave moduli) elastic parameters generally decrease monotonically with the clay plus kerogen content. The variation of the elastic moduli can be explained in terms of the Voigt and Reuss limits predicted by end-member components. However, the elastic properties of the shales are strongly anisotropic and the degree of anisotropy was found to correlate with the amount of clay and organic content as well as the shale fabric. We also found that the first-loading static modulus was, on average, approximately 20% lower than the unloading/reloading static modulus. Because the unloading/reloading static modulus compares quite well to the dynamic modulus in the rocks studied, comparing static and dynamic moduli can vary considerably depending on which static modulus is used.

This investigation deals with resolving reflections from thin beds rather than the detection of events that may or may not be resolved. Resolution is approached by considering a thinning bed and how accurately measured times on a seismic trace represent actual, vertical two‐way traveltimes through the bed. Theoretical developments are in terms of frequency and time rather than wavelength and thickness because the latter two variables require knowledge of interval velocities. These results are compared with similar studies by Rayleigh, Ricker (1953), and Widess (1973, 1980). We show that the temporal resolution of a broadband wavelet with a white spectrum is controlled by its highest terminal frequency [Formula: see text], and the resolution limit approximates 1/(1.5 [Formula: see text]), provided the wavelet’s band ratio exceeds two octaves. The practical limit of resolution, however, occurs at a one‐quarter wavelength condition and approximates 1/(1.4 [Formula: see text]). The resolving power of zero‐phase wavelets can be compared quantitatively once a wavelet is known in the time domain.

Application of conventional elevation static corrections and migration to wavefield data recorded on irregular surfaces may result in poor reconstructions of complex subsurface features. Particulary poor images may be obtained at locations where the depths to target structures are comparable to undulations in the surface topography. For example, topographic relief of only 1-2 m may be important for the processing of georadar data. We describe an algorithm that allows georadar data to be migrated directly from gently to highly irregular acquisition surfaces. When applied to a variety of complicated synthetic data sets, topographically migrated images are observed to be markedly superior to those produced by two standard processing schemes. Extensive tests demonstrate that topographic migration should be considered in regions characterized by surface gradients ≫10% (i.e., dips ≫6°). For effective topographic migration, lateral and vertical coordinates of the georadar antennas should be determined to better than 10% of the dominant georadar wavelength, and velocities should be known to within 10–20% (e.g., 0.01–0.02 m/ns) of their true values. When applied to data collected across a moderately dipping (∼14°) rock glacier in the Swiss Alps, georadar sections resulting from two standard processing schemes have reflectors with depths and dips that differ by a significant 10–15% from those in the topographically migrated images.