BOMTOM

BOMTOM (Bureau of Mines tomography) is a simultaneous iterative reconstruction technique (SIRT) tomographic program for crosshole seismic travel times. BOMTOM will generate synthetic travel times if the iteration limit equals -1. Input, output and data file names are entered from the keyboard. Interactive instructions are given for creating a new input file if the specified input file is not found. There is an output file with titles for printing, and a data file in which results are saved every 10 iterations and at the end. This data file can be used as the input file when resuming a run. Options can be changed from the keyboard interactively. Options include applying constraints, smoothing, and changing initial velocity guesses. Execution can be stopped by holding control-break until BOMTOM writes to the screen, every 10 iterations. Correction factors are weighted by the fraction of a given ray in a given pixel (cell) divided by the sum of fractions of ray paths in that pixel, and by an optional weight accounting for relative reliability of data.

Written by Daryl Tweeton, U.S. Bureau of Mines, Minneapolis, MN, 1986. Latest revision November, 1991. BOMTOM produces a grid for SURFER contours.

The Bureau of Mines expressly declares that there are no warranties expressed or implied which apply to the software contained herein. By acceptance and use of said software, which is conveyed to the user without consideration by the bureau of mines, the user expressly waives any and all claims for damage and/or suits for or by reason of personal injury, or property damages, including special, consequential, or other similar damages arising out of or in any way connected with the use of the software contained herein.

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Description of data input read from input file.

All data are in list-directed format. Input numbers must be separated by a space or comma. They do not need to be in particular columns.

header
One line of comments for the top of output file. Leave first column blank.

mdata mwt mstor mcor mbore msmth mdif

• Use mdata = 0 to input travel times separately from transmitter and receiver positions with position identification numbers. Ident numbers need not be sequential, but must be integers with absolute value less than 32767.
• Use mdata = 1 for positions and corresponding times on the same line.
• Set mwt = 1 to use individual weighting factors for accuracy of travel times.
• Use mstor = 0 to recalculate path segments each iteration or = 1 to store and recall path segments (more memory but faster execution). See comments following dimension statement.
• Use mcor = 0 for multiplicative correction factors and = 1 for additive. They give similar results.
• Set mbore = 1 to fix velocities in pixels containing transmitter or receiver positions to the initial values. Would be used with borehole sonic logs.
• Set msmth = 1 for smoothing after each iteration. Weighting is 20, 4, 1 for pixel, its nearest neighbors, and corner neighbors, respectively.
• Set mdif = 1 to find difference in velocities between this and a prior run.

• itrmax = maximum number of iterations allowed. Set itrmax = -1 to generate synthetic travel times for the initial velocities.
• itrsav = number of iterations that have been performed; 0 when starting a new run, not 0 when continuing run using the data file as input.
• Tolabs and tolinc are convergence criteria for ending iterations. Iterations stop if the average absolute value of the difference between calculated and experimental travel times is less than tolabs, or if the decrease in that average error is less than tolinc for two successive iterations.
• relax = relaxation parameter. Leaving relax = 1.0 is safe, though convergence may be quicker if it is adjusted.

• ipdat = 1 causes printing of positions, travel times, and weights.
• ipivg = 1 causes printing of initial velocity guesses.
• ipfrc = 1 causes printing of the sum of the fractions of paths in each pixel.
• iperr = 1 causes printing of the errors (delta) for each travel time.
• ipseg = 1 causes printing of segment lengths for each path and pixel.
• ipgra = 1 causes printing of graphical dot matrix display of velocities.
• isgra = 1 causes graphical screen display of velocities every 10 iterations.
• Any value other than 1 suppresses the corresponding printing or display.

• posp1x, posp1y, and posp1z are the x, y, and z coordinates of the center of pixel 1 (the top left pixel).
• pospnx, pospny, and pospnz are the x, y, and z coordinates of the center of pixel npixh*npixv (the bottom right pixel).
  • They should be set so that the transmitters and receivers are centered as well as possible in pixels. If pixel 1 is too far above or to the left of the paths, then pixel indices may be larger than the dimension. If pixel 1 is below or to the right of paths, then pixel indices will be negative. Converse directions apply to pixel npixh*npixv.

• npixh number of columns of pixels (counting horizontally).
• npixv number of rows of pixels (counting vertically).
• If desired pixel height is epixv, set npixv = 1 + (pospnz - posp1z)/epixv.
• nlitop and nlibot are the number of laterally invariant rows at top and bottom of the grid. The velocity in each of those rows is set equal to the average for that row after each iteration.
• nfxlft and nfxrht are the number of columns at the left and right sides of the grid in which the velocities are fixed at the initial values.

npst npsr adjdis

• npst, npsr are the number of transmitter, receiver positions
  
• adjdis is added to all horizontal distances between boreholes. It is added to the receiver position.
  

• idpst(ipst) is the identification number of the transmitter position. they do not need to be sequential.
  
• postx, posty, and postz are x, y, and z coordinates of transmitter positions. z increases with depth.

• idpsr(ipsr) is the identification number of the receiver position.
• posrx, posry, and posrz are x, y, and z coordinates of receiver positions.

• nexptt is the number of experimental travel times.
• adjtt is added to all experimental travel times.

• idextt(iexptt) idextr(iexptt) exptt(iexptt) (weight(iexptt), if mwt = 1) (one line for each iexptt = 1 to nexptt).
  • idextt and idextr are the identification numbers of the transmitter and receiver positions for the travel time exptt(iexptt).
  • weight(iexptt) is an optional weighting factor for accuracy of data. Correction factors are multiplied by the corresponding weight. If all data are equally reliable, set every weight = 1.0 or set mwt = 0.

• nexptt adjdis adjtt
• idpath(iexptt) postx(iexptt) posty(iexptt) postz(iexptt) posrx(iexptt) posry(iexptt) posrz(iexptt) exptt(iexptt) (weight(iexptt), if mwt = 1). (one line for each iexptt = 1 to nexptt).
  • idpath(iexptt) is the identification number of a path and the corresponding travel time. They do not need to be sequential.
  • exptt(iexptt) is the experimental travel time for path iexptt.

• smfpll is the lower limit for the sum of fractions of path lengths in a pixel (segment length is pixel/length of path from trans to rec). If the sum is less than or equal smfpll, then the velocity for the pixel is displayed as ###.
• vlocal and vhical are the low and high limits for the calculated velocities. If a velocity is out of that range, it is set = the limit. If no limit is desired, set the limit to -99. A compact display with velocities scaled to the range 0 to 9 is generated, and a dot matrix graphical display is an option (set ipgra = 1).
• If vlodsp (or vhidsp) is -99., then the lowest (or highest) velocity displayed is the minimum (or maximum) calculated by BOMTOM. If vlodsp (or vhidsp) is not - 99., then the lowest (or highest) velocity displayed is vlodsp (or vhidsp). When differences between the velocities in this run and a prior run are displayed, vlodsp and vhidsp are replaced by vlodif and vhidif.
• invopt specifies the option for inputting the initial guesses of velocities.

• v(1)
• BOMTOM sets initial velocity = v(1) for every pixel.

If invopt = 2, input is row by row and the format is:

• irowv v(irowv) (one line for each row, npixv lines).
• irowv is the row number. Rows can be input in any order. BOMTOM sets initial velocities = v(irowv) for all pixels in that row. This option facilitates varying the pattern of initial guesses to test the uniqueness of a solution.

• irowv (v(i), i = 1, npixh) (one line for each row, npixv lines).
• irowv is the row number.
• v(i) is the initial velocity for row irowv, column i. This option is used when resuming a run using a data file as input.

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The constraint that the velocity is not varied for pixels containing a transmitter or receiver is activated by setting MBORE = 1. The pixels at the borehole are those for which the velocity is most probably known. An option for fixing the velocity in columns at the sides is also provided by setting NFXRHT and NFXLFT equal to the desired number of columns. The program is easy to modify to fix the velocities in other pixels because the array LGLCOR controls whether the velocity is varied for the corresponding pixel. If LGLCOR(PIXEL) is set to FALSE in FORTRAN or 0 in BASICA, then the velocity in the corresponding pixel will not be varied.

NLITOP and NLIBOT are used to set the number of laterally invariant rows along the top or the bottom of the model. This constraint was expected to prevent artifacts of vertical strips of contrasting velocity passing through the ray path region. It will be satisfied in many applications in in situ mining above the water table because the top of the pixel grid will represent a region with no leachate and the bottom will represent a saturated region. An option was added to BOMTOM for designating the number of rows at the top and bottom in which the velocity for all pixels in the row is set equal to the average velocity for that row. The option does not specify the average velocity nor that the average velocity for any row is related to the velocity in any other row.

A second constraint consists of setting the velocities near the boreholes to known values and not allowing them to change. This constraint could be applied to in situ mining if sonic logs were run in the boreholes.

Another constraint is to limit the calculated velocity to a specified range. This constraint was not helpful in the tests unless the upper limit was set quite close to the maximum velocity in the model. In practice, one may not know the limits precisely enough to help the reconstruction significantly.

Smoothing provides another type of constraint on the model. Smoothing consists of replacing the velocity in each pixel with a weighted average velocity, averaged over that pixel and its neighbors. The smoothing option in BOMTOM uses weighting factors of 20, 4, and 1 for the pixel whose velocity is being replaced, its nearest neighbors, and its corner neighbors, respectivity. Smoothing is performed after each iteration. With more pixels than ray paths, some of the pixels do not contain any rays. Without smoothing, there is no basis for changing the velocity in them. With smoothing, those pixels have their velocity adjusted by the effect of their neighbors. The reconstruction without smoothing is so uneven that it would be difficult to interpret. With smoothing, patterns are more evident. Smoothing has been reported to provide a better looking reconstriuction with field data. The purpose of smoothing is to average random inconsistencies in the data, so smoothing would not be beneficial with self-consistent synthetic data. The inconsistencies with field data arise only partially from experimental errors in measureing the travel times and position. They occur also because the real velocity distribution can vary continuously with position. Real data come from a very large number of very small pixels. Tomography uses fewer, larger pixels, each containing a constant velocity.

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