A4 - Earth and Environmental Sciences
Contents
1. 1989 Thus at its heart Arvert is completely dependent on the assumptions that go into the multidomain diffusion MDD model There is now an extensive literature on this subject and some excellent work and reviews by the UCLA group on the validity of this conceptual model as a description for Ar diffusion in feldspar If for some reason you reject the MDD model then Arvert is not the program for you The text by McDougall and Harrison 1999 is an excellent place to start for a discussion of Ar Ar thermo chronology and the MDD model To be clear here are the assumptions upon which Arvert is based Ar diffusion in feldspars occurs by volume diffusion with similar mechanisms and kinetics operating in nature as during Ar extraction in the laboratory Feldspars are divided into discrete diffusion domains of differing sizes or diffusivity or both Although the code can handle domains of differing activation energy experience shows this to be unnecessary the code expresses variation among domains in terms of size variation but mathematically variations in D have exactly the same influence as variations in size Arvert 4X User s Manual Arvert assumes that variations within an age spectrum are entirely due to accumulation of Ar by radioactive decay and loss of Ar by thermally activated diffusion acting in the sample s domain structure it 1s assumed that the sample contains no extraneous Ar2. parameter is determined Next the program goes into its main loop and begins to sequentially create new thermal histories keeping or discarding them depending on whether they represent a better fit than the current worst member of the pool if a good fit is found the Arvert 4X User s Manual worst member of the pool is discarded The program continues until it reaches the specified number of iterations or has brought all histories in the pool to converge within the specified limits New CRS thermal histories are made as follows A subset of about 10 thermal histories is randomly selected from the main pool plus one more The histories in the subset are averaged and then a new history is made by reflecting the additional selected history through the averaged values subject to an amplification factor that might range between 1 1 and 1 5 Figure 1 gives what is probably a more clear depiction of this process Page 6 1 Select random subset from pool oo 2 Determine centroid of subset will approximate mean of pool but only roughly Figure 1 CRS algorithm for creating a new thermal history ee 3 Randomly select one more history from pool 4 Make new history using amplified projection through centroid Q I 3 How is Arvert best used Unless you start tinkering with its code or until you use it for a while Arvert will appear to you as the quintessential bla
3. s Manual Page 15 The mean percent deviation is simply the unweighted average over the fitted heating steps of the absolute values of the percent deviations between observed and measured age values It is simple and most of the testing and development of Arvert to date has used this parameter One drawback is that it can be hard for the model to reach very low values because of even minor areas of mismatch fits that are overall pretty good on visual inspection may not yield low values as misses both above and below the goal spectrum accumulate Another drawback is that the uncertainty on the age is not taken into account The other available fitting option is a type of mean square of the weighted deviates MSWD MSWD is commonly used by geochemists when comparing observed and predicted data as in regression For Arvert 3 2 0 and later MSWD is calculated by summing the squared differences between the model spectrum to the goal spectrum at each step weighting each term by the reciprocal of the variance and then averaging by dividing by the number of fitted steps Arguing by analogy with the MSWD as used for geochemical data a value of about 1 0 means that the deviation between model and goal spectrum is just consistent with the assigned uncertainty and values greater than 2 3 would indicate the model is most likely a mismatch So using a value of 3 as the cutoff criterion would mean that the model would terminate when the worst fitting the
4. 2 3 Compiling the code PPPPPPPPPPPPPPPPPPPP 10 11 3 1 Program inputs and outputs 11 inputs file crs in 11 inputs file domains in 19 inputs file goal in P 21 inputs file helium in 22 OULDUES annie neler Er EROS NE SEE Sr SS SEER RENDE KEE eens 24 32 Ni wing esult eneren rei 26 3 3 Modeling considerations 26 while modeling 26 when you re done 27 3 4 Warnings and issues 28 4 Special peeeeeeee ui none lonse klages 32 4l History of Arvex head i e 32 42 SPOLORM ANER 33 4 3 Future versions of Arverrrr ans 34 5 References and Suggested Reading 35 6 Appendix Convergence Sequence Sample Results 36 Section One Introduction 1 1 What is Arvert Arvert is a numerical model that inverts K feldspar Ar Ar age spectra for thermal history Given a measured age spectrum and kinetic and domain parameters determined from the Ar released during the step heating experiment Arvert will try to find those thermal histories that would result in an age spectrum like the one measured The latest version of Arvert can include He age data in the inversion This manual assumes that readers and prospective users of Arvert have an understanding of geoch
5. File 2 domains in this file contains the domain structure of your sample Once you have created it you normally would not modify this file during a series of runs The format is as follows e number of diffusion domains The one comment to make here is that is has been shown by Lovera and others that having extra domains does no harm but skimping creates problems So be sure that you have adequately analyzed your sample s Arrhenius behavior and include sufficient domains to account for subtleties in its R Ro plot Let me reiterate this you must properly characterize your sample s domain distribution or Arvert will not give reliable results Arvert 4X User s Manual Page 19 e groups of three lines giving the kinetic parameters for the number of domains specified The sequence is activation energy kcal mol log D a and volume fraction Heed the earlier warning that the diffusion geometry used to determine these parameters MUST be the same as that specified in the inversion file crs in Be sure to use the 10 based log of the frequency factor D a for each domain The volume fractions should total to 1 0 The following is a valid Arvert input file domains in number of diffusion domains domain 1 activation energy domain 1 log D a domain 1 volume fraction domain 2 etc domain 3 etc Arvert 4X User s Manual Page 20 File 3 goal in this file contains the measured age spectrum of your sampl
6. Six Appendices Convergence Sequence and Sample Results The on line Avert distribution contains a package of sample input and output files you can use to check your installation Below I provide an example of a typical Arvert convergence sequence and some sample results for synthetic data While it s gratifying to see Arvert work so well keep in mind that for the synthetic data Arvert damn well better work since the synthetic data were created by the versions of the same lovera and helium routines that are at the core of Arvert The first sequence of images gives the convergence sequence and summary results from a model of synthetic data these were calculated for a multi domain sample experiencing linear slow cooling at 10 C m y Monte Carlo pool After 200 CRS iterations Arvert 4X User s Manual Page 36 500 CRS iterations 1000 CRS iterations 2000 CRS iterations Final pool 5599 CRS iterations Arvert 4X User s Manual Page 37 40 gt Age spectra after 1000 CRS iterations 20 Final age spectra after 5599 CRS iterations Arvert 4X User s Man
7. components or that these have been corrected for The inverse portion of the Arvert code uses the controlled random search CRS algorithm of Price 1977 as adapted by Willet 1997 for the inversion of apatite fission track data This algorithm retains the advantages of a Monte Carlo approach in searching parameter space for true minima while converging far more rapidly due to the learning component inherent in the CRS method It is beyond the scope of this guide to discuss inverse methods as they have been applied to thermochronometric data see the article by Willett 1997 and references therein as a Start Arvert minimizes the misfit between a measured age spectrum and those that it calculates This objective function in the case of Arvert can take two forms either a simple mean percent deviation between the steps of the observed and modeled spectra and He age or a mean square of weighted deviates that takes into account assigned errors on each heating step and the He age Page 5 In detail Arvert works as follows Initially a pool of 100 to 300 thermal histories is randomly generated subject to any constraints supplied by the operator explicit constraints are in the form of maximum and minimum temperatures for the problem space implicit constraints are in the form of maximum and minimum heating and cooling rates An age spectrum is calculated for each thermal history and its fit
8. handle what are called embarrassingly parallel problems without trouble such as Apple s new Xgrid_ technology which allows easy parceling out of jobs to client machines Although Arvert already runs pretty quickly I think the latter may offer some possibilities My hunch is that the Lovera routine doesn t provide lots of opportunities for parallelization but the overall CRS routine looks better The challenge is that run in parallel the routine would require clients to share access to the same CRS pool and I m not sure how much communication and coordination this would require and how this would compromise performance Clearly one would not want individual clients to keep undercutting the efforts of another I suppose that as a real simplistic approach one could write a shell script or Applescript that launched multiple runs on different machines so that one was simultaneously trying out different combinations of parameters But at a few minutes per reconnaissance run and given the effort to set up all the parameters and then peruse the output I m not sure it s worth the effort with much faster machines already on the market and in the pipeline Page 33 4 3 Future versions of Arvert At this point nothing is in the works If there is user demand I could open out the other mineral routine to be more generic and so include U Pb and Ar Ar data I have no plans at this point to add a GUI to Arvert
9. CRS constraints will end up ignored If you are really bothered by this you can always filter your data manually after the run One last note about time nodes and thermal histories To try and minimize progressive bias when generating the Monte Carlo histories Arvert uses an alternating approach developed by Sean Willett Rather than start from one end and making temperatures at sequential time nodes Arvert first chooses a time node at random and then works up and down as it makes each history Number of constraining brackets for thermal histories You can place explicit constraints on portions of the problem space in a somewhat crude fashion by specifying permissible temperature ranges at specific times between these specified times Arvert just extrapolates linearly You must place at least two constraints on the model and no more than 10 The first and last constraints must be at the model start and end at times lt modelduration gt and 0 m y If you don t want to enter any constraints then simply choose to create two and make their Arvert 4X User s Manual Page 13 minimum and maximum temperatures be something like 0 C and 500 Cc N constraints format lt time gt lt min Temp C gt lt max Temp C gt Enter as many rows of constraints as you have chosen using the format given above Be sure that the time values decrease progressively Also be sure that the constraints don t conflict with the implicit rate constrain
10. If you do this you should have a rationale for omitting steps and some consistent set of criteria e g step has extraction temperature above 1150 C step is first step of isothermal replicate etc Don t farnarkle around and fall into the trap of just picking steps that look good Simply flag any steps you want to omit with a 0 Only those steps flagged with a 1 will be used in Arvert s fitting routines Arvert 4X User s Manual Page 21 The following is a valid Arvert input file goal in number of steps less one loss age error fit flag File 4 helium in this file contains information about the U Th He sample that can be used as a constraint and also contains the flag indicating that this constraint is active or not Thus the file must always be present even if you do not plan to use helium data as a constraint use dummy data in this case The format is as follows e mineral used 0 apatite 1 zircon Arvert needs to know which mineral you are using so that it can use the correct U alpha stopping distance Also you will want a record of the mineral constraint you used e Activation energy kcal mol Arvert s helium diffusion routine uses spherical geometry The kinetic data you supply must have been derived using this geometry e Grain radius microns and diffusion coefficient cm7 s Make sure you supply D not D a Unlike feldspars it appears that for the most part He diffusio
11. any applications of K feldspar thermochronology your goal is an understanding of process and timing at the level of precision that geologic data and realistic often under determined thermal models can provide Given the current and improving speed of most personal computers and workstations if you devote 2 3 hours to multiple background runs of Arvert you should be in good shape Start by running multiple models for only a few thousand iterations each perhaps changing the duration of the model to permit different prehistories to come into play Try allowing some re heating unless you are absolutely certain that this could not apply Alter the number of time nodes to see whether this is introducing an artifact for your particular case Check to see if there is a portion of your age spectrum that is not fitting well possibly due to an error in domain structure After all this you can then try a few final runs that continue for longer durations and attempt to achieve statistical convergence Arvert 4X User s Manual Page 8 Section Two Obtaining and Installing Arvert 2 1 Obtaining code or applications Arvert source code a compiled application example inputs and outputs and helper applications should be available at http www ees lehigh edu geochron ology html Alternatively as a second resort you can contact Peter Zeitler at peter zeitler lehigh edu and I can email you the code and any appl
12. arvert4X Inversion of Ar P Ar Age Spectra User s Manual Peter Zeitler Earth amp Environmental Sciences Lehigh University peter zeitler lehigh edu www ees lehigh edu geochronology html release arvert4X vers 1 updated 1 July 2007 User Agreement Arvert is freeware You can download use and modify it without cost However your use of Arvert is subject to the following conditions e Please acknowledge use of this code e You can t sell or charge for the use of Arvert code modified or not e Notify me of any non trivial changes you make e I ll try to help you if I can but I m under no obligation to provide technical support in the downloading compilation operation or use of this program e Lehigh University and Peter Zeitler take no responsibility for any errors that might arise during the use of Arvert due either to the code itself or in the instructions for its use and are not liable for any consequences of such errors do promise to express chagrin if you find a howler e Please notify me of any bugs you find and pass along suggestions for improvements Contents 1 INtrOdUCLON 352s sensei ee ea ee ees 4 Tel Whal it ARVESEN 4 1 2 How does Arvert work P 4 1 3 How is Arvert best used 7 2 Obtaining and Installing Arvert 0000 eee 9 2 1 Getting code or applications 9 2 2 Overview of running the application 9
13. as the current version is nicely cross platform in its simplicity If the world all six users demands a GUI then the most likely approach would be to use something like LabVIEW or RealBasic to write the interface and then just call a compiled version of Arvert as a routine As for tapping into multiple processors see the comments above The only motivation for looking into parallelization would be if there were a need to dynamically couple Arvert into some Ur geodynamic or thermal model like Pecube Arvert 4X User s Manual Page 34 Section Five References and Suggested Reading Meesters A and Dunai T J 2002 Solving the production diffusion equation for finite diffusion domains of various shapes Part II Application to cases with alpha ejection and nonhomogeneous distribution of the source Chemical Geology 186 1 2 57 73 McDougall I and Harrison T M 1999 Geochronology and thermo chronology by the Ar Ar method Oxford University Press Oxford 2nd edition 269 pp Lovera O M Richter F M and Harrison T M 1989 The Ar Ar thermochronometry for slowly cooled samples having a distribution of diffusion domain sizes Journal of Geophysical Research 94 12 17 917 17 935 Willett S D 1997 Inverse modeling of annealing of fission tracks in apatite 1 A controlled random search method American Journal of Science 297 10 p 939 969 Arvert 4X User s Manual Page 35 Section
14. at the former as Page 24 the nature of the Monte Carlo pool can condition the path the inversion takes towards convergence and can also influence the appearance of the thermal histories outside the region of convergence If the verbose output option is requested you will see output files for 500 1000 and 2000 CRS iterations as well as the final summary files and you will also see other files with this spacing if you have used the restart option This provides a means of viewing the interesting initial stages of the inversion process Otherwise these files will not be written and the output directory will not be so crowded Finally the file goalspec out rewrites the goal age spectrum into a format that can be plotted by Excel and compared to the model results Arvert 4X also includes this goal spectrum data into its age output files Arvert places all output except the utility files in a directory named Results suffix If you rerun a model without changing the file suffix Arvert does not overwrite earlier results but instead starts creating numbered directories having the same name All output files except the utility files and the summary file are tagged with Microsoft Excel as the file creator This allows you to open them directly into Excel by double Arvert 4X User s Manual clicking All files are basic text files and can be opened by any text editor or word processor Output file format The co
15. b delimited data file select all or select just the first few summary columns see above and use the chart wizard to choose the scatter plot option with lines The drawback of using Excel is the lack of good ways to set preferences for plots and make changes in a global fashion You will be faced with 100 300 data series each of which has its own line style and 3 3 Modeling considerations While modeling Earlier I discussed the importance of not treating this model as a black box and of taking the time to work through a series of models to explore the significance of your sample There s not much to add in this regard except to reiterate that you should first explore what the options are with some quick runs then do experiments to see how robust the solutions are and then go through some final runs more carefully A very useful and comforting thing to do is to rerun some models with a few minor changes in parameters just to see that despite different randomly generated starting points the model Arvert 4X User s Manual that might hold acceptable solutions color This can be ok for routine use and presentations but won t be adequate for publication This is where a more advanced program like Igor Pro might come in handy That or you would need to look into scripting Excel to gain control over formatting Id love to have someone send me a solution Your final option is to transfer the plot to a drawing pr
16. ce Avert is still perhaps two generations of processor upgrades away from being real time interactive but its performance is much improved from the days not Arvert 4X User s Manual favor of Oscar Lovera s code which is in principle more accurate As a footnote it turns out that for routine work the finite difference code is as fast and not that different in accuracy There followed some excursions into LabView programming of helper apps and then a descent into darkness as I tried to make the inversion more reliable and easier to use this included over the years user specified time nodes an input pain and prone to user bias randomly variable time nodes nice idea but the CRS routine would tend to grab hold of certain nodes and fatally select against the others and then Chebyshev type curves where the CRS routine worked on polynomial coefficients not thermal histories hard to corral these coefficients to produce non wacko histories The current version of Arvert returns to simplicity incorporates U Th He constraints and seems to work reliably at least in the hands of a skilled user who doesn t expect too much Feel free to contact me if for some inexplicable and self destructive reason you want to learn more about the guts of this code and how it got here long ago when overnight runs were the norm and input typos were cause for tears On a gigahertz machine you should be able to run a typical sur
17. ck box and it will be tempting to treat it as such Avoid this temptation Make an effort to understand what the main inversion parameters do and how constraints and parameters can bias your results sometimes in subtle ways Arvert 4X User s Manual Arvert is best used to investigate what classes of thermal history might serve as explanations for a particular age spectrum given whatever firm geological constraints you have in hand Once you know what the possibilities are one option is to then continue using manually directed forward modeling to complete the fitting of the age spectrum However this approach sacrifices one of the Page 7 potential advantages of the inverse approach and that is to obtain a feeling for confidence limits on various parts of the derived thermal history With careful use and an understanding of some of its pitfalls Arvert can provide this information but see Section 3 5 What you should NOT do is just run Arvert once for countless iterations and then take this single result as the truth You must make some effort to see how different constraints influence the model and how well your derived diffusion domain structure is permitting the model to function ill defined kinetic and domain data can make it difficult for Arvert to fit parts of an age spectrum causing over convergence to false precision to occur for parts of the thermal history It is important to remember that in m
18. ctory as the application they must retain their exact names Within these files it is best to delimit same line parameters with tabs What follows is a lengthy discussion of the contents of these files and where needed a discussion of what the parameters do and what ranges of values to use A fundamental description of each parameter is given in bold face additional comments on the parameter are in italics The files are crs in domains in goal in and helium in To repeat some critical advice the input text files must have the correct line terminator which for use in Mac OS X is a line feed LF some text editors refer to this as UNIX format Input files in other formats will not work and will lead Arvert to crash because it will not read correct inputs File 1 crs in this file contains all the controlling parameters for the inversion and is the file you will be modifying between runs The format is as follows e String giving run info maximum 100 characters e File suffix appended to output files maximum 10 characters Not critical but very helpful in sorting output from different runs e Number of iterations for the CRS algorithm Most runs will terminate based on this parameter Usually it is not worth doing fewer than 2000 iterations but on the other hand resist the urge to do too many iterations until you are ready as you can always keep restarting the model after having a quick check of results U
19. d the like have been beaten out of the program However there are some issues that might appear Despite extensive use and testing keep in mind that Arvert uses random numbers for a number of procedures and creates new data sets out of complex combinations of data Thus it is possible that on occasion a random sequence will produce a glitch or error that is not caught creating divide by zero or out of bound array indices Given the nature of C the latter in If you have a single step that seems to represent some sort of burp I suppose it would be ok to flag it for omission particular can lead to unexpected results but not run time errors One symptom of a problem probably some sort of corruption in one of the main working arrays is a reversal of the reported fit values such that the best fit is reported to have a larger value than the worst fit If you see this something is wrong and you should not trust the model run If you experience a bad run or odd looking data please double check your input parameters If these are ok then try re running the model a few times with exactly the same parameters If the problem persists let me know If it goes away it usually does you can assume it was a random glitch Section Four Special Topics 4 1 History of Arvert It s been a long strange trip You really don t want to know the history of Arvert in any detail What follows is already much more than too m
20. e which will serve as the goal for the inversion This is another file you normally would not change during a series of inversion runs The format is as follows e number of heating steps less one By convention the last heating step for an age spectrum reaches a fractional loss of 1 00 for which one cannot calculate a diffusion coefficient So if you have measured 48 heating steps you would enter 47 for this parameter e N steps format lt fractional loss gt lt age Ma gt lt error in age Ma gt lt fitting flag O no 1 yes gt Remember to express the Ar loss as a fractional loss not a percentage loss Age and error in age are obvious if you choose to use mean percent deviation than age error is not important but a placeholder value still needs to be entered Note that you need to specify the age error without the error in the J factor the latter is a systematic error in your age spectrum and you are interested in the location of steps relative to one another The fitting flag allows you to indicate which steps of an age spectrum should be used by the inversion You may want to omit certain steps early in the age spectrum due to problems with excess or fluid inclusion hosted Ar and late in the release you may want to omit steps in which Ar was released by partial melting not diffusion Or you can specify a block of steps early or late in an age spectrum to focus Arvert on just a particular portion of the thermal history
21. eep an eye on the ages and losses calculated by the model for the early steps Flag for number of reports during run 0 for short 1 for verbose Arvert will always report its progress to the console every 50 CRS histories and every 1000 CRS histories it will write an interim report file call lt CRSRolling gt that captures the current pool of thermal histories If you set this report flag to verbose mode Arvert will also write several additional thermal history files at the start of the run which are informative about the early convergence of the model This will happen whether in restart mode or not To keep the number of files Arvert generates low choose the short mode Arvert 4X User s Manual Page 18 The following is a valid Arvert input file crs in obviously the real file consists of just the left hand side BT 15 non linear test 3 10 model info Nonlin file suffix 7000 number CRS iterations 100 model duration m y 10 number of time nodes 4 number of explicit constraints 100 450 500 time minTemp max Temp 90 0 500 time minTemp max Temp 10 0 500 time minTemp max Temp 0 0 500 time minTemp max Temp 10 0 20 0 max heat amp cool rates Monte Carlo 10 0 100 0 max heat amp cool rates CRS 1 2 amplification factor 10 150 pool size subset size 2 0 fitting criterion type of fit mpd or mswd diffusion geometry restart option discretization temperature step series cut off criterion option for report length
22. er models and go only until the model converges or begins to stall You may also want to re examine a problem spectrum to see why Arvert can t seem to turn the Page 28 corner is it a funky thermal history problem area is you can always turn with complexity like rapid or subtle off fitting in the problem region and changes or is there a problem with see what kind of history you then the spectrum or its derived domain get structure To see how important the 3 4 2 Biases from constraints model Also note that a Earlier I discussed how it s possible consequence of using a set of to produce a rather odd looking pool histories as shown in Figure 2 is that of Monte Carlo histories by in the regions near but not in the allowing fast cooling but no or little directly constrained region the heating An example is shown in mode will give the appearance of a Figure 2 Arvert can cope with such trend in temperatures that is merely a start but if you were expecting inherited from the starting pool The there to have been a fast cooling preceding is a subtle but important pulse you must recognize that you point are serving up this result to the Temperature CC Time Ma Figure 2 Starting Monte Carlo thermal history pool generated with constraints allowing no heating and cooling at rates of up to 100 C m y Note potential bias in these starting histories towards fast cooling scenarios Arver
23. h care Temperature step in C for discretization of temperature histories This is an advanced parameter that determines how the Lovera forward model breaks apart thermal histories for its use the routine does this at regular temperature intervals rather than regular time intervals to ensure adequate discretization during periods of rapid heating or cooling A value of 10 or even 20 C will work for routine and quick models but you will want to reduce this to I or 2 C for final runs Arvert 4X User s Manual Page 17 Permissible values range from I C slower better resolution to 20 C faster poorer resolution Fractional cut off for terminating infinite series in Lovera routine This is a convergence criterion for the slow converging series involved in the Lovera algorithm expressed as a fractional change in successive values The series converges very slowly only for the low values of Dt a associated with early heating steps so for routine work you can keep this value as high as le 3 0 1 However for complete accuracy for all steps and adequate coverage for small steps values of le 7 or le amp or recommended The permissible range is le 3 fast less accurate to le amp slower more accurate Even then it is possible that if you specify extremely small fractional losses for your first step or two that the lovera routine will not have converged or will have reached the double precision limit so in such cases k
24. ications as attachments I use and develop Arvert under Mac OS X so helper applications and the compiled code will work only on Macs The latest version runs as a console application under OS X and should be very easy to port to other platforms If you wish to use Avert on a different platform you will need to recompile and link the source code See Section 2 3 2 2 Overview of running the application For reasons of time mine and programming incompetence mine Arvert runs as a command line program in a terminal window At some point I may figure out how to bring the code into the modern world but I wouldn t hold your breath The fact is that until computer speeds increase by another factor of 20 or so Arvert will not be an interactive program so the lack of a GUI isn t a big deal To actually run Arvert you invoke it in standard UNIX fashion on a Mac launch Terminal app navigate to the directory containing both the executable and all needed input files and type arvert4x 1 Note that double clicking the executable in the Finder will not work you will Arvert 4X User s Manual cause terminal to launch and the program to start but it will terminate in a bus error You are then presented with a list of what Arvert thinks are your inputs You should check these for blunders or silly values to avoid wasting time Arvert does use assertions to check for bad values but there are still many ways to launch u
25. ies that have been processed as well as the current best and worst fits of the age spectra in the CRS pool This updates every 50 histories to convince you that Arvert is alive Arvert use two utility files to carry out the restart option The main file involved is CRSrestart which contains the state of the final thermal history pool at the end of the previous run The file CRScount in attempts to track the total number of CRS iterations that have been run for a given model assuming that the restart option has been used These files are placed in the same working directory as Arvert itself Arvert 4X User s Manual A summary of the model run including inputs and performance stats is placed in the text file Modelinfo suffix This serves as the record of your numerical experiment The main Arvert output consists of files named CRStTyyy xxxx and CRSageyyy xxxx where xxxx represents either the relevant number of CRS iterations in which case yyy is null or the sample suffix in which case yyy final The file CRStT rolling contains the most recent set of thermal histories and is updated every 1000 CRS histories this provides a record of what was happening should the program crash and provides a means of peeking at model progress for longer runs There are also two files MONTEtT suffix and MONTEage suffix that record the original Monte Carlo pool used to start the inversion It can be important to look
26. is a critical but subtle parameter If the number is too high at times Arvert may crash because it will not be possible to generate legal Monte Carlo histories that satisfy all constraints usually a problem with models that allow heating But if the number is too low be aware that you begin to limit the representation of the thermal history to only a few line segments that are fixed and widely spaced in time such a model will not be able to handle histories with sharp inflections The absolute limit in nodes is 2 which gives you only the model start and its end at 0 Ma and means you will be modeling the thermal history as a single line segment Generally speaking you will want to keep your number of time nodes about the same as the subset size see Willett 1997 You may wonder how Arvert distributes its time nodes Early versions of the program distributed them evenly To allow better resolution at times when temperatures might be changing later versions permitted the user to specify the time nodes However I felt that this permitted too much fiddling and user intervention that might bias results So Arvert 4 x now distributes time nodes based on the lowest and highest ages in the age spectrum Two nodes always have to go to the start and end of the Arvert 4X User s Manual Page 12 model If only three nodes are specified Arvert tosses the one extra node into the middle of the time span bracketed by the age spectrum If four are s
27. n in apatite and zircon sees the grain size as the Arvert 4X User s Manual Page 22 effective diffusion dimension Therefore you will be supplying the grain size of your measured sample as an independent parameter If you have actual kinetic data for your sample that involves the frequency factor you will have to break out apart your D a value to obtain separate values for diffusion coefficient and size Important note because Arvert uses spherical geometry for helium diffusion you must convert the dimensions of your sample s grains into spherical equivalent As discussed by Meesters and Dunai 2002 this is done by determining the radius of the sphere that has the same surface to volume ratio as your unknown Sample age and error in age m y not alpha corrected Arvert solves the accumulation loss function with the effects of alpha ejection included because alpha ejection modification of the diffusion profile could be important in some special cases as for a sample lingering in the partial retention zone Therefore its direct output is an uncorrected age and this is also what is directly measure for unknowns Therefore it makes most sense to perform the inversion using the uncorrected age as the constraint The only problem with this is that is harder to directly relate the uncorrected age to the thermal history at least by eyeball Get used to it Weighting factor for U Th He constraint dimensionless When calculating fit
28. o fix its misfit In the course of doing this it may discover histories that are incrementally better due to changes in regions outside the problem area So what happens is that the model Over converges as it gradually makes tiny overall improvements This reduces diversity in the CRS pool and can result in the convergence of parts of the history that are outside any reasonable region that could be constrained by Arvert 4X User s Manual web you weave the less likely you ll be deceived recognize them in your work you could end up being embarrassed Here are some important things to keep in mind the actual age spectrum e g at very low or high temperatures or at times well outside that bracketed by the age spectrum Such behavior can also be induced by a starting Monte Carlo pool that offers insufficient diversity for the model to use to generate thermal histories of the shape it needs the number of time nodes can also play a role here try specifying just two nodes and see what happens An essential point is that you should keep your eye on just that part of the thermal history your age spectrum has a chance of constraining You should not think that running the model forever will eventually get you to a good place more is not always better If you drive the model too far you will get a spindly little over converged history that is absurdly tight along its length It s far better to run a series of short
29. ogram like Illustrator but if you have ever done this you will know how tedious it can be to deal with Excel s output does or does not converge to the same result Keep in mind that Arvert will try to bring a histories in the CRS pool to agreement with the observed data There is nothing magic about this convergence however So if you are having trouble getting the model to converge and find that attempts to do so are causing over convergence you can run the model for fewer iterations and then look at the sorted results for just those that are acceptable fits Also if for geological reasons you are unhappy about some of the results you could write code to parse the output and extract only those histories that make geological sense you could Page 26 write a program or do this directly in Excel Important Be sure to look not only at your time temperature results but also your age spectra and list of He ages if you re making use of this constraint If you have a gnarly sample or you have not done a good job in assessing your sample s domain structure or you have made a blunder in input parameters or you have entered illogical constraints Arvert will still chug happily along doing the best it can When you re done I strongly urge you to look at the paper by Willett 1997 for a clear discussion of what the results from a model like this mean I will parrot some of what he says here in abbre
30. owing high rates and then see if the CRS results agree see also Section 3 5 below Maximum heating and cooling rates for CRS histories You must also specify heating and cooling rate constraints for the CRS histories These can be identical to the Monte Carlo values if you prefer or not Note that for most typical runs having more than 10 time nodes these implicit rate constraints often end up being ignored see discussion of time nodes above CRS amplification factor usually 1 1 to 1 5 Arvert 4X User s Manual Page 14 This parameter controls how aggressively Arvert searches parameter space because it determines how much amplification is used to generate a new CRS thermal history see discussion above and Figure 1 Typical values are between 1 1 and 1 5 with values of 1 1 producing a subtle model that converges more slowly and values of 1 5 producing a rather noisy model that converges more rapidly Both sorts of value can be useful in exploring subtleties or stirring up a better search of temperature space Note that you are allowed to enter amplification factors between 0 5 and 2 0 but values below 1 0 tend to collapse the inversion and very high values tend to slam new histories up against the explicit constraints or violate implicit constraints Number of histories in subset min 5 max 50 and in main pool max 300 Interplay between these two seemingly simple parameters can change the course of the inversion Generall
31. pecified Arvert places time nodes near the age maximum and minimum If more than four are specified Arvert then tries to distribute any remaining nodes across the age spectrum s time span putting a little more effort into the regions near the maximum and minimum ages One advantage of this is that it minimizes wasted nodes in regions far outside areas of interest However be aware that Arvert s time nodes may not jive perfectly with your sample s needs particularly if the precise timing of a heating or cooling pulse is critical If you suspect this is the case you can always try adding or subtracting a time node to see if this makes a large difference in Arvert s behavior Be aware that as the number of time nodes climbs it will be increasingly difficult for Arvert to make CRS histories that completely satisfy the implicit constraints If you think about the ball of yarn that is the Monte Carlo pool many combinations of these will produce a segment or two that is too steep or if only cooling is allowed that actually increases in temperature By the time you reach 15 to 20 time nodes there is almost no chance that Arvert will satisfy your CRS implicit constraints At the moment the program tries fully 1000 times to make a legal history and then gives up and takes the last one generated So when the number of time nodes increases the program will slow a little as it churns through possible histories and in many cases your implicit
32. r as plain text files This feature can be changed or removed without any ill effect although it amounts to a nice convenience Arvert 4X User s Manual An obvious hint is to move the Arvert application and its input files into a new directory for each sample you want to model so that Arvert puts its output directories in a logical place Note Be sure that the input text files have the correct line terminators choose UNIX the terminator is line feed Depending on the system compiler and IDE that you are using you may need to take steps to cause standard output using printf go to some sort of window or the command line under OS X arvert4x just reports to the command line in Terminal app Finally based on dim memories of past misadventures it s possible that on some systems you may run into glitches with file import but the routines I ve used are simple standard C and all data files are read from the application s working directory so I doubt changes will be needed Arvert s current release arvert4X has been built and tested as a universal binary using Apple s Xcode and the gcc compiler I m no more than a n00b when it comes to Xcode so beyond supplying you the the project file s I used you ll have to find your own way Good luck Page 10 Section Three Using Arvert 3 1 Program inputs and outputs Inputs To work Arvert requires four text files to be present in the same dire
33. re output files are in tab delimited format and can be plotted in Excel or in plotting programs like Igor Pro For the age spectrum files the first column gives the Ar losses the next column gives the ages for the goal spectrum the third column gives the average of all the modeled spectra and the subsequent columns give the ages for the individual modeled spectra sorted in order best to worst fit For the thermal history files the first column gives the time nodes in m y the second column gives the average temperature over all the histories and the third and fourth columns given the high and low temperature envelope around the model histories The remaining columns give the temperatures in C for each history again sorted in order best to worst fit the fit belonging to its associated age spectrum Thus you can easily plot just summary info or summary info plus the best fits It is important to note that the average thermal history and in particular the temperature envelopes are not necessarily good fit solutions Willett 1997 has found that the average history is usually not too bad a representation of the CRS pool but the temperature envelopes must be viewed more as boundaries between temperature spaces that are not permitted in any Page 25 circumstances given model boundary conditions and spaces 3 2 Viewing results The easiest way to view results is to use Microsoft Excel Simply import the ta
34. rmal history was just about acceptable That seems like a reasonable way to proceed Important Note you need to specify the internal absolute uncertainty on each step if you plan to use the MSWD option Do not include the uncertainty due to the J factor or other systematic errors Note that both these fitting parameters apply to the overall fit It is possible that to have good fits over large parts of the age spectrum and just a few localized mismatches It is up to you to decide if this is something you will view as only a second order glitch or as a sign that some assumption about domain structure or correction for excess Ar has been violated One thing you can do is run subset models in which you fit just parts of the age spectrum However I strongly urge moderation in this do not arbitrarily cut out parts of the goal spectrum other than to focus on the low or high temperature parts Typical values for mean percent deviation might be 1 2 whereas values for MSWD would be between I to 3 Arvert 4X User s Manual Page 16 Type of fit 1 for mean percent 2 for MSWD This parameter flags the type of fit to be used in the CRS algorithm and in testing for convergence see discussion immediately above Diffusion geometry 1 for sphere 2 for infinite slab This is an essential parameter but not one that will change from model to model I repeat it is essential to get this right as you must choose the same geometry here that wa
35. ronology and know the basic principles of thermochronology including the multi domain model for argon diffusion in feldspars 1 2 How does Arvert work Being an inverse model Arvert attempts to determine fundamental controlling parameters ie a thermal history from observations of a complex observed phenomenon i e an age spectrum and a U Th He age The program has two main components a pair of forward models that can calculate an age spectrum and helium age for a Arvert 4X User s Manual So if the first paragraph was Greek to you Run Away Note the current release of Arvert arvert4X1 is essentially the same as the previous release Arvert 4 0 1 This involved mostly a few minor tweaks to facilitate compilation using Apple s Xcode and the gcc compiler on Mac the code now runs as a console application in Terminal app it s been built as a universal binary for both PPC and Intel machines Input files used with Arvert 4 0 1 will need a minor change to alter their line terminators to UNIX style line feeds given thermal history and an algorithm that reshapes a starting pool of random thermal histories into a set of solutions that increasingly minimize the mismatch between calculated and observed age spectra and He ages The core forward model is taken from Oscar Lovera s original code for the calculation of age spectra Page 4 from samples incorporating multiple diffusion domains Lovera et al
36. s to the observed data Arvert independently determines fits for the age spectrum and for the single U Th He age It then combines the two as a weighted average where the fit to the Ar Ar data has weight 1 0 and the fit to the U Th He age has a weight that can range from 0 0 to 500 To treat the helium age as equal to one heating step choose a weight of 1 fitted steps to have the helium data take equal weight to the Ar data choose a weight of 1 0 It s up to you to decide how to weight the U Th He age At this point I have no idea why I left the option for the weight being as high as 500 Flag for helium data 0 don t use 1 use as constraint This flag tells Arvert whether to use the U Th He age as a constraint or not If you are not using He data you still need the helium in file to be present so that this input line will tell Arvert to skip He calculations Arvert 4X User s Manual Page 23 The following is a valid Arvert input file helium in 0 mineral 33 activation energy kcal mol 100 1 0e2 7 15 0 5 radius microns and diffusion coefficient cm2 s uncorrected He age error in age m y 1 0 weighting factor for helium age 1 flag to use He age as constraint or not Outputs Arvert creates a number of text files to record its outputs and also issues a status message while running The file suffix that you specify is appended to most of these files The status message reports the number of CRS histor
37. s used in determining your sample s kinetic and domain information Restart option 0 for fresh Monte Carlo pool 1 for restart with previous CRS pool A value of 0 begins a fresh model run that includes generation of Monte Carlo histories as a starting point A value of I means that the model will restart using the state of the CRS pool when the model last ended This option allows you to run the model in stages and with care make changes to several inversion parameters as you go along Of greatest interest you could make changes to the implicit and explicit constraints the amplification factor fitting criteria and the advanced controls that govern the operation of the Lovera routine see below Thus for example you could run a less accurate and faster set of runs using a modest amplification factor then increase the model accuracy and increase the amplification to keep the model from searching for false minima and over converging Note that you CANNOT change most of the other model parameters like model duration time nodes pool size etc Such items impact array sizes and the nature of the data in the restart file and changes in them will produce erratic behavior or most likely a crash Similarly you can t make changes to the goal spectrum file or the domain structure file This version of Arvert provides NO PROTECTION against making such fatal changes however so it is up to you to use the restart option wit
38. seless runs Once you ve checked your inputs your only options are to abort the run or to proceed Once the program is running you can quit the application in the standard way cntrl C but you will effectively lose your calculated data Arvert is an ok citizen with respect to multitasking and you can switch Page 9 away from it to do other work Note that it is processor intensive and may slow down the operation of other tasks so your Snood playing will not be as enjoyable Likewise if you load the processor with other jobs you will slow down Arvert s progress as well You communicate with Arvert using text files See Section 3 1 below 2 3 Compiling the code If you are using a Wintel Unix or Linux system or you are using a Mac but wish to make changes you will have to recompile the Arvert source code to get a working program Arvert is written in standard C not ANSI strict The source code consists of a number of small source files that will have to be compiled and linked as a project This should be straightforward As usual several minor areas may require attention There are some calls to standard timing routines that should work but could cause a glitch on some systems These can be expunged without any trouble or rewritten if you really want timing feedback Next to make working with Arvert s output files more convenient I set file extensions that will either open output files in Excel o
39. sually a total of 5000 to 20000 iterations will be sufficient e Model duration in millions of years Arvert 4X User s Manual Page 11 You should be sure to leave adequate model time before initial closure especially if you wish to permit reheating Otherwise your model results may be unduly influenced by your chosen starting constraints On the other hand it would be silly to run a 1000 Ma model for a sample that was only 10 Ma in maximum age as this would waste compute time and lower the model resolution because most time nodes would be wasted outside the region where the sample has constraining power Warning you need to make sure that the model duration and the time of the first explicit constraint if any are the same Unless you have data such as a U Pb age to constrain your sample s higher temperature history you might want to leave 30 50 m y between the start of the model run and the time of first closure Tip Because Avert always uses 0 Ma as one of its model boundaries if you are modeling an older sample and know that more recent thermal events are unlikely you might consider engineering a static shift in your data lowering all the ages in your goal age spectrum by the same amount This will maximize the number of time nodes Arvert distributes around the period of interest to your age spectrum Number of time nodes minimum of 2 maximum of 15 The number of time slices at which Arvert generates temperatures This
40. t analyzing feldspars you should ask yourself what you are trying to accomplish and what sort of resolution is required to answer the questions you are interested in Do you need precise or just general timing of inflections in cooling rate as a measure of tectonic or erosional processes Do you need accurate and precise information about paleotemperatures or will hot medium cool be enough If one of the talents relevant to modeling is to know when to do it another important talent is to know when to stop And above all don t forget Page 27 geological constraints and intuition and data from other dating systems In this game the more tangled the 3 4 Warnings and issues Yes yes Arvert is wonderful but like any model it comes with baggage and many pitfalls If you don t become aware of these and 3 4 1 Over convergence Like all its previous incarnations the current version of Arvert often has a hard time meeting the specified fitting criterion usually because of minor errors in domain structure or a few steps of a spectrum that aren t ideal To a degree determined by how much overlap there is among domains most parts of a thermal history affect most parts of an age spectrum even if there is also some degree of independence So if after making some progress Arvert starts fussing with a piece of an age spectrum it can t match it just keeps going generating new CRS histories and trying in vain t
41. t 4X User s Manual Page 29 Figure 2 gives a simple common and obvious example of how you might introduce possible biases but similar features can creep in in other ways You might specify a model duration that starts the model too close to initial cooling to allow it to explore temperature space Perhaps you might have chosen some explicit constraints that are legal but in a subtle way act to rule out certain histories due to interactions with rate constraints It can be hard to anticipate all such problems and you might question the whole 3 4 3 Choosing Steps to Fit You will have to make some informed judgments about which steps from your age spectrum can be used for fitting At high levels of Ar release KF spectra often go a little funny just when incongruent melting occurs and the kinetic properties of the sample become undefined In other samples the age spectrum seems to sail right past this point The conservative thing to do is to only fit steps below the incongruent melting point because only these steps will have been released by the process of volume diffusion which is the only process Arvert models Keep in mind that the presence of impurities quartz in myrmekite albite in exsolution lamellae will likely cause melting to happen at lower Arvert 4X User s Manual premise that inverse modeling can overcome the operator biases that can pollute forward modeling The answer is once again to run m
42. ts you specified lest Arvert spit the dummy or get confused Maximum heating and cooling rates for Monte Carlo histories You must specify what the maximum values for heating and cooling rate are during the generation of the initial Monte Carlo pool of thermal histories To rule out either cooling or heating enter a value of 0 the units of this parameter are C m y The permitted range is between 0 and 1000 C m y Note that for typical models runs of 10 m y or more with upper constraints of 500 C or so you will never be able to use a rate of 1000 C m y since this would be equivalent to only 0 5 m y in time and for older models Arvert won t distribute time nodes with that resolution Note also that allowing high rates during the Monte Carlo routine can introduce a potential bias into the model especially if you rule out say heating but allow fast cooling What happens is that whenever Arvert makes a low temperature value the history becomes trapped at low temperatures because heating isn t permitted Thus Monte Carlo histories generated under such a model will be dominated by those that plunge to low temperatures and the CRS pool will tend to inherit this sigmoidal shape It is probably healthiest to make the inversion find the rate you suspect rather than pre supplying it with such histories A useful technique is to run models in which the initial Monte Carlo pool is run once allowing only low rates and then again all
43. ual Page 38 Model Mean Model limit Model Limit Best Fit Model True History Summary of results for linear model Note that Arvert output files contain this sort of information in the first few columns of data making it easy to produce summary plots like this The next sequence of images shows summary data and summary results from a model of synthetic data that include a He age as a constraint and that were calculated for a non linear cooling history Also shown are results of an inversion where the He data are not included as a constraint Arvert 4X User s Manual Page 39 600 4 With helium age as constraint Without helium age as constraint Model Mean Model limit Model limit Best Fit Model True History No Helium Mean Summary of model runs for synthetic data non linear cooling history Arvert 4X User s Manual Page 40
44. uch Back in the mid 1980 s when I was a research fellow at RSES in Arvert 4X User s Manual Canberra I took some Crank Nicolson diffusion code for thermal modeling that ultimately traces back through Mark Harrison to Garry Clarke at UBC and converted it to model Ar diffusion profiles By the time I left Canberra in 1988 this code could generate age spectra for Page 31 any given thermal history and domain distribution At Lehigh I was bothered by the under determined nature of age spectra and the potentials for operator bias during forward modeling so I stumbled ahead to create a crude purely Monte Carlo inverse model We actually got some interesting results but in retrospect this approach was hilariously futile and naive given the number of possible thermal histories that can exist and the relatively small proportion that are solutions During a visit to Dalhousie in the mid 1990 s Sean Willett introduced me to his application of the CRS algorithm to the inversion of fission track data After a little effort Arvert was born using the Crank Nicolson code as a core forward model and the CRS algorithm to guide the inversion A few years went by tweaking this model and learning its ins and outs all the work being concentrated in occasional patches when I d find the time and the interest to push things a little further A few years ago I decided to abandon the finite difference core in 4 2 Performan
45. ultiple models with different starting conditions and see what you get Try feeding the model a starting set like that shown in Figure 2 and then try the reverse starting it with a pool showing only shallow slopes Overlay the two or more results to get a more robust picture of what your sample can and cannot tell you temperatures than you d expect for pure K feldspar At low levels of Ar release the main problem is usually fluid inclusion hosted Ar and if you use isothermal replicates to explore this phenomenon you will likely have a spectrum that overall descends while oscillating in detail Some of these often small steps have relatively large uncertainties If no correction for Cl correlated Ar is possible then you will have to decide which if any of the younger ages in the replicate zone might be reliable What about fitting non contiguous steps My own view is that early in an age spectrum if there is clear evidence for fluid inclusion hosted Ar then it is ok to fit alternate steps although this does introduce an element of subjectivity In the Page 30 middle and later parts of an age spectrum I would be very wary of starting to omit the odd step as this is a dangerous and subjective game 3 4 4 Crashes and unsociable behavior At this point Arvert 4X is fairly robust and I have not seen a crash in quite some time as I believe all issues with memory including leaks array indices pointers an
46. vey model of a few thousand Page 32 histories in a few minutes For instance on my 1 25 Ghz G4 Mac laptop Arvert will do about 750 CRS histories per minute while coexisting with a bunch of other live processes This is for a hefty model with 6 diffusion domains and some 60 heating steps My new MacBook Pro runs about five times faster than that Arvert s performance scales pretty much linearly with number of domains and number of heating steps as these increase the number of loops in the core lovera routine The CRS bookkeeping and other routines account for only a small part of the total CPU usage although under some conditions you can make the CRS routine struggle as it tries to create a new thermal history that s legal I ve been ruminating lately about how easily Arvert could be changed to handle the rapid increase in the number of parallel computing opportunities I am neither an expert programmer nor an applied mathematician isn t it obvious I looked into Altivec coding on the G4 chips used by many Macs to take advantage of this technology but ran away scared The next things to consider are dual processor machines and again this looks a little intimidating Then there are commercial options for parallel coding that are pricey in dollars and academic options that for me would be pricey in time note the word pricey Then finally there are Arvert 4X User s Manual solutions that can
47. viated form relevant to what you might do once you have a bundle of thermal histories in hand Let s say you have a bundle of thermal histories you are happy with How do you use and describe them First Willett 1997 has shown that to a first approximation the average thermal history of the converged bundle isn t a bad representation of the solutions but it is important to realize that this average may not be a best fit solution A simply way to assess or depict the constraining power of your sample is to plot the average history and then the envelopes surrounding the total bundle of results However these envelopes Arvert 4X User s Manual to minimize misfits even if this effort is not very good If the inversion gets stuck at a rather high fit value but then is allowed to continue to run you can get into a situation where the time temperature results look very tightly converged in places but the model age spectra diverge widely from the observed spectrum If you are having concerns and troubles with with I suggest you look into Oscar Lovera s autocorrelation code that compares age spectra and LogRRo plots are definitely not a solution and more accurately should be thought of as dividing regions of temperature time space that cannot be part of the solution from regions that may be part of the solution My last bit of advice is that before you embark on inverse modeling and in fact before you even star
48. y the subset size should be close to the number of time nodes chosen Consider that if the pool size is very large compared to the subset convergence will take longer because there are simply more histories to work through and the subset average will less closely represent the pool average The latter is an important point as this interplay controls the tension between random exploration learning and convergence in this algorithm Too much randomness and the model will converge too slowly but too much learning and the model will falsely converge because all available variance will be expunged consider the degenerate case where the pool and subsetsize are the same such a model must collapse to false convergence The subset is constrained to be within the range 5 to 50 and less than a third the size of the main pool The main pool can have as many as 300 members but must be at least three times greater than the subset size Fitting criterion mean percent deviation mpd mean square of weighted deviates mswd In theory this is the trigger parameter that will terminate the model and flag that it has converged this rarely happens in practice Note that Arvert tries to get all thermal histories in the pool to fit so even if the model does not converge it s still likely there will be a number of good fitting histories There are two options for this parameter the choice of which is made by the next input line Arvert 4X User
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