Statistical analysis of the relationships between faults attributes

[1] The statistical analysis of fault attributes scaling relationships is discussed. Dependences of length, width of damage zone and thickness of fault core on displacement were studied assuming power law relations. The approximation forms a piecewise-linear function with few slopes in log-log scale. The Bayesian Information Criterion (BIC) was used to find the best fit for an optimal number of parameters. Numerical tests show that the best fit was obtained when using power law relations with two slopes. Bayesian analysis of model parameters' probability distribution was performed. For length-displacement relation (L-D), the slope decreases from one scale of faults to another. This change occurs at ∼1 m displacement for reverse and normal faults in siliciclastic rocks, at ∼1500 m displacement for strike slip and at ∼300 m displacement for normal faults in non-siliciclastic rocks. The slope of the damage zone width-displacement (W-D) relation decreases at ∼10 m, while it slightly increases for fault core thickness-displacement (T-D) relation at ∼10 cm. The result of the probability density of changepoints confirms the calculated changepoints, which correspond to maximal BIC in most cases. We propose an evolutionary growth pattern of faults based on the statistical results, in which faults lengthen during the initial stage. During subsequent overlapping and linkage between the faults, mainly displacement accumulates. Fault damage zone and fault core form early in the process of faulting. In mature faults, the development of damage zone would be slower than for small faults, whereas fault core slightly thickens with further localization.

[1]  C. Rizzi.  Statistical Methods , 2020, Springer Theses.

[2]  A. Torabi,et al.  Scaling of fault attributes: A review , 2011 .

[3]  T. Mitchell,et al.  Scaling of fault damage zones with displacement and the implications for fault growth processes , 2011 .

[4]  E. Brodsky,et al.  Collateral damage: Evolution with displacement of fracture distribution and secondary fault strands in fault damage zones , 2011 .

[5]  A. Braathen,et al.  Extensional faults in fine grained carbonates – analysis of fault core lithology and thickness–displacement relationships , 2010 .

[6]  Sooyoung Cheon,et al.  Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo , 2010, Comput. Stat..

[7]  A. Nicol,et al.  A geometric model of fault zone and fault rock thickness variations , 2009 .

[8]  D. Reeves,et al.  Dependence of displacement-length scaling relations for fractures and deformation bands on the volumetric changes across them , 2008 .

[9]  A. Torabi.  Deformation bands in porous sandstones, their microstructure and petrophysical properties , 2008 .

[10]  C. Wibberley,et al.  The influence of layering and pre-existing joints on the development of internal structure in normal fault zones: the Lodève basin, France , 2008 .

[11]  C. Wibberley,et al.  Recent advances in the understanding of fault zone internal structure: a review , 2008 .

[12]  K. Mair,et al.  Deformation bands in sandstone: a review , 2007, Journal of the Geological Society.

[13]  R. Lunn,et al.  How thick is a fault? Fault displacement-thickness scaling revisited , 2006 .

[14]  K. Davis,et al.  Thrust-fault growth and segment linkage in the active Ostler fault zone, New Zealand , 2005 .

[15]  G. D. Toro,et al.  Fault plane processes and mesoscopic structure of a strong-type seismogenic fault in tonalites (Adamello batholith, Southern Alps) , 2005 .

[16]  S. Weisberg.  Applied Linear Regression: Weisberg/Applied Linear Regression 3e , 2005 .

[17]  James P. Evans,et al.  The Geometry and Thickness of Deformation-band Fault Core and its Influence on Sealing Characteristics of Deformation-band Fault Zones , 2005 .

[18]  D. Sanderson,et al.  The relationship between displacement and length of faults: a review , 2005 .

[19]  Agust Gudmundsson,et al.  Effects of Young's modulus on fault displacement , 2004 .

[20]  Z. Shipton,et al.  A conceptual model for the origin of fault damage zone structures in high-porosity sandstone , 2003 .

[21]  A. Nicol,et al.  An alternative model for the growth of faults , 2002 .

[22]  M. R. Gross,et al.  Normal fault growth in layered rocks at Split Mountain, Utah: influence of mechanical stratigraphy on dip linkage, fault restriction and fault scaling , 2002 .

[23]  Robert J. Knipe,et al.  Empirical estimation of fault rock properties , 2002 .

[24]  Jeff Gill,et al.  What are Bayesian Methods , 2008 .

[25]  Z. Shipton,et al.  Damage zone and slip-surface evolution over μm to km scales in high-porosity Navajo sandstone, Utah , 2001 .

[26]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[27]  H. Fossen,et al.  Possible absence of small faults in the Gullfaks Field, northern North Sea: implications for downscaling of faults in some porous sandstones , 2000 .

[28]  D. Sanderson,et al.  Damage zones around strike-slip fault systems and strike-slip fault evolution, Crackington Haven, southwest England , 2000 .

[29]  O. Papasouliotis,et al.  One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships , 1999 .

[30]  A. Beach,et al.  Reservoir damage around faults; outcrop examples from the Suez Rift , 1999, Petroleum Geoscience.

[31]  Brendan McCabe,et al.  Modified Stationarity Tests With Data-Dependent Model-Selection Rules , 1999 .

[32]  Richard J. Behl,et al.  Influence of mechanical stratigraphy and kinematics on fault scaling relations , 1997 .

[33]  D. Sanderson,et al.  Modeling tip zones to predict the throw and length characteristics of faults , 1997 .

[34]  Rolf V. Ackermann,et al.  Geometry and scaling relations of a population of very small rift-related normal faults , 1996 .

[35]  A. Beach,et al.  Spatial and mechanical controls on normal fault populations , 1996 .

[36]  Andrew Nicol,et al.  Fault size distributions — are they really power-law? , 1996 .

[37]  R. Caflisch,et al.  Quasi-Monte Carlo integration , 1995 .

[38]  T. Lai.  Sequential changepoint detection in quality control and dynamical systems , 1995 .

[39]  C. Mansfield,et al.  Fault growth by segment linkage: an explanation for scatter in maximum displacement and trace length data from the Canyonlands Grabens of SE Utah , 1995 .

[40]  Ian Davison,et al.  Damage zone geometry around fault tips , 1995 .

[41]  J. Angelier,et al.  Fractal Distribution of Fault Length and Offsets: Implications of Brittle Deformation Evaluation—The Lorraine Coal Basin , 1995 .

[42]  W. Ryan,et al.  Quantitative fault studies on the East Pacific Rise : a comparison of sonar imaging techniques , 1994 .

[43]  P. Gillespie,et al.  Limitations of dimension and displacement data from single faults and the consequences for data analysis and interpretation , 1992 .

[44]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[45]  Adrian F. M. Smith,et al.  Hierarchical Bayesian Analysis of Changepoint Problems , 1992 .

[46]  D. Sanderson,et al.  Displacements, segment linkage and relay ramps in normal fault zones , 1991 .

[47]  Randall Marrett,et al.  Estimates of strain due to brittle faulting : sampling of fault populations , 1991 .

[48]  D. Peacock.  Displacements and segment linkage in strike-slip fault zones , 1991 .

[49]  Patience A. Cowie,et al.  Determination of total strain from faulting using slip measurements , 1990, Nature.

[50]  Agust Gudmundsson,et al.  Formation and geometry of fractures, and related volcanism, of the Krafla fissure swarm, northeast Iceland , 1989 .

[51]  E. Carlstein.  Nonparametric Change-Point Estimation , 1988 .

[52]  R. Krantz.  Multiple fault sets and three-dimensional strain: Theory and application , 1988 .

[53]  Anil K. Bera,et al.  A test for normality of observations and regression residuals , 1987 .

[54]  T. Villemin,et al.  Distribution logarithmique self-similaire des rejets et longueurs de failles: exemple du bassin houiller Lorrain , 1987 .

[55]  J. Watterson.  Fault dimensions, displacements and growth , 1986 .

[56]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[57]  L. Broemeling,et al.  Some Bayesian Inferences for a Changing Linear Model , 1980 .

[58]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[59]  D. Elliott,et al.  A Discussion on natural strain and geological structure - The energy balance and deformation mechanisms of thrust sheets , 1976, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[60]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .