A probabilistic procedure to assess the uncertainty of fractal dimensions from measurements     

I. Lerche 《Pure and Applied Geophysics》1993,140(3):503-517

In order to assess the degree of uncertainty of fractal dimensionality, a procedure is given which provides a cumulative probability measure of uncertainty of fractal dimensionality in terms of assessments of range and most likely value. The procedure allows for a variation of the model proposed (i.e., variability of the parameters involved in the fractal relation) and leads to a relevant estimate of the uncertainty. The procedure is simple to apply and useful in providing a statistically valid comparison of results.As an illustration, the procedure was used on the fractal dimensions of faults measured from shear zones of different scale magnitudes. Results suggest that these shear zones are indeed quantitatively similar with a fractal dimension around 1.5. It is also shown that the range of uncertainty of the fractal dimensionality (90% likelihood range) is sensitive to the amount of data used to calculate the fractal dimension of the faults.  相似文献   

Thermal focusing in complex stratigraphic regions: Lithology and porosity effects, and equivalent vertical and horizontal thermal conductivities     

I. Lerche 《Mathematical Geology》1992,24(1):1-25

Thermal focusing or defocusing by spatial variations in thermal conductivity caused by lithology and porosity fluctuations impacts the mean vertical geothermal gradient, localized fluctuations in temperature, and lateral bending of heat flow lines. Using mean field renormalization techniques, in which spatial fluctuations are treated as being randomly distributed around slowly varying mean values, estimates are given of the relative importance of lithologic and porosity variations in influencing thermal focusing. It is shown that, except for massive halite and/or evaporate variations, nearly all other geological situations can be viewed as having only a slowly varying mean lithology: fluctuations in porosity dominate thermal focusing. The mean vertical geothermal gradient is shown to be decreased by roughly 5–10% (with a maximum possible decrease of 25%) by the presence of porosity variations, relative to the mean gradient that exists in the same average medium but without fluctuations in porosity. The equivalent mean vertical thermal conductivity is shown to be increased by a maximum of about 12% relative to the non-fluctuating medium case. Root mean square temperature fluctuations vary in the typical range of 3–30°C depending on the correlation length scale of the porosity fluctuations. A correlation length of 1 km produces temperature fluctuations of around 3°C. Lateral bending of heat flux lines is implied by the thermal focusing; estimates suggest a root mean square bending angle of around 8–10°, with a corresponding mean equivalent lateral thermal conductivity of around 14% of the equivalent vertical thermal conductivity. These values are sufficiently large to suggest that fluctuations in stratigraphic sequences can lead to compartmentalized domains of juxtaposed hotter and cooler sedimentary volumes, thereby impacting the regimes of hydrocarbon generation. A simple estimate suggests that the depth of the top of the oil window may be increased by up to 0.5 km by such considerations. Effects due to anisotropic thermal conductivities, temperature dependence of thermal conductivity, and anisotropic correlated behavior of porosity and lithology fluctuations, need to be investigated to assess their significance.  相似文献   

Thermal impact of salt: Simulation of thermal anomalies in the gulf of Mexico     

Z. Yu  I. Lerche  A. Lowrie 《Pure and Applied Geophysics》1992,138(2):181-192

Salt and related structures have played important roles in controlling hydrocarbon accumulations in the Gulf of Mexico. Using a two-dimensional fluid flow/compaction model, which allows for both conduction and convection of heat, an examination is given of the effects on thermal patterns of the combined influence of multiple salt features, including diapirs, pillows, sheets and wedges. The focusing and defocusing of heat due to the higher thermal conductivity of salt are accounted for in the modeling. The results show that there could be as much as a 30°C anomaly above multi-salt bodies due to the focusing of heat by salt, and as much as 50°C temperature contrast between internal salt positions and sediments external to the salt in the deep part of a section. The magnitude of the thermal anomaly depends on the size (or width) of the salt and on the depth of the rooted salt. The modeled results provide estimates of the influence of salt in expanding the oil generation window by approximately half of the salt thickness.  相似文献   

Vitrinite reflectance distributions and thermal history of sediments: An end-member sensitivity analysis     

J. Horkowitz  I. Lerche  J. Pantano 《Mathematical Geology》1989,21(4):463-481

An end-member analysis was performed using algorithms ofExtended cabfac qmodel on 21 sample distributions of vitrinite reflectance (VR) by depth from the Inigok well in the National Petroleum Reserve of Alaska (NPRA). Eight end members, which account for 99% of the variance, adequately recreate the VR distributions. These eight end members contain stratigraphic information based on systematically increasing or decreasing mixing proportions with depth. Paleoheat flux determined from end members, or from orthogonally filtered sets of end members, is not significantly different from paleoheat flux determined from arithmetic mean values of VR, indicating that the arithmetic mean provides an adequate representation of each VR distribution analyzed in this well. Additionally, use of filtering devices to assess the degree of trustworthiness of signal in VR distributions enables an assessment to be made of the degree of stability of paleoheat flux variation estimates.  相似文献   

Inversion of dynamical indicators in quantitative basin analysis models. III. Multiwell information and two-dimensional case histories     

Z. Yu  I. Lerche  Q. Bour 《Mathematical Geology》1995,27(1):41-68

A dynamical tomography method, which inverts dynamical indicators to evaluate the parameters controlling geological processes as well as those in intrinsic equations of state, was introduced into a 2D fluid flow/compaction model termed GEOPETII (developed at the University of South Carolina), with the assumption of invariance to spatial location of parameters in equations of state, but allowing geologic process parameters to change with well location. Synthetic tests, including sensitivity analysis, are given to illustrate the operation of the system. The nonlinear inverse two-dimensional tomography method, together with a systematic linear search procedure, provides a useful approach to determine and constrain the parameters entering quantitative models of dynamical sedimentary evolution. Applying the method to an interpreted section from a seismic line in the Navarin Basin. Bering Sea. Alaska, the predictions of present-day formation thicknesses, porosity, and fluid pressure with depth are improved at four controlling well locations (Amoco Mishu No. 1, Exxon Redwood 1, Exxon Redwood 2, and Amoco Danielle), relative to previous results which used only a forward model. In this way the geohistory and structural development of the basin can be defined better, which helps in the reconstruction of thermal history, and so of hydrocarbon generation, migration, and accumulation histories in relation to structural and stratigraphic development.  相似文献   

Global cyclostratigraphy: a model of carbonate growth patterns     

Y.Y. Li  I. Lerche  M.A. Perlmutter 《Marine and Petroleum Geology》1993,10(6)

Cyclostratigraphy is the study of cyclic depositional patterns produced by climatic and tectonic processes. A global-scale quantitative cyclostratigraphic model is described which simulates carbonate growth patterns controlled by tectonic and climatic processes. The model uses seven factors simulating the effects of physical and chemical environments on the deposition rates of carbonate accumulations. These factors are sea-level change, the rate of basement subsidence, food supply (influence of nutrients), available sunlight, temperature, salinity and dissolved oxygen. The factors are considered as functions of climatic and tectonic processes. The model also integrates Milankovitch-induced short-term climatic changes with the long-term tectonic evolution of basins to examine the potential carbonate accumulation patterns. The two-dimensional computer model results provided here show that: (1) carbonate growth patterns in different climates and under different tectonic processes can be modelled quantitatively; (2) carbonate production increases towards the equator (decreasing latitude) as the temperature and nutrition supply increase in tropical belts, and production changes because of expansion or contraction of the tropical belt in different climatic periods; (3) when matched with the turbidity, the model describes different carbonate accumulation patterns in different climatic patterns; (4) at either abnormally high or low salinity, carbonate accumulation rates decline sharply, and the salinity becomes normal away from the strand line; and (5) cyclic sea-level changes cause a cyclic change of carbonate accumulation. A case study is presented from the Upper Pennsylvanian of Texas. The simulation results indicate that carbonate growth patterns observed from field, well or seismic data are accurately modelled by the quantitative procedure given here.  相似文献   

Arcuate and growth faults in basin models, with an application to a south Louisiana roll-over structure     

Z. Yu  I. Lerche 《Mathematical Geology》1995,27(4):513-547

Using a two-dimensional fluid-flow/compaction code an investigation is given of the influence of dynamically evolving curved faults in impacting the overpressure development of a sedimentary basin. Four synthetic cases are examined: an homogeneous sandy-shale section, and a mixed layered section of sand and shale, with fault conditions investigated being open to fluid flow, and closed to fluid-flow, respectively. Fault throws can be instantaneous either in time (such as a gravity slump) or can be progressive in time (such as a growth fault). A case history from south Louisiana also is examined to illustrate typical response patterns.  相似文献   

Offset dependent amplitudes: Effects of wavefront and reflector curvature in homogeneous and layered media     

N. C. Banik  I. Lerche  R. T. Shuey 《Pure and Applied Geophysics》1989,130(1):99-125

We analyze the effect of reflector curvature on the angular dependence of reflection amplitude using ray theory. Defining the curvature effect, CE, as the ratio of reflected amplitude from a curved boundary to that from a flat boundary at the same depth, we obtain 1/CE ²=(1+Z/a ^xcos²)(1+Z/a ^y), where is the angle of incidence,Z the depth of the boundary, anda ^x anda ^y are the principal radii of curvature of the reflector in the plane, of incidence and in the perpendicular plane, respectively. At =0 this reduces to the formula given byHilterman (1975). The angular dependence ofCE involves onlya ^x, which appears to shorten at wider angles. This causes an augmentation of the dimming effect of an anticlinal geometry at far offsets. For synclinal structures, the amplitude increases with offset when |Z/a^x|<1 and decreases with offset when |Z/a^x|<1.In addition we examine the effects of wavefront curvature and of a layered overburden in modulating the curvature effect. We find that there is a significant difference in the curvature effect between plane waves and spherical waves impacting on a curved boundary. In addition results are given showing simple examples of the effect of layered overburden in distorting the curvature effect of a horizontal, but curved, reflector and, more interestingly, of a dipping, but planar, bed. These results strongly suggest that we still have but a rudimentary knowledge, in general, of the combined effects of wavefront curvature, reflector curvature and overburden layering in modulating and/or producing amplitude with offset behavior observed on seismic records.  相似文献   

Book reviews     

A. D. Sneyd  W. E. Sharp  Ian Lerche 《Mathematical Geology》1989,21(3):395-400

  相似文献   

Inversion of multiple thermal indicators: Quantitative methods of determining paleoheat flux and geological parameters. I. Theoretical development for paleoheat flux   总被引：2，自引：0，他引：2  

I. Lerche 《Mathematical Geology》1988,20(1):1-36

The quantitative inversion of present-day downhole thermal indicator information enables (a) assessment of the effective paleoheat flux recorded by thermal indicators, and (b) determination of geological parameters related to the dynamical burial history of sedimentary strata. The logic of the general inversion scheme underlying seven thermal indicators, viz. vitrinite reflectance, sterane, and/or hopane isomers, sterane aromatization, optical rotation,³⁹Ar/⁴⁰Ar, pollen translucency, and fission scar tracks in apatite is presented, and their capability for resolving paleoheat flux is noted. In a second paper, determination of chemical and physical parameters, as well as several other quantities of geological interest (such as the sizes and erosion times of multiple unconformities, stratigraphic ages, paleo-overpressure, igneous intrusion timing, overthrust timing and frictional heat generation, fault and slump timing, thermal effects due to radioactive layer emplacement, and salt emplacement and dissolution timing) are discussed. Such events impact on both burial and thermal histories of sedimentary layers.Resolution problems are discussed also in the second paper, as is an attractive scheme called thermal indicator tomography for sorting out degrees of resolution, precision, and uniqueness of the relevant geological parameters for each process in combination with determination of the effective paleoheat flux. Detailed statements on the mechanics of implementing the tomographic approach are provided.  相似文献