using fractal crustal magnetization models in magnetic interpretation1 evidence from borehole susceptibility logs and the spectral analysis of aeromagnetic data suggests that the three dimensional distribution of magnetization within the crust can be described as fractal this property can be exploited in magnetic interpretation methods which explicitly require statistical information on the spatial variation of magnetization specifically we address the problem of magnetic source depth estimation through downward continuation and gridding aeromagnetic survey data using the method of kriging when magnetic data are continued downwards the depth at which the power spectrum flattens out the white depth can be taken to be an estimate of the top of the source distribution this procedure assumes that individual sources are uncorrelated with each other taking into account the correlation of the magnetization using a fractal description leads to a reduction in this depth estimate gridding of randomly distributed magnetic measurements using kriging requires an estimate of the covariance of the data compared with the assumption of a white uncorrelated magnetization distribution using fractal covariances for kriging produces gridded estimates which more closely reflect the statistics of the underlying magnetization process and produce maps with a justifiable degree of smoothness

modelling of magnetic data for scaling geology interpretation of magnetic data can be carried out either in the space or frequency domain the interpretation in the frequency domain is computationally convenient because convolution becomes multiplication the frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution this approach is modified to include random and fractal distribution of sources on the basis of borehole data the physical properties of the rocks exhibit scaling behaviour which can be defined as p k ak where p k is the power spectrum as a function of wave number k and a and are the constant and scaling exponent respectively a white noise distribution corresponds to 0 the high resolution methods of power spectral estimation e g maximum entropy method and multi taper method produce smooth spectra therefore estimation of scaling exponents is more reliable the values of are found to be related to the lithology and heterogeneities in the crust the modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method the method has found applicability in estimating the basement depth curie depth and filtering of magnetic data

geophysical parameter estimation seismic exploration for oil and gas is a parameter estimation problem geological properties and fluid content of subsurface reservoirs are sensed from the earth s surface seismic data are acquired by generating elastic waves at the surface and recording the reflections off subsurface targets using large receiver arrays at present it is not practical to determine earth parameters by iteratively refining an earth model until simulated seismic data match recorded field data the computational demands of accurately simulating viscoelastic wave propagation in a 3 d heterogeneous earth are prohibitive instead seismic data are processed to remove many complexities of wave propagation in the real environment like multipath attenuation dispersion shear waves and interface waves with these complexities removed the processed data conform to simpler propagation models which can be solved in reasonable computer time the cost of each simplification however is the loss of some information about the subsu

quantifying lateral heterogeneities in fluvio deltaic sediments using three dimensional reflection seismic data offshore gulf of mexico scale invariant statistics and strong anisotropy in rock properties are documented from well log and three dimensional seismic data in pleistocene fluvial and deltaic deposits in the eugene island 330 field gulf of mexico systematic quantification of lateral lithologic heterogeneity within a stratigraphic framework using reflection seismic data reveals that fluvial and deltaic depositional systems exhibit statistical behavior related to stratigraphic fabric well log and seismic data profiles show a decay in power spectra with wavenumber k according to k with between 1 and 2 3 vertical and horizontal well log data exhibit power law scaling behavior with between 1 and 2 horizontal seismic horizon slices were extracted from within fluvial and deltaic deposits seismic data from fluvial and deltaic deposits exhibit distinct differences in variance and each depositional system reveals directional anisotropy in one dimensional seismic data profiles from the fluvial deposit reveal anisotropy along depositional strike 1 1 and dip 2 2 the higher correlation observed in the direction of stratigraphic dip for the fluvial deposit may reflect the depositional fabric associated with channel systems correlation parameters obtained in specific depositional environments can potentially be used to quantify rock fabric and provide constraints in the modeling of sedimentary processes

fractal behavior and detectibility limits of geophysical surveys the detectibility limits of a large scale geophysical measuring network such as arrays of seismometers for seismic hazard assessment arrays of air guns and vibrators in seismic profiling and station spacing in gravity magnetic magnetotelluric and other geophysical surveys for exploration of oil minerals and groundwater depends on the fractal dimension of the network and the anomaly lovejoy et al 1986 korvin 1992 the geophysical anomaly resulting from the fractal nature of sources turcotte 1992 such as length of fault okubo and aki 1987 robertson et al 1995 velocity inhomogeneities sato 1988 nonrandom distribution of density thorarinsson and magnusson 1990 and susceptibility pilkington and todoeschuck 1993 pilkington et al 1994 maus and dimri 1994 1995 1996 reflectivity todoeschuck et al 1990 dimri 1992 etc cannot be accurately measured unless its fractal dimension does not exceed the difference of the 2 d euclidean and fractal dimension of the network

imaging and interpreting the shallow crystalline crust abstract in the past many tests of high resolution seismic imaging methods utilizing off the shelf technology from hydrocarbon exploration have had only limited success some problems associated with the application of seismic profiling in the shallow crystalline crust differ from those encountered in sedimentary basins perhaps the most fundamental distinction stems from differences in statistical properties of the reflection coefficient time series analysis of power spectra derived from borehole data indicates that the reflection coefficients in the crystalline crust are depleted in the seismic bandwidth relative to sedimentary basins this fundamental difference must be considered in the design of shallow crustal seismic surveys in order to achieve success to a first approximation acoustic impedance variations in sedimentary basins are controlled by velocity changes whereas velocity and density can vary independently in the crystalline crust and changes in density may be relatively more important in controlling reflectivity in certain instances density fluctuations outweigh velocity fluctuations for example physical rock property data from mining districts in the canadian shield suggest that massive fe oxide or sulphide bodies will generate strong seismic reflections

scale dependence of reflection and transmission coefficients well logs show that heterogeneities occur at many different depth scales this study examines the effects of these heterogeneities on the propagation of seismic waves and specifically the dependence of reflection and transmission on the spatial scale content of the medium wavelet transformations are used to filter certain spatial scales from an acoustic sonic log the scale filtered logs are used to construct layerstack models for which reflection and transmission seismograms are computed the modified logs are also used to calculate frequency dependent reflection and transmission coefficients as functions of scale content it is observed that features shorter than one fourth of the dominant wavelength have little effect on the reflection and transmission of seismic waves features larger than the dominant wavelength affect arrival times of individual packets within the wavetrain but often these features hardly alter the overall appearance of individual wave packets reflection and transmission coda ar

scaling nature of crustal susceptibilities scale invariant or self similar properties have been demonstrated for a wide range of geophysical processes and rock properties evidence from well logs and inferences from aeromagnetic field power spectra suggest that crustal susceptibility also shows this behaviour with a power spectrum proportional to the 4 power of the spatial frequency we examine two large susceptibility measurement data sets and find that they both support the scaling hypothesis

itrf2000 a new release of the international terrestrial reference frame for earth science applications 1 for the first time in the history of the international terrestrial reference frame the itrf2000 combines unconstrained space geodesy solutions that are free from any tectonic plate motion model minimum constraints are applied to these solutions solely in order to define the underlying terrestrial reference frame trf the itrf2000 origin is defined by the earth center of mass sensed by satellite laser ranging slr and its scale by slr and very long baseline interferometry its orientation is aligned to the itrf97 at epoch 1997 0 and its orientation time evolution follows conventionally that of the no net rotation nnr nuvel 1a model the itrf2000 orientation and its rate are implemented using a consistent geodetic method anchored over a selection of itrf sites of high geodetic quality ensuring a datum definition at the 1 mm level this new frame is the most extensive and accurate one ever developed containing about 800 stations located at about 500 sites with better distribution over the globe compared to past itrf versions but still with more site concentration in western europe and north america about 50 of station positions are determined to better than 1 cm and about 100 sites have their velocity estimated to at or better than 1 mm yr level the itrf2000 velocity field was used to estimate relative rotation poles for six major tectonic plates that are independent of the trf orientation rate a comparison to relative rotation poles of the nuvel 1a plate motion model shows vector differences ranging between 0 03 and 0 08 m y equivalent to approximately 1 7 mm yr over the earth s surface itrf2000 angular velocities for four plates relative to the pacific plate appear to be faster than those predicted by the nuvel 1a model the two most populated plates in terms of space geodetic sites north america and eurasia exhibit a relative euler rotation pole of about 0 056 0 005 m y faster than the pole predicted by nuvel 1a and located about 10 n 7 e more to the northwest compared to that model

the broad band fractal nature of heterogeneity in the upper crust from petrophysical logs in situ measurements of petrophysical properties of the upper crust from wire line logs provide a direct means of assessing fluctuations in these properties with depth and thus allow for the statistical characterization of crustal heterogeneity wire line logs from a cluster of nine boreholes 1000 1500 m deep have been analysed using four different techniques autocorrelation semi variogram rescaled range and power spectra six of the boreholes are vertical the remainder inclined all penetrate clastic and pyroclastic rock the analysis techniques have been tested on synthetic data for which we have precise control on the scaling in order to assess their robustness the results for the borehole data show broad band fractal scaling with a fractal dimension of 1 62 to 1 97 autocorrelation 1 59 to 1 79 rescaled range and 1 61 to 2 0 power spectra the use of different techniques to estimate the fractal dimension provides an excellent constraint on the results furthermore it allows us to determine which model for crustal heterogeneity best describes the data a band limited von karman function or unbounded fractal scaling in order to test the possible anisotropy in the scaling parameters the horizontal scaling properties for this area have been calculated by correlation spectra analysis of neighbouring wells this suggests that upper crustal correlation lengths are of the order of kilometres and anisotropic being over four times greater in the horizontal direction the origins of the observed power law scaling are complex analysis of long term correlations between logs and televiewer data points towards the influence of fracture porosity within the pyroclastics but a fractal distribution of pore spaces within the clastics also controls the log fluctuations separating the logs into clastic and pyroclastic subsets reveals slight differences in fractal scaling as determined by autocorrelation and semi variogram these differences are attributed to the dominance of either primary or fracture porosity within each geological unit

synthetic stratigraphy with a stochastic diffusion model of fluvial sedimentation abstract models of stratigraphic completeness and bed formation in fluvial depositional environments have most often assumed that successive depositional and erosional events deposit or erode amounts of sediment independently this results in a random walk model for the total amount of deposited sediment locally as a function of time we consider an extension of the random walk model of sedimentation in an alluvial plain in which deposition or erosion is concentrated in randomly avulsing channels and sediment transport is modeled by the diffusion equation culling s model in contrast to the random walk model this model results in an anticorrelated sequence locally as a function of time i e after an area has aggraded it has a higher elevation and a lower rate of future aggradation in a p evious paper we analyzed the topography generated by the model and argued that porosity variations could be associated with topographic variations the power spectrum s the square of the coefficients in a fourier series of one dimensional transects of topography and porosity horizontally and vertically in this model have a power law dependence on wave number k s k k s with values of s close to those observed in this paper we show that the model deposits sediment with a rate depending on time interval as a power law with exponent 3 4 more consistent with observations than the random walk model the model produces an exponential bed thickness distribution with a skew depen ent on the sedimentation rate of the basin in accordance with observations we also examine the persistence in the series of bed thicknesses as a function of depth for the stochastic diffusion model of sedimentation no persistence is observed if the model fully characterizes the autocyclic dynamics in fluvial sedimentary basins the lack of persistence in the synthetic bed sequences suggests that observed persistence and cyclicity in real bed thickness sequences must be the result of allocyclic processes

robust library building for autonomous classification of downhole geophysical logs using gaussian processes machine learning techniques such as gaussian processes can be used to identify stratigraphically important features in geophysical logs the marker shales in the banded iron formation hosted iron ore deposits of the hamersley ranges western australia form distinctive signatures in the natural gamma logs the identification of these marker shales is important for stratigraphic identification of unit boundaries for the geological modelling of the deposit machine learning techniques each have different unique properties that will impact the results for gaussian processes gps the output values are inclined towards the mean value particularly when there is not sufficient information in the library the impact that these inclinations have on the classification can vary depending on the parameter values selected by the user therefore when applying machine learning techniques care must be taken to fit the technique to the problem correctly this study focuses on optimising the settings and choices for training a gps system to identify a specific marker shale we show that the final results converge even when different but equally valid starting libraries are used for the training to analyse the impact on feature identification gp models were trained so that the output was inclined towards a positive neutral or negative output for this type of classification the best results were when the pull was towards a negative output we also show that the gp output can be adjusted by using a standard deviation coefficient that changes the balance between certainty and accuracy in the results

fractal heterogeneities in sonic logs and low frequency scattering attenuation cycles in sedimentary strata exist at different scales and can be described by fractal statistics we use von karman s autocorrelation function to model heterogeneities in sonic logs from a clastic reservoir and propose a nonlinear parameter estimation our method is validated using synthetic signals when applied to real sonic logs it extracts the fractal properties of high spatial frequencies and one dominant cycle between 2 5 and 7 m results demonstrate non gaussian and antipersistent statistics of sedimentary layers we have derived an analytical formula for the scattering attenuation of scalar waves by 3d isotropic fractal heterogeneities using the mean field theory penetration of waves exhibits a high frequency cutoff sensitive to heterogeneity size therefore shear waves can be attenuated more than compressional waves because of their shorter wavelength

gaussian scaling noise model of seismic reflection sequences evidence from well logs a simple model for reflection series is desirable for two reasons first to have a means of generating model reflection sequences on which to test geophysical data processing techniques specifically methods of predictive deconvolution and second to suggest a way of parameterizing real reflection sequences for classification and further geologic study in this note we wish to discuss a model suggested by hosken 1980 our discussion is founded upon the powerful ideas of self similarity and scaling developed by mandelbrot 1983 and on the paucity of typical lengths in geology typical lengths are common in physics problems for example the length of an organ pipe governs the wavelengths of the notes played when taking photographs geologists include some manmade object to give scale to the photo otherwise it is very hard to tell if say folds are of centimeter size or form whole mountains

fractional levy motion as a model for spatial variability in sedimentary rock a new approach to the modeling of spatial variability in sedimentary formations is introduced this approach avoids the assumption of gaussian behavior specifically borehole measurements of physical properties of sedimentary rock from contrasting geological settings are shown to have a statistical character consistent with fractional levy motion successive increments in the measurement sequences are accurately modeled as having levy stable distributions the levy parameters are similar for boreholes in the same sedimentary basin but vary from basin to basin thinly bedded formations have smaller values for the levy index suggesting that the levy index may be a useful measure of heterogeneity the measurement sequences are also statistically self similar and have long range negative dependence among the increments antipersistence in addition to reproducing the statistical properties of well logs the new model also mimics the most striking visual features of sedimentary formations

lithologic characterization of a reservoir using continuous wavelet transforms we consider the problem of characterizing the lithology of a reservoir using gamma ray logs as well as seismic traces around the well we first calculate the continuous wavelet transform of the the data and then use the fact that the energy of such transformation is proportional to a power of its scale the technique consists in estimating the power transformation obtaining a set of values of the same size as the original data and then modeling the distribution of these values using a double exponential we find that wells that are predominantly sand correspond to distributions that are significantly different from those that correspond to wells that are predominantly gravel this happens in both cases gamma rays and seismic traces we use this characterization to classify other points in the reservoir

an investigation of the spectral properties of primary reflection coefficients this paper investigates the form of the nonwhiteness found in the reflection coefficients from a wide variety of rock sequences around the world in all but one case densities are taken as constant due to the paucity of suitable density data the reflection sequences are pseudo white only above a corner frequency below which their power spectrum falls away according to a power law f where is between 0 5 and 1 5 this spectrum can be adequately modelled in practice very simply with an arma 1 1 process which acts on a white innovation sequence the corollary of this is that before wavelet estimation methods are applied all of which except those based on synthetic seismograms presuppose white reflection sequences or deconvolution filters estimated seismic traces should be filtered with the inverse of this process interestingly the estimated arma processes group themselves into two clearly differentiated categories having very different indices of predictability or strictly indices of linear determinism the two categories apparently correlate precisely with two kinds of sedimentation one which consists largely of sequences of rocks with repeating properties called repetitive in this paper but perhaps loosely describable as cyclic and the other which is randomly bedded with no apparent pattern of components the former has indices of predictability which are two to four times as great as those of the latter another probably related property is that for the repetitive sequences tends to be greater than that for non repetitive rock columns the observed power spectra are shown to be consistent with a simple model for the logarithm of acoustic impedance consisting of a mixture of processes where the distribution of time scale parameters is reciprocal detailed effects of block averaging and sampling the logs are shown to depend on the type of sequence under examination

guadalupe island mexico as a new constraint for pacific plate motion 1 we use gps data collected on isla de guadalupe and in northern baja california mexico to estimate site velocities relative to pacific plate motion the velocities of all three geodetic monuments on guadalupe fit a rigid pacific plate model with residuals of 1 mm yr using the guadalupe data and data from five igs stations on the pacific plate chat kokb kwj1 mkea and thti we estimate an angular velocity for this plate that is consistent with other recently published estimates our results indicate that isla de guadalupe lies on the pacific plate and that gps data collection on the island usefully constrains pacific plate motion and rigidity

rock as a critical point system and the inherent implausibility of reliable earthquake prediction summary the statistical mechanics of critical point thermodynamic systems provide a powerful conceptual tool with which to examine the plausibility of reliable earthquake prediction the issue turns on how rock is heterogeneous if the correlation range of a spatially fluctuating rock property is bounded by a characteristic length then the spatial average of that property over dimensions greater than may be regarded as defining an effective continuum value for that property ideas about earthquake preparation in rock with an effective continuum mechanical strength can plausibly focus on failure that is initiated at small anomalous zones and grows to instability with access to a continuous volume of strain energy the dimensions and temporal evolution of the growing anomaly can then be expected to relate to the size location and timing of the impending seismic event borehole log evidence indicates however that rock heterogeneity correlation lengths are unbounded and hence that the effective continuum approximation for rock must be applied with discretion an infinite correlation length indicates a statistical mechanical critical point system in which the correlation length is related to a singularity in a physical property in thermodynamic critical systems the singularity occurs at the critical system temperature tc 1 t tc in rock the singularity occurs at the critical percolation probability pc 1 p pc statistical physics descriptions of critical point spatial correlations are based on nearest neighbour inter actions at every scale length nearest neighbour interactions at one scale say that of large failure structures the loci of large earthquakes involve minimal coupling to structures at other scales in particular small scale failure structures the loci of small earthquakes the mechanics of nearest neighbour interactions plausibly form a fundamental constraint on the role of small scale failure or related nucleating activity as a prelude to large scale failure in light of 1 the evidence against rock being an effective medium notionally supporting localized precursory activity that reliably grows to large scale mechanical failure and 2 the history of failure to identify reliable precursors to major earthquakes the onus should now be on advocates of earthquake prediction schemes to evaluate their claims for precursory activity in terms of rock as a critical point system

topographically generated gravity waves in the brooks range alaska amplified wind events are identified over the brooks range in alaska with observed wind speed increasing from calm to 5 ms 1 over 24 to 36 hours in simulations using an limited area climate system model the wind events are captured consistently although generally display greater strength than observed cooling associated with the wind events lead to an identification of the ne region of the north slope of alaska below the inversion as the source region for the air flow analysis of the wind event of 7th january 1992 supports the nonlinear hydraulic model of gravity waves

fractals in petrology abstract a fractal power law distribution is the only statistical distribution applicable to a scale invariant process one of the major problems in petrology is the distribution of trace elements in the earth s crust extreme values of this distribution result in ore deposits there is accumulating observational evidence that tonnage grade statistics of ore deposits are often fractal power law rayleigh distillation and chromatographic models can explain power law fractal distributions for the extreme values of trace element concentrations an alternative fractal approach to problems in petrology is to use self affine fractals the standard approach is to take a fourier transform of a continuous signal an example would be the concentration of a mineral along a linear track if the fourier coefficients scale as a power law of the wavelength the distribution is a self affine fractal many well logs give this result multifractal analyses can also be applied to problems in petrology

chaos fractals nonlinear phenomena in earth sciences many problems in geophysics can be solved using linear equations examples include seismic waves the earth s gravity and magnetic field and problems involving heat flow and elasticity however other problems are essentially non linear the classic example is fluid turbulence in the past twenty years major advances have been made in the understanding of nonlinear problems in the past four years many of these advances have been applied to geophysical problems

revel a model for recent plate velocities from space geodesy 1 we present a new global model for recent plate velocities revel describing the relative velocities of 19 plates and continental blocks the model is derived from publicly available space geodetic primarily gps data for the period 1993 2000 we include an independent and rigorous estimate for gps velocity uncertainties to assess plate rigidity and propagate these uncertainties to the velocity estimates the velocity fields for north america eurasia and antarctica clearly show the effects of glacial isostatic adjustment and australia appears to depart from rigid plate behavior in a manner consistent with the mapped intraplate stress field two thirds of tested plate pairs agree with the nuvel 1a geologic 3 myr average velocities within uncertainties three plate pairs caribbean north america caribbean south america and north america pacific exhibit significant differences between the geodetic and geologic model that may reflect systematic errors in nuvel 1a due to the use of seafloor magnetic rate data that do not reflect the full plate rate because of tectonic complexities most other differences probably reflect real velocity changes over the last few million years several plate pairs arabia eurasia arabia nubia eurasia india move more slowly than the 3 myr nuvel 1a average perhaps reflecting long term deceleration associated with continental collision several other plate pairs including nazca pacific nazca south america and nubia south america are experiencing slowing that began 25 ma the beginning of the current phase of andean crustal shortening

scale invariant topography and porosity variations in fluvial sedimentary basins we consider a model offloodplain evolving with channelvulsion deposition nd erosion avulsion is modeled asrndom process in spce and time sediment transport is modeled by the diffusion equation culling s model the power spectrum of vritions in the topographic profiles predicted by the model s k is proportional to k 2 where k is the wvenumber this is the brown noise often observed in topography the power spectrum of wristions in the local elevation in time is proportional to f s where f is the frequency the model prediction of brown noise floodplain topography is roughly consistent with spectralnlyses of microtopography measured with lserltimetry we inferred brown noise pleotopogrphy by comparing the pir correlation function of showing wells in the denvernd powder river basins with a synthetic oil field bsed on caprock with brown noise topography topographic control of variations in the grain size of deposited sediment suggests that porosity vritions my exhibit the scale invrince predicted for the topographic profile to illustrate vertical scale invariance in porosity vritions we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the gulf of mexico at spatial scales bove 3 m we find anverge power spectral exponent of 1 4 close to our model prediction of 1 5

global positioning system constraints on fault slip rates in southern california and northern baja mexico we use global positioning system gps estimates of horizontal site velocity to constrain slip rates on faults comprising the pacific north america plate boundary in southern california and northern mexico we enlist a simple elastic block model to parameterize the distribution and sum of deformation within and across the plate boundary we estimate a pacific north america relative plate motion rate of 49 3 mm yr one standard deviation consistent with nuvel 1a estimates we are able to resolve robust slip rate estimates for the southernmost san andreas san jacinto and elsinore faults 26 2 9 2 and 6 2 mm yr respectively and for the imperial and cerro prieto faults 35 2 and 42 1 mm yr respectively accounting for about 86 of the total plate motion the remaining 14 appears to be accommodated to the west of these fault systems probably via slip along the san clemente fault and or the san miguel vallecitos rose canyon and newport inglewood fault systems these results are highly consistent with paleoseismic estimates for slip rates implying that off fault strain accumulation within the deforming zone of the plate boundary is largely elastic we estimate that the seismically quiescent southernmost san andreas fault has incurred about 8 2 m of slip deficit over the last few hundred years presumably to be recovered during a future large earthquake

power law random behaviour of seismic reflectivity in boreholes and its relationship to crustal deformation models abstract there is good evidence for the fractal nature of some fault systems both from field observations and the frequency magnitude distribution of earthquakes recently two models with fundamentally different dynamics have been employed to explain seismicity low order non linear slider block models have successfully explained activity on part of the san andreas fault system and in the nankai trough while high dimensional self organised critical cellular automaton models convincingly reproduce the gutenberg richter frequency magnitude relationship output variables from these two models fall respectively into two distinct data classes chaotic deterministic and random using a predictability algorithm which can distinguish between random and chaotic datasets we examine the distribution class of in situ fractures as inferred from borehole seismic reflectivity logs in three chalk layers off the south coast of ireland we find that fractures are distributed in a non deterministic manner consistent with self organised critical dynamics therefore we may infer that deterministic seismicity should not occur on structures over the scale range covered by the logs at least in the end member case where the frequency magnitude distribution of earthquakes is controlled by the fractal distribution of faults

submarine fan environment inferred from turbidite thickness distributions recent studies of turbidite bed thickness distributions have demonstrated power law as well as log normal statistical distributions the different distributions may reflect different fan processes and environments and therefore could be used as a quantitative method to help identify those environments including those devoid of sequential patterns the cumulative distributions of well known turbidite deposits spanning a range of interpreted fan subenvironments are used to illustrate the potential correlation between cumulative distribution and environments assuming that power law distributions may for some systems be the primary input signal one dimensional modelling allows semi quantitative characterization of the effects of different fan processes such as erosion and bed amalgamation environments indicative of different fan processes may be characterized based on the degree to which processes have acted as a filter to modify the assumed power law distribution systematically this model of the effect of fan processes on the power law distribution is used to help to account for bed thickness distributions observed in several field sites