geometry and evolution of a fault bend fold mount bertha anticline mount bertha anticline is a major thrust associated fold in the rocky mountains of western canada well displayed in a 900 m thick middle paleozoic carbonate sequence that forms the core of the fold this carbonate sequence may be divided into three mechanical stratigraphic units of roughly similar thicknesses a lower massive dolostone a middle layered dolostone and an upper micritic limestone substantial variations in structural geometry occur along strike these variations correlate with changes in the thickness of the lower dolostone unit in the core of the fold that result from an oblique hanging wall ramp a mode i fault bend fold develops along most of the exposed strike length of mount bertha anticline this configuration corresponds to regions where a full thickness of the lower dolostone unit occurs in the core of the fold where the lower dolostone unit is thin or absent in the hanging wall of the mount bertha thrust the configuration of mount bertha anticline is dominated by second order fault propagation and detachment folds developed in the upper two mechanical stratigraphic units along the length of the mount bertha structure the limestone unit has been progressively attenuated and or faulted in the lower forelimb region and overridden by the advancing thrust sheet the fold geometry of the central part of mount bertha anticline compares favorably with geometric models of fault bend fold structures that allow forelimb thinning except for parts of the fold affected by the tectonic removal of rock from the lower forelimb existing geometric models of fault bend folds do not consider this process a companion fold within the hanging wall of the mount bertha thrust cranswick anticline is interpreted to be a mode i fault bend fold that has been significantly modified by second order fault propagation folding during the waning phases of movement along the mount bertha thrust

an analytical model of hanging wall and footwall deformation at ramps on normal and thrust faults abstract we determine stress strain and structural evolution for an analytical model of moderate angle 10 20 ramps developed on both normal faults normal ramps and thrust faults thrust ramps in the model a frictionless sliding surface with ramp configuration separates two incompressible isotropic viscous half spaces of different viscosity hanging wall and footwall ramps are planar but ramp flat corners are locally rounded deformation is due solely to translation across the ramp and regional extension or shortening is ignored sliding down a normal ramp causes vertical extension and horizontal shortening in both the hanging wall and the footwall this conforms with reverse faults seen in experimental models of normal ramps the stress in the footwall has the same magnitude as that in the hanging wall but the footwall strain rate is reduced in magnitude by the ratio both a hanging wall syncline and a footwall anticline form the normal ramp migrates in front of the rising footwall at a rate v ss v where v is the sliding velocity but the ramp does not change shape the continuous ramp motion in the model may correspond to the creation of an extensional duplex or chaos zone in brittle rocks at a normal ramp mean compressive stress is lowered and deviatoric stress is raised favoring local faulting and fracture sliding up a thrust ramp causes stresses strain rates and strains of the opposite sign horizontal extension and vertical shortening in both walls is consistent with normal faulting both a hanging wall anticline and a footwall syncline form passively although the deviatoric stress is raised at the ramp so is the mean compressive stress inhibiting fracturing however the mean compressive stress is lowered on the adjacent flats favoring fracturing there

the velocity description of deformation paper 2 sediment geometries associated with fault bend and fault propagation folds abstract a general tectono sedimentary forward modelling equation is used to derive two dimensional numerical models of sediment geometries associated with developing fault bend and fault propagation folds these styles of folding are described in terms of velocity models of deformation and are linked with syn tectonic erosion transport and sedimentation the resultant two dimensional numerical models simulate pre growth and growth strata in both submarine and subaerial settings the geometries and relationships produced by the models are broadly similar to those seen in natural examples however complex stratal geometries may be generated which are significantly different to those produced by previous models growth strata associated with fault bend and fault propagation folds are also compared and the distinguishing features of each mode of folding discussed the forward models presented in this paper have predictive capabilities in terms of possible sediment geometries associated with fault bend and fault propagation folds and also in terms of the amount of deformation or erosion that a part of a structure may have undergone

geometric analysis of fold development in overthrust terranes abstract fault bend folding fault propagation folding and detachment or decollement folding are three distinct scenarios for fold thrust interaction in overthrust terranes simple kink hinge models are used to determine the geometric associations implicit in each scenario bedding maintains constant thickness in the models except in the forelimb of the fold the forelimb is allowed to thicken or thin without limit the models address individual folds and the calculated fold geometries are balanced structures each mode of fold thrust interaction has a distinct set of geometric relationships final fold geometry is adequate in itself to discern many fault bend folds this is not the case for fault propagation and detachment folds these two fold forms have very similar geometric relationships some knowledge of the nature of the underlying thrust or decollement zone is usually needed to distinguish between them the geometry of a fold is altered in a predictable fashion by transport through an upper ramp hinge and by fault parallel shearing of the structure the shearing results in a tighter fold whereas transport through the ramp hinge produces a broader fold the viability of the geometric analysis technique is demonstrated through its application to a pair of detachment folds from the canadian cordillera the geometric analysis is also used to evaluate cross sections through subsurface structures in an example from the turner valley oil field the analysis indicates how the interpretation should be altered so as to balance the cross section the analysis reveals hidden assumptions and specific inconsistencies in structural interpretations

bed by bed fold growth by kink band migration sant llorenc de morunys eastern pyrenees ahstract rowth strata deposited over and against the flank of the sant llorenc de morunys fold during its final stages of deformation have been mapped at high resolution as the basis for unraveling the kinematics of fold growth we use restoration techniques based on normal balancing assumptions to decipher the detailed kinematic history of folding the progressive restorations as well as balanced forward modeling show that the last few hundred meters of fold growth were dominated by kink band migration of a sort that is typical of much faultrelated folding the kink band migration has produced complex anticlinal hinge zone geometry including segmented fold hinges linked by disconformities and unconformities which has direct and detailed explanation in terms of fluctuations in deposition rate relative to curved hinge kink band migration rate large fluctuations in the convolution of non steady sedimentation and deformation are demonstrated although the absolute fluctuations in deformation and sedimentation are unknown at a length scale of 100 m kink band migration with little or no deposition is interspersed with sedimentation with little or no deformation at the length scale of 500 m deposition ranges from 200 to 50 of uplift 0 1997 elsevier science ltd all rights reserved

an observational study of the evolution of horizontal convective rolls abstract a comprehensive observational dataset encompassing the entire temporal evolution of horizontal convective rolls was obtained for the first time florida illinois and kansas measurements from preroll conditions through the development of well defined rolls to their dissipation were utilized to determine the factors influencing roll evolution when the buoyancy flux reached a critical value of 35 50 w m 2 the first form of boundary layer convection resolved by radar was rolls it was noted that two dimensional convective rolls can evolve in a convective boundary layer in the absence of significant wind speed and shear in fact the value of wind speed or shear in itself did not seem to determine when or if rolls would form although it did influence roll evolution well defined two dimensional rolls only occurred while zi l where zi is the convective boundary layer depth and l is the monin obukhov length was less than 25 which is consistent with previous studies as zi l increased through

numerical modeling of fold initiation at thrust ramps abstract the movement of the hangingwall over the footwall at thrust ramps produces a variety of structures found commonly at different scales in fold and thrust belts the nature of the structure depends on the relative rigidity of the hangingwall and footwall friction along the fault fault dip fault displacement and the boundary conditions of the deformation structures include fault bend style folds fault propagation style folds and wedge folds we investigate the initial stages of development of such structures using the finite difference code flac the rock layers are represented as continua with elastic plastic mohr coulomb constitutive relations and the fault and bounding bedding planes are assigned normal and shear stiffnesses and coefficients of friction under conditions with all layers compressed antisymmetric fault propagation style folds develop in both the hangingwall and footwall with rigid footwall and restricted far field slip in the hangingwall a single fault propagation style fold develops with far field displacement of the hangingwall allowed broader antisymmetric wedge folds develop if hangingwall and footwall are deformable and a single fault bend style fold develops if the footwall is rigid all structures become accentuated with increasing slip on the fault where both hangingwall and footwall are deformable the deformation reduces the ramp angle and tends to minimize distortion of the rock adjacent to the fault fault propagation style folds paired wedge folds and fault bend style folds are common in nature and small scale examples can be found in various stages of development continued slip on thrust faults may lead to the mature structures commonly seen in fold and thrust belts

evaluation of the impact of horizontal grid spacing in terra incognita on coupled mesoscale microscale simulations using the wrf framework abstractcoupled mesoscale microscale simulations are required to provide time varying weather dependent inflow and forcing for large eddy simulations under general flow conditions such coupling ne

a scale adaptive turbulent kinetic energy closure for the dry convective boundary layer abstracta pragmatic scale adaptive turbulent kinetic energy tke closure is proposed to simulate the dry convective boundary layer for a variety of horizontal grid resolutions from 50 m typical of large eddy simulation models that use three dimensional turbulence parameterizations closures up to 100 km typical of climate models that use one dimensional turbulence and convection parameterizations closures since parameterizations closures using the tke approach have been frequently used in these two asymptotic limits a simple method is proposed to merge them with a mixing length scale formulation for intermediate resolutions this new scale adaptive mixing length naturally increases with increasing grid length until it saturates as the grid length reaches mesoscale model resolution the results obtained using this new approach for dry convective boundary layers are promising the mean vertical profiles of potential temperature and heat flux remain in good agreement for different resolutions a contin

geometries of syntectonic sediments associated with single layer detachment folds abstract three kinematic models have been proposed to account for the geometry and kinematics of detachment folds involving a homogeneous competent layer detached over a ductile unit model 1 variable limb dip constant limb length model 2 constant limb dip variable limb length and model 3 variable limb dip variable limb length because the same fold shape can be generated by any of the above mechanisms fold kinematics are best determined by the geometries of syntectonic sediments in single layer detachment folds growth strata patterns are controlled by axial surface activity limb rotation limb lengthening fold uplift rates sedimentation rates and deformation mechanisms of the syntectonic sediments asymmetric kink folds have been modelled and compared with natural examples from the southern spanish pyrenees under conditions of high sedimentation rates model 1 folds produce characteristic fanning growth stratal wedges that initially onlap and then progressively overlap the detachment anticline whereas at low sedimentation rates anticlines with fanning growth wedges on both limbs are formed model 2 folds under conditions of high syntectonic sedimentation rates form anticlines with growth strata largely parallel to the pre growth units and thinned over the fold crest in contrast at low sedimentation rates model 2 folds show offlapping growth strata onto both limbs model 3 growth folds under conditions of high syntectonic sedimentation rates form anticlines with intermediate features from model 1 and model 2 at low sedimentation rates anticlines are formed with offlapping growth structures

growth fault bend folding at southeast lost hills san joaquin valley california synsedimentary deformation has created complex structural and stratigraphic relationships along the west side of the san joaquin valley california this case study of lost hills anticline documents how a simple structural process fault bend folding results in complex growth stratigraphy lost hills anticline is a fault bend fold caused by a step in the lost hills thrust the thrust steps up to the northeast at 27 from a detachment at the base of the tertiary to an upper detachment in the reef ridge formation the lower and upper detachments are at 20 000 ft 6 km and 13 000 ft 4 km displacement on the lower detachment is approximately 4 mi 6 5 km folding consumes 1 2 mi 2 km and the remaining 2 8 mi 4 5 km continues northeast beneath the san joaquin va ley forward and back limb dips of 42 and 27 respectively are consistent with fault bend fold theory pliocene pleistocene sediments onlap a time transgressive unconformity on the northeast front limb but have uniform dip and thickness on the southwest back limb this characteristic growth fault bend fold geometry indicates basinal sediments rolled through an axial surface onto the back limb whereas contemporaneous sediments deposited above the front limb are undeformed basinal sediments onlapping the fold crest indicates fault slip is greater than ramp length onlapping growth sediments indicate folding began during deposition of the etchegoin formation 8 ma and continued to the late pleistocene or holocene corresponding to an average displacement rate on the lost hills thrust of 2 700 ft m y 820 m m y continuous burial of the fold during growth caused each material e physical point in the fold to be at its maximum depth of burial contours of equal density and seismic velocity are relatively flat so that the anticline causes little or no gravity anomaly and less than expected pullup in seismic time sections the geometry of growth sediments imaged on seismic lines indicates lost hills and adjacent anticlines grew by uniform displacement to the northeast with no significant rotation oblique convergence between the pacific and north american plates is manifested as synchronous but spatially separate transcurrent and compressive displacements thus lost hills anticline and perhaps other folds in the area are more appropriately described as compressive folds in a transpressive region than as transpressive folds duplicated lower tertiary strata beneath the lost hills kettleman hills trend are potential targets for petroleum exploration

convectively induced secondary circulations in fine grid mesoscale numerical weather prediction models abstractmesoscale numerical weather prediction models using fine grid o 1 km meshes for weather forecasting environmental assessment and other applications capture aspects of larger than grid mesh size convectively induced secondary circulations ciscs such as cells and rolls that occur in the convective planetary boundary layer pbl however 1 km grid spacing is too large for the simulation of the interaction of ciscs with smaller scale turbulence the existence of ciscs also violates the neglect of horizontal gradients of turbulent quantities in current pbl schemes both aspects poorly resolved ciscs and a violation of the assumptions behind pbl schemes are examples of what occurs in wyngaard s terra incognita where horizontal grid spacing is comparable to the scale of the simulated motions thus model ciscs m ciscs cannot be simulated reliably this paper describes how the superadiabatic layer in the lower convective pbl together with increased horizontal resolution allow the critical ra

fault related folding in sandbox analogue models of thrust wedges abstract the nucleation and growth of thrust fault related folds has been simulated using high resolution sandbox coulomb wedge type analogue models thrust related anticlines grew progressively from initial layerparallel shortening to decollement folding thrust tip folding and eventually thrust ramp folding thrust ramps nucleated in the central sector of the overturned forelimb of decollement folds as a consequence of limb thinning thrust tip folding occurred during outward migration of the ramp tips the fault propagation rate was greater at the lower ramp tip which quickly joined the basal thrust flat while folding continued beyond the upper tip the development of the analogue model thrust fault related folds by progressive changes in kinematics from decollement folding to thrust tip folding and finally thrust ramp folding compares well with analyses of naturally occurring thrust fault related folds

geometric and numerical model of progressive limb rotation in detachment folds a simple area balanced geometric model of progressive limb rotation in detachment folds allows the quantification of displacement uplift and rotation and the assessment of their effect upon growth strata geometries translation of this geometric model into a velocity model of deformation allows the modeling of associated growth strata resulting from background sedimentation and local erosion transport and deposition we show that with constant displacement and sedimentation rate this model predicts a progressive unconformity indicating the onlap and eventual overlap of the fold limb caused by a decreasing uplift rate this decrease is a consequence of the kinematics of progressive limb rotation increases in displacement rate with sedimentation rate kept constant can lead to offlap and angular unconformities although subsequent onlap does not necessarily reflect a return to a lower displacement rate modeled growth strata geometries exhibit many of the features reported from the literature

viscous plastic finite element models of fault bend folds abstract in finite element models of fault bend folds viscous and plastic material properties are used to simulate pressure solution creep and cataclasis respectively plastic deformation occurs primarily above ramp hinges however a band of high plastic strain is created in the lower hanging wall as material moves over the ramp hinges viscous deformation dominates above the ramp and flats where plastic deformation is negligible hanging wall material undergoes layer parallel shortening on the lower flat and lower part of the ramp layerparallel extension on the upper part of the ramp and upper flat and layer parallel shortening farther along the upper flat the stress invariant j 2 is highest above the ramp hinges and below the ramp whereas stress invariant j 1 is highest above and below the ramp the high j 1 below the ramp suppresses plastic deformation so that footwall deformation is predominantly viscous in multilayer models strain is concentrated in the weak layers especially on the limbs of the hanging wall anticline in models with bedding parallel slip surfaces in the hanging wall the strain on fold limbs is accommodated by interlayer slip and layers between slip surfaces develop individual neutral surfaces the models indicate that the relative and absolute amounts of deformation in fault bend folds resulting from pressure solution creep and cataclasis vary as a function of structural position and history

kinematic modeling of cross sectional deformation sequences by computer simulation we derive a kinematic algorithm which permits simulation of postulated cross sectional deformation sequences in sedimentary rocks affected by faulting fault related folding and simple shear the transformations are to a more deformed state and are formulated analytically in terms of the less deformed configuration forward modeling lagrangian description the medium is subdivided into domains of constant dip and homogeneous displacement vector fields which are delimited by the axial planes of the fault inflections the displacement trajectory is of constant length for all the displaced particles throughout the medium and parallel to the underlying active fault segment as a consequence the deformation path is continuous but not smooth and causes an angular style of parallel folding except at the deformation front where the layer thickness is not conserved the inhomogeneity of the displacement vector field across axial planes introduces longitudinal and angular shear strains whereas the area of the medium remains constant these strains which are superposed on the externally applied simple shear make the mapping transformation unconformal we define the stratigraphic layering of the undeformed medium by an approximating body of finite quadrilateral elements evaluate the defined displacement functions for the grid nodes and graph the deformed mesh eventually we create with the algorithm synthetic deformation sequences for simple boundary conditions and try in a specific case study to match the resulting synthetics with the available observational and experimental data

self determining numerical modeling of compressional fault bend folding we present the application of the hca hybrid cellular automata numerical modeling technique to the evolution of compressional fault bend anticlines involving layers that have competency contrasts and a mechanical stratigraphy the new modeling results show that for competent hanging wall layers 1 the fault style is not preserved in the overlying fold 2 fold development is not self similar and rotational growth wedges develop in the forelimb when syntectonic sedimentation occurs and 3 balanced fault bend anticlines can develop for ramp cutoff angles as high as 60 these results compare favorably with field examples and laboratory analogues and dramatically broaden the applicability of fault bend folding to model the evolution of thrust related anticlines

the convective boundary layer in the terra incognita numerical simulations of a convective boundary layer cbl are performed to investigate model behavior in the terra incognita also known as the gray zone the terra incognita of the cbl refers to a range of model grid spacing that is comparable to the size of the most energetic convective eddies which are on the order of the boundary layer depth using the rayleigh benard thermal instability as reference a set of idealized simulationsisused toshow that grayzone modelingisnot onlya numericalchallenge but also poses dynamical difficulties when the grid spacing falls within the cbl gray zone grid dependent convection can occur the size of the initial instability structures is set by the grid spacing rather than the natural state of the flow this changes higher order flow statistics and poses fundamental difficulties for gray zone modeling applications

multibend fault bend folding this paper shows how slightly complex but angular fault shapes with only a few bends lead to broadly curved and or highly complex folds a common perception exists that simple angular fold geometries are a necessary consequence of the normal assumptions of fault bend fold theory namely angular fault bends straight faults and flexural slip to the contrary it is shown here that exact application of these low level assumptions produces great complexity from simple fault shapes this complexity is caused by the combination of 1 generation of new axial surfaces by displacement of hangingwall cut offs past successive fault bends and 2 fragmentation of axial surfaces by mutual interference the result is entwined arrays of fold axial surfaces that produce quasi curved and or complex folds from discrete angular fault bends fold complexity grows in a highly non linear way in the most extreme case the number of fold axial surface segments grows as the fourth power of the number of fault bends this paper presents examples of the immense variety of complex fold geometries that are thus generated 0 1997 elsevier science ltd all rights reserved