A Nonlinear Least Squares Technique for Determining Multiple-Mechanism, High-Temperature Creep Flow Laws David K. Parrish, David K. Parrish Center for Tectonophysics, Departments of Geophysics and Geology Texas A&M University, College Station, Texas 77843Search for more papers by this authorAnthony F. Gangi, Anthony F. Gangi Department of Geophysics, Texas A&M Universitycollege Station, Texas 77843,Search for more papers by this author David K. Parrish, David K. Parrish Center for Tectonophysics, Departments of Geophysics and Geology Texas A&M University, College Station, Texas 77843Search for more papers by this authorAnthony F. Gangi, Anthony F. Gangi Department of Geophysics, Texas A&M Universitycollege Station, Texas 77843,Search for more papers by this author Book Editor(s):N.L. Carter, N.L. CarterSearch for more papers by this authorM. Friedman, M. FriedmanSearch for more papers by this authorJ.M. Logan, J.M. LoganSearch for more papers by this authorD.W. Stearns, D.W. StearnsSearch for more papers by this author First published: 01 January 1981 https://doi.org/10.1029/GM024p0287Citations: 10Book Series:Geophysical Monograph Series AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Summary This chapter contains sections titled: Calculation of Apparent Activation Energy Calculation of Stress Exponents Linear Least Squares Method Nonlinear Least Squares Technique Application of Nonlinear Least Squares Technique Conclusions Appendix A: Nonlinear Least Squares Fitting of Multimechanism Creep Laws Appendix B: Estimation of Errors Citing Literature Mechanical Behavior of Crustal Rocks: The Handin Volume, Volume 24 RelatedInformation

Experimental observations have been made of the transmission and reflection of Rayleigh waves by wedges. Results are reported for Rayleigh waves in aluminum wedges. It is observed that the wave shapes of the transmitted and reflected waves differ from that of the incident wave and depend on the angle of the wedge. The change of shape is attributed to an interference between part of the incident wave‐form and the radiation from a line source placed at the vertex. A procedure is given for the calculation of the partition between the two terms.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2009Tensor spaces and anisotropy: A tutorialAuthors: Anthony F. GangiAnthony F. GangiDepartment of Geology & Geophysics, Texas A&M University, College Station, TX, USA 77843‐3115Search for more papers by this authorhttps://doi.org/10.1190/1.3255588 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Vector spaces have been well defined and are commonly used to advantage. The extension of vector spaces to include independent functions as the base objects or elements (or “directions” or indicies) is also well known.Permalink: https://doi.org/10.1190/1.3255588FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 2009ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2009 Pages: 4338 publication data© 2009 Copyright © 2009 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 14 Oct 2009 CITATION INFORMATION Anthony F. Gangi, (2009), "Tensor spaces and anisotropy: A tutorial," SEG Technical Program Expanded Abstracts : 3491-3494. https://doi.org/10.1190/1.3255588 Plain-Language Summary PDF DownloadLoading ...

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2007Effects of pressure on seismic velocities of fractured rocksAuthors: Hoa Q. BuiRichard L. GibsonAnthony F. GangiHoa Q. BuiTexas A&M Univ., College Station, TXSearch for more papers by this author, Richard L. GibsonTexas A&M Univ., College Station, TXSearch for more papers by this author, and Anthony F. GangiTexas A&M Univ., College Station, TXSearch for more papers by this authorhttps://doi.org/10.1190/1.2792778 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InReddit Abstract Changes in the seismic velocities of fractured reservoirs detected by time‐lapse seismic experiments provide important constraints on changes in fluid saturations and pressures. Effective models for variations in elastic properties as a function of pressure are important for properly interpreting such field data. Here we investigate the validity of a model that explains changes in elastic moduli as a result of the contact of rough fracture surfaces with asperities of varying heights (Gangi, 1978, 1981). Increases in effective pressure cause an increase in fracture stiffness as the asperities are brought into contact and deform. Since the asperities are modeled as cylindrical rods to derive the analytic solution, the result is sometimes referred to as the “bed‐of‐nails” model. Inverting measurements of velocity as a function of pressure for a large set of clastic, carbonate and igneous rocks shows that while the model predicts the general trend in velocity, it is less accurate for some rocks, especially for some clastics, and does not predict detailed variations in velocity well. The original, analytic solution assumes a power‐law distribution of asperity heights, so to determine whether this is the source of error, we generalized the model to allow for arbitrary distributions. Inversions with this new model reduce residual error to negligible values, suggesting that this is a much better description of the rock properties. The new model therefore has the potential to facilitate modeling and interpretation of applications such as time‐lapse seismic investigations of fractured reservoirs.Permalink: https://doi.org/10.1190/1.2792778FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 2007ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2007 Pages: 3124 publication data© 2007 Copyright © 2007 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 14 Sep 2007 CITATION INFORMATION Hoa Q. Bui, Richard L. Gibson, Jr., and Anthony F. Gangi, (2007), "Effects of pressure on seismic velocities of fractured rocks," SEG Technical Program Expanded Abstracts : 1485-1489. https://doi.org/10.1190/1.2792778 Plain-Language Summary PDF DownloadLoading ...

ABSTRACT We present an analysis of scattering diagrams (i.e., Feynman‐like diagrams for wave scattering) of the correlation‐type representation theorem for ordinary inhomogeneous media with both positive stiffnesses and positive Poisson's ratios. This analysis reveals scattering events whose scattering diagrams include “negative” bending (i.e., bending in the opposite direction of that of scattering diagrams in ordinary inhomogeneous media). Unlike common scattering events, these events are inconsistent with the current interpretation of some of the basic physical laws, such as Snell's law, just like the so‐called “negative refraction” in optics. Yet we find them very useful, for instance, in suppressing some undesired events from scattering data.

ABSTRACTHydrocarbon depletion and fluid injection cause compaction and stretching of the reservoir and overburden layers. 4D prestack seismic data can be used to detect these changes because compaction/stretching causes changes in traveltimes and seismic velocities. We show that, by using two different petro‐elastic models at varying effective pressures, a good approximation is to assume that the fractional changes in layer thickness, ΔL/L, and seismic velocity, Δv/v, are related by a linear function of ΔL/L. The slope of this function (the dilation factor, α= (Δv/v)/(ΔL/L)) is negative and its absolute value generally decreases (shale, low porosity) or increases (sandstone, high porosity) with increasing layer thickness and decreasing effective pressure. The analysis is mainly performed for isotropic deformations. The dilation factor for uniaxial deformations is smaller in absolute value.The dilation factor, which can be calculated from time‐lapse data, can be used to predict reservoir compaction/stretching as a function of depth and surface subsidence.

We present a mathematical analysis of borehole stability when drilling through rock salt. First, we consider an elastic transversely isotropic medium and find the optimal mud weight as a function of the vertical overburden and horizontal tectonic stresses. Then, the Zener and Maxwell mechanical models are used to model the effects of transient and steady-state creep flow, respectively, in isotropic media. Under certain conditions such as the absence of dilatational anelasticity, the Burger model can be used to describe the steady-state flow, including transient creep effects. The type of creep is regulated by critical octahedral-stress values that depend on temperature and pressure. A typical drilling results in conditions of plane strain, whose solution is given by Kirsch’s equations. In this case, the borehole is subject to minimum and maximum horizontal stresses, which differ from the vertical stress. The analysis provides expressions for the shape of the borehole-cross section, the borehole-wall closure time, and the optimal mud weight to avoid wall collapse or expansion. It is shown that an anisotropic state of tectonic stress may require mud pressures exceeding the overburden stress and that the calculation should consider the joint optimization of the shape and area of the borehole cross section.

The components of the surface motions of a plane free surface are computed for the incidence of plane body waves.

The reflection and transmission coefficients for plane P/SV waves at an interface between two dissimilar fluid-saturated porous media have been determined in this study. By eigen-decomposing the Biot equations, the governing equations for wave propagation in fluid-saturated porous media, we express the displacement/stress vector in terms of an upgoing-/downgoing-wave vector. Then the boundary conditions on the interface are used to relate the upgoing and downgoing waves in the media above and below the interface. The reflection coefficients are obtained from the ratios of upgoing waves and downgoing waves in any one medium, and the transmission coefficients from the ratios of upgoing waves and downgoing waves in different media. We calculated the reflection and transmission coefficients and corresponding reflection and transmission angles for the interface between a Teapot sandstone and a Foxhills sandstone. For conventional (fast) P and SV waves, the variations of reflection and transmission coefficients with incident angles are very similar to those for single-phase elastic media. The main differences between them occur near the critical angles. For the other type of wave existing in porous media (that is, the slow P wave), the reflection and transmission coefficients are smaller than those for the fast P and SV waves and very sensitive to the frequency of the wave.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 1989Wavelet response of seismic arraysAuthors: Anthony F. GangiMark A. BensonAnthony F. GangiTexas A&M University and Mark A. BensonTexas A&M Universityhttps://doi.org/10.1190/1.1889561 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Permalink: https://doi.org/10.1190/1.1889561FiguresReferencesRelatedDetailsCited ByPerformance of seismic arrays in the presence of weathering layer variations18 June 2016 | Arabian Journal of Geosciences, Vol. 9, No. 8Seismic array response in the presence of a dipping shallow layer12 June 2011 | Signal, Image and Video Processing, Vol. 7, No. 2 SEG Technical Program Expanded Abstracts 1989ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 1989 Pages: 1375 publication data© 1989 Copyright © 1989 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 10 Feb 2005 CITATION INFORMATION Anthony F. Gangi and Mark A. Benson, (1989), "Wavelet response of seismic arrays," SEG Technical Program Expanded Abstracts : 663-666. https://doi.org/10.1190/1.1889561 Plain-Language Summary PDF DownloadLoading ...

: Results are presented of an effort directed toward the improvement of geophysical data acquisition, processing, and interpretation. Much of the discussion centers around the adaptation of existing or the development of new computer programs and their methodologies for processing and interpreting data acquired from electrical resistivity, microgravity, and seismic methods. Three programs for processing and interpreting electrical resistivity are discussed: (a) RESDIR computes the apparent resistivity as a function of electrode spacing for a given model of vertical subsurface resistivity variations; (b) RESINV calculates the model of vertical subsurface resistivity variation given the apparent resistivities acquired in the field; and (c) RESDAT is a general purpose resistivity program which handles data acquired from horizontal profiling and vertical sounding surveys. Three programs used in conjunction with microgravity surveys are documented: (a) TIDES computes the theoretical variation in gravity caused by earth tides at any location; (b) TALGRAD calculates gravity and gravity-gradient profiles across two-dimensional subsurface models; and (c) HILBERT computes the Hilbert transform which is used to determine the vertical velocity gradient. Two gravity methodologies presented describe: (a) a technique which reduces errors in microgravity surveying through use of optimal gravity station schemes, and (b) the use of polynomial surface fitting for determination of the required field component from a set of data.