Subsurface Point Research Articles

Shear wave anisotropy of laminated lower crust at the Urach geothermal anomaly

Deep seismic reflection studies have shown that ‘lamellae’ are a widespread reflectivity pattern of the lower crust of the central European Variscan belt. This pattern has been interpreted, inter alia, as alternating subhorizontal layering of mafic and felsic rocks implying a tectonic process of structural and textural ordering. Consequently, laminated lower crust should be elastically anisotropic. The specific type of anisotropy should provide some insight into the mineral composition and the preferred orientation of minerals in the lower crust. We have investigated this problem in the area of the Urach geothermal anomaly (South Germany) where a ‘classical’ example of lower-crust lamellae is found. A restricted range of subsurface points was probed in a controlled-source expanding spread seismic experiment with two orthogonal azimuths of observation up to 90-km source-geophone offset. Both P- and S-waves were recorded with 3-component geophones at 80–140 m geophone spacing. Based on polarization analysis and traveltime interpretation the following results were obtained: (1) S-wave splitting is observed only for S MS arrivals (not for shallower reflections) implying that the lower crust is anisotropic; (2) the type of anisotropy is quasihexagonal (transversely isotropic) implying that there is no preferred mineral orientation within the horizontal plane; (3) the coefficient of S-wave anisotropy [ (V max − V min ) V min ] is estimated at 6–13% for SV-type waves; the SH-wave velocity shows only small variation with offset; (4) the observed relation between direction and velocity of S-wave propagation can be explained by mafic rocks containing a high amount of orthopyroxene minerals horizontally aligned in the pure shear stress regime.

Drip Irrigation in Heterogeneous Soils: Steady‐State Field Experiments for Stochastic Model Evaluation

AbstractIn many drip‐irrigated fields, spatial variations in soil properties induce variations in wetting patterns about the drippers, resulting in uncertainty in the interpretation and use of sensor‐based soil water information. In previous work, analytical tools to quantify the effects of spatial variation in soil hydraulic properties on wetting patterns were developed. The objective of this study was to validate some of these analytical results. Following the characterization of the soil hydraulic properties in the study site, water was supplied from arrays of surface and subsurface point sources at constant flow rates. About 160 tensiometers and 100 time domain reflectometry (TDR) probes were installed at fixed positions relative to the source (for each flow rate and source location) and were monitored daily. The resulting spatial moments of matric head and water content were compared with analytical model predictions. Results revealed a large discrepancy between measurements and predictions based on the field‐estimated variability in α (the exponent of the unsaturated hydraulic conductivity function). Better agreement was obtained when a reduced variability in α was used. This suggests that soil hydraulic properties measured under ponding may be biased by the presence of large pores. Overall, the analytical model was capable of using information on the (permanent) spatial variability in soil hydraulic properties to predict the variability in flow attributes. However, even with better soil characterization and smaller soil variability, model predictions should be viewed as first approximations of the extent of variability in matric head and water content.

Soil as a complementary treatment component for simultaneous wastewater disposal and reuse

Field experiments were conducted to verify the hypothesis that soil performs as a complementary biofilter for secondary domestic treated wastewater disposal. The soil surrounding a subsurface point source functions as a biofilter for effluent used in agricultural irrigation. This hypothesis was examined in an outdoor experiment in which poliovirus was injected into the subsurface drip irrigation system. According the results, high virus concentration in applied effluent resulted in a very limited penetration into tomato plants via the roots. However, no viruses were detected in the leaves and the fruits.

A new method for the migration velocity analysis of noisy seismic data

We present a method for the determination of optimum migration velocities that is especially suited to datasets, such as deep crustal seismic data, in which both incoherent and coherent noise are present. Slowness weights are evaluated for each point in a time section in order to separate coherent and incoherent noise from signal, which can be identified by its characteristic slowness. These weights are calculated from slant stacks in a single pass through the data. Thereafter the weights may be summed along suites of diffraction curves corresponding to different velocity models to produce coherency estimates for each subsurface point as a function of velocity. After contouring these functions optimum migration velocities may be picked. Synthetic examples are presented illustrating the improved efficiency and velocity sensitivity of this method over previous ones, and showing the applicability of the technique to pre-stack, post-stack, and converted phase migration. A real example taken from a marine survey is used to demonstrate the utility of applying the method to deep crustal data.

Bayesian estimation in seismic migration

Seismic migration is a technique widely used in seismic oil exploration for wavefield reconstruction and for imaging the geometrical distribution of the reflection surfaces within the Earth from the seismic data recorded on the Earth surface. These data are usually corrupted by noise (white noise, surface waves, multiple reflections, etc.) that degrades the result of the migration. Another factor which influences the migration is the inadequate knowledge of the distribution of the acoustic wave propagation velocity in the subsurface of the Earth. The authors use estimation theory techniques to find the MAP (maximum a posterior) estimate of the wave propagation velocity and the geometrical distribution of the subsurface reflector points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Imaging of rough surfaces for impulsive and continuously radiating sources

Synthetic experiments are employed to investigate the possibility of using focused imaging to reconstruct the subsurface structure. The technique of focusing two arrays of receivers on a subsurface point and cross correlating the outputs is known as the split array cross correlation (SACC) processing. Each point in a subsurface grid is assumed to be the source of scattered Huygens wavelets. The SACC processing gives the relative strengths of the scatterers. A correlation image is constructed from diffracted and reflected signals using the SACC processing. It shows the locations and the strengths of the Huygens sourcelets. Post correlation stack results show the diffraction pattern is enhanced relative to that of the reflection. The SACC processing works for known impulsive sources and continuously radiating random sources. Numerical model experiments were made for an assemblage of wedges, which gives rise to reflections from the facets and diffractions from the apexes and the ‘‘V’’ bottoms. The synthetic seismograms are computed based on the impulse solution for reflection and diffraction from a rigid wedge, adapted from the Biot–Tolstoy impulse theory of diffraction. The controlled source correlation image shows the diffractors and the portions of plain surfaces where reflections occur. The correlation image region is bounded by the ellipse of constant travel time from source to scatterer to receiver. The source and the receiver are at the foci of the ellipse. The correlation image of continuously radiating sources shows high intensities at the diffractors and the mirror images of the sources in the reflecting planes.

Theoretical far‐field radiation from a low‐frequency horizontal acoustic point force in a vertical borehole

A subsurface point body force can be realized using a body force on the axis of a small‐radius borehole drilled perpendicular to the force. This observation, originally made by Kitsunezaki (1980), is having a significant impact in shear‐wave logging, and may potentially affect downhole seismic sources. Applying the principle of reciprocity to this finding, a horizontal vibration sensor on the axis of a vertical hole will be unaffected by the existence of the hole at low frequencies. Numerical methods determine both the frequency below which, and the offset beyond which, borehole‐related effects are negligible. If the shear wavelength is greater than ten times the diameter of the hole and if the measurement is made at least one shear wavelength from the point force, then the borehole effects will be minimal.

Migration of seismic data as W.K.B. approximation

The purpose of seismic migration is to find the coordinates of inaccessible subsurface points by use of seismic reflection measurements taken on the earth's surface. The three most popular conventional migration methods are the finite-difference method, the Kirchhoff method, and the frequency—wavenumber method. They are each based on a stratified model; that is, a two-dimensional model in which all the interfaces encountered by propagating waves must be horizontal. Such a model is called a sol1 2 dimensional (1.5D) model, because a true two-dimensional model would allow dipping interfaces. The 1.5 D model corresponds to a one-dimensional W.K.B. approximation to the wave equation. The surface seismic data can be downward continued (i.e. backtracked) into the earth in conventional migration because the 1.5D model has only flat horizontal interfaces, so no unknown dips are ever encountered. If in the real earth there is just one dipping interface, then all the conventional migration results below this interface are wrong. Thus in any practical situation, finite-difference migration, Kirchhoff migration, and frequency—wavenumber migration suffer serious specification errors. Larner depth migration, which in practice is replacing the 1.5D methods, uses a true two-dimensional, and, although it is more difficult to implement, it is correctly specified. As a justification for the use of the 1.5D wave equation migration on seismic data, in this paper we propose the random reflector-dip hypothesis. This statistical justification is the only reason that conventional migration methods give satisfactory results on actual seismic data.

Inverse Problems for Reflection Seismograms

The purpose or seismic migration is to rind the coordinate of inaccessible subsurface points by use of seismic reflection measurements taken on the earth's surface. The three most popular conventional migration methods are the finite difference method, the Kirchhoff method, and the frequency wavenumber method. They are each based on a stratified model, that is a two-dimensional model in which all the interfaces encountered by propagating waves must be horizontal. Such a model is called a 1 1/2 dimensional (1.5D) model, because a true two-dimensional model would allow dipping interfaces. The 1.5D model corresponds to a one-dimensional W.K.B, approximation to the wave equation. The surface seismic data can be downward continued (i.e. backtracted) into the earth in conventional migration because the 1.5D model has only flat horizontal interfaces, so no unknown dips are ever encountered. If in the real earth there is just one dipping interface, then all the conventional migration results below this interface are wrong. Thus in any practical situation, finite-difference migration, Kirchhoff migration, and frequency wavenumber migration suffer serious specification errors. Larner depth migration, which in practice is replacing the 1.5D methods, uses a true two-dimensional model, and, although it is more difficult to implement, it is correctly specified. As a justification for the use of 1.5D wave equation migration on seismic data, in this paper we propose the random reflector-dip hypothesis. This statistical justification is the only reason that conventional migration methods give satisfactory results on actual seismic data.

Late Oligocene transgression of middle Atlantic Coastal Plain

The subsurface Piney Point Formation of the coastal plain of Maryland, Delaware, and New Jersey contains planktonic foraminifera of late Oligocene age. The transgressive Piney Point Formation was deposited in inner to middle shelf environments on an eroded Eocene surface. The disconformity that separates the Piney Point from the Eocene formations below resulted from a major lowering of global sea level in early Oligocene time. This eustatic regression correlates with severe climatic changes noted elsewhere in the geologic record of this time.

Reply by author to the discussion by William A. Schneider

I appreciate Schneider’s comments on the subject paper, and it would appear that we are in complete agreement concerning the relative importance of diffraction effects in the recordings of reradiated wave fields. The point in question, however, is the importance of this diffracted energy in the inverse problem as applied in petroleum exploration. In other words, in the wave field reconstruction step described in Appendix B of the paper, do those hydrophones which record specular energy from a given subsurface point contribute more or less information to the final geologic picture than those hydrophones recording possible diffraction energy from the same subsurface point? A related question is whether the diffracted energy alone is sufficient for imaging moderately complex geology. Schneider suggests that diftraction energy alone is sufficient. I would like to discuss some observations which have led me to the opinion that diffraction energy alone is insufficient.

Estimating Flow Conditions for River Models

River water quality models are important management tools for assessing the impact of point and diffuse pollution loads on the chemical and biological characteristics of the water at various points in a river network. In a river basin, the magnitude of the flow at any point and time is a dominant characteristic affecting pollutant concentrations. Flows from headwaters, surface and subsurface lateral inflow, point loads, and diversions, are input as boundary conditions to water quality models so that the flow at any location on the river network can be computed. This paper describes a “man-in-the-loop” computer model developed to utilize available historical streamflow data and user judgement to estimate flow boundary conditions for a water quality model. Applications of the model include the efficient allocation of irrigation water, and performing mass balances on any conservative substance, such as salinity.

On: “Computer migration of oblique seismic reflection profiles,” by William S. French (GEOPHYSICS, December 1975, p. 961–980)

In his excellent paper, French cites a caveat for 2-D and 3-D imaging which I repeat for completeness: “The data collection area must contain the specular raypath from a subsurface reflection point if that point is to be seen in the results of migration.” As a general rule of thumb for planning a seismic survey, I have no dispute with the above statement. However, I feel the author overstates the case for specular reflection from curvilinear surfaces. As is well known, complex surfaces reradiate incident energy by both specular reflection and diffraction. The relative importance of the diffraction term depends upon the wavelength of the impinging pulse and the radius of curvature of the structure.

Vertical Stress Components Produced by Axially Symmetrical Subsurface Loadings

From a consideration of the Mindlin solution relating to the stresses produced by a subsurface point load in a semi-infinite, homogeneous, isotropic, linearly elastic medium, equations are developed for the intensity of vertical stress on the axis of loading caused by a number of axially symmetrical distributions of subsurface load. The results are also presented in the form of tables of stress coefficients which permit the rapid evaluation of stresses. In the case of a uniform distribution of pressure, the errors associated with the neglect of the depth, below the surface of the medium, at which loading is applied are evaluated. Sufficient data is given to permit the production of influence charts of the Newmark type to cover other distributions of subsurface loadings.

Radioactive Markers in Oil-field Practice

Abstract This paper describes a method to provide identification of particular depths ina borehole through the use of radioactive markers. The correlation of a marker, placed in the wall of a borehole, with known points of the electrical log andwith the casing collars in the cased hole permits accurate positioning of toolswith respect to a formation, regardless of absolute depth. Such a process isparticularly useful in gun perforation of a casing in a well. Technique andequipment are discussed and illustrated. Examples are given of practicalapplication in the field. Introduction During the past decade the search for petroleum has increased the importance oftesting zones at depths in wells which have become progressively deeper. Thedevelopment of new techniques, such as electrical logging, has permitted theidentification of producing formations which consist of comparatively thinstrata. When thin beds are to be produced at great depths, the problem ofpositioning tools accurately to place the well in production becomesacute. Continuous consideration is being given in the petroleum industry towards theimprovement of depth measurements in a borehole. The accuracy in absolute depthmeasurements, whether made in an open or cased hole, whether determined by a cable or a drill pipe, depends upon a number of factors, such as tension, temperature, and calibration. For example, the effects of tension from the weight of 10,000'Ft of drill pipeand the thermal expansion of this length of pipe, where its average temperaturehas increased 50'F, will produce an elongation as much as 8 ft. The effects ofsuch factors can be minimized through the use of care in depth measurements, the application of corrections based on experience, and continuous calibrationor checking. The fact that different methods and different tools are used to determine thedepths of formations in wells will sometimes give rise to a difference betweenmeasurements. It is evident that an important requirement in a well is theability to locate at will any subsurface point. While absolute depthmeasurements have improved in recent years, it is reassuring to have othermeans to verify, for example, that a casing is perforated at a particular placewith reference to a zone within a formation. Such a check on measurements maybe had by placing a reference marker at a point known with respect to theelectrical log of the borehole. That point is usually chosen to be in proximityto the zone to be perforated. Thus, only short relative depth measurements aremade and any inaccuracy becomes very small and of minor importance. T.P. 2261