6_Parameter_Definition.tex 60 KB
 Tilman Steinweg committed Oct 01, 2015 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 \chapter{Parameter definition with json input file} \label{Definition-parameters_json} %------------------------------------------------------------------------------------------------% The geometry of the FD grid and all parameters for the wave field simulation and inversion have to be defined in a parameter file. DENISE uses a parameter file according to the JSON standard wich is described in this chapter. In the following we will first list a full input file for a forward modeling as an example and later explain every input parameter section in detail: \input{DENISE_FW.json} All lines in the parameter file are formated according to the JSON standard (\href{www.json.org}{www.json.org}) and organized as follows: {\color{blue}\begin{verbatim} "VARNAME" = "Parameter value", \end{verbatim}} where VARNAME denotes the name of the global variable in which the value is saved in all functions of the program. A comment line can look like this: {\color{blue}\begin{verbatim} "Comment" = "This is a useful comment", "2D Grid information" = "comment", \end{verbatim}} Sometimes possible values are described in comments, feel free to add own comments. Basically all non JSON conform line will be ignored. The order of parameters can be arbitrarily organized. The built-in JSON parser will search for the need parameters and displays found values. If critical parameters are missing the code will stop and an error message will appear.\\ If you use the json input file some default values for the forward modeling and the inversion are set. The default values are written in the following subsections in red. The input file \texttt{DENISE\_FW\_all\_parameters.json} in the directory \texttt{par/in\_and\_out} is an input file for a forward modeling containing all parameters that can be defined. Analog to that the input file \texttt{DENISE\_INV\_all\_parameters.json} is an example for an inversion input file. The input files \texttt{DENISE\_FW.json} and \texttt{DENISE\_INV.json} contain only the parameters that must be set by the user.\\ % In the beginning of the code development DENISE used a different kind of input parameter file. The current version is still able to read this old input file. The old parameter file was organized as follows: % {\color{blue}{\begin{verbatim} % description_of_parameter_(VARNAME)_(switches) = parameter value % \end{verbatim}}} % where VARNAME denotes the name of the global variable in which the value is saved in all functions of the program. The possible values are described in switches. A comment line is indicated by a \# on the very first position of a line. You can find an example of such a parameter file in \texttt{par/in\_and\_out/DENISE\_HESSIAN.inp}. You can switch between the two possible input files via the file extension. Use .inp'' as file extension to read in the old input file or the file extension .json'' to use the new input file. \section{Domain decomposition} {\color{blue}{\begin{verbatim} "Domain Decomposition" : "comment", "NPROCX" : "4", "NPROCY" : "2", \end{verbatim}}} Parallelization is based on domain decomposition (see Figure \ref{fig_grid_json}), i.e each processing element (PE) updates the wavefield within his portion of the grid. The model is decomposed by the program into sub grids. After decomposition each processing elements (PE) saves only his sub-volume of the grid. NPROCX and NPROCY specify the number of processors in x-, y-direction, respectively (Figure \ref{fig_grid_json}). The total number of processors thus is NP=NPROCX*NPROCY. This value must be specified when starting the program with the mpirun command: \newline \textit{mpirun -np $<$NP$>$ ../bin/DENISE DENISE.json} (see section \ref{compexec1}). \newline If the total number of processors in DENISE.json and the command line differ, the program will terminate immediately with a corresponding error message. Obviously, the total number of PEs (NPROCX*NPROCY) used to decompose the model should be less equal than the total number of CPUs which are available on your parallel machine. If you use LAM and decompose your model in more domains than CPUs are available two or more domains will be updated on the same CPU (the program will not terminate and will produce the correct results). However, this is only efficient if more than one processor is available on each node. In order to reduce the amount of data that needs to be exchanged between PEs, you should decompose the model into more or less cubic sub grids. In our example, we use 2 PEs in each direction: NPROCX=NPROCY=2. The total number of PEs used by the program is NPROC=NPROCX*NPROCY=4. \begin{figure} \begin{center} \includegraphics[width=7cm,angle=0]{figures/sketch_grid.png} \end{center} \caption{Geometry of the numerical FD grid using 2 processors in x-direction (NPROCX=2) and 2 processors in y-direction (NPROCY=2). Each processing element (PE) is updating the wavefield in its domain. At the top of the numerical mesh the PEs apply a free surface boundary condition if FREE\_SURF=1, otherwise an absorbing boundary condition (PML). The width of the absorbing frame is FW grid points. The size of the total grid is NX grid points in x-direction and NY gridpoints in y-direction. The size of each sub-grid thus is NX/NPROCX x NY/NPROCY gridpoints. The origin of the Cartesian coordinate system (x,y) is at the top left corner of the grid.} \label{fig_grid_json} \end{figure} \FloatBarrier \newpage \section{Order of the FD operator} {\color{blue}{\begin{verbatim} "FD order" : "comment", "FDORDER" : "2", "MAXRELERROR" : "0", \end{verbatim}}} The order of the used FD operator is defined by the option FDORDER (FDORDER=2,\,4\,6 or 8). With the option MAXRELERROR the user can switch between Taylor (MAXRELERROR=0) and Holberg (MAXRELERROR=1-4) FD coefficients of different accuracy. The chosen FD operator and FD coefficients have an influence on the numerical stability and grid dispersion (see chapter \ref{grid-dispersion}). \section{Discretization} {\color{blue}{\begin{verbatim} "2-D Grid" : "comment", "NX" : "500", "NY" : "100", "DH" : "0.2", \end{verbatim}}} These lines specify the size of the total numerical grid (Figure \ref{fig_grid_json}). NX and NY give the number of grid points in the x- and y-direction, respectively, and DH specify the grid spacing in x- and y-direction. The size of the total internal grid in meters in x-direction is NX*DH and in y-direction NY*DH. To allow for a consistent domain decomposition NX/NPROCX and NY/NPROCY must be integer values. To avoid numerical dispersion the wavefield must be discretized with a certain number of gridpoints per wavelength. The number of gridpoints per wavelength required, depends on the order of the spatial FD operators used in the simulation (see section \ref{grid-dispersion}). In the current FD software, 2nd, 4th, 6th and 8th order operators are implemented. The criterion to avoid numerical dispersion reads: DH\le\frac{v_{s,\text{min}}}{2 f_c n} \label{eq_dispersion_json} where $\frac{v_{s,\text{min}}}{2 f_c}$ is the smallest wavelength propagating through the model and $v_{s,\text{min}}$ denotes the minimum shear wave velocity in the model, and $f_c=1/TS$ is the center frequency of the source wavelet. The program assumes that the maximum frequency of the source signal is approximately two times the center frequency. The center frequency is approximately one over the duration time TS. The value of n for different FD operators is tabulated in table \ref{grid_disp.2}. The criterion \ref{eq_dispersion_json} is checked by the FD software. If the criterion is violated a warning message will be displayed in the DENISE output section --- CHECK FOR GRID DISPERSION ---. Please note, that the FD-code will NOT terminate due to grid dispersion, only a warning is given in the output file. \section{Time stepping} {\color{blue}{\begin{verbatim} "Time Stepping" : "comment", "TIME" : "0.5", "DT" : "5.0e-05", \end{verbatim}}} The propagation time of seismic waves in the entire model is TIME (given in seconds). The time stepping interval (DT in s) has to fulfill the stability criterion \ER{courandt:1} in section \ref{courandt}. The program checks these criteria for the entire model, outputs a warning message if these are violated , stops the program and will output the time step interval for a stable model run. \newpage \section{Sources} \label{sec:sources} {\color{blue}{\begin{verbatim} "Source" : "comment", "QUELLART" : "4", "QUELLART values: ricker=1;fumue=2;from_SIGNAL_FILE=3;SIN**3=4; Gaussian_deriv=5;Spike=6;from_SIGNAL_FILE_in_su_format=7" : "comment", "SIGNAL_FILE" : "./ormsby.dat", "QUELLTYP" : "3", "QUELLTYP values (point_source): explosive=1;force_in_x=2;force_in_y=3; rotated_force=4" : "comment", "SRCREC" : "1", "SRCREC values : read source positions from SOURCE_FILE=1, PLANE_WAVE=2" : "comment", "SOURCE_FILE" : "./source/sources.dat", "RUN_MULTIPLE_SHOTS" : "1", "PLANE_WAVE_DEPTH" : "0.0", "PHI" : "0.0", "TS" : "0.032", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: SRCREC=1 \end{verbatim}}} Five built-in wavelets of the seismic source are available. The corresponding source time functions are defined in \texttt{src/wavelet.c}. You may modify the time functions in this file and recompile to include your own analytical wavelet or to modify the shape of the built-in wavelets. Ricker wavelet (QUELLART=1): r(\tau)=\left(1-2\tau^2\right)\exp(-\tau^2) \quad \mbox{with} \quad \tau=\frac{\pi(t-1.5/f_c-t_d)}{1.0/f_c} \label{eq_ricker} Fuchs-M\"uller wavelet (QUELLART=2): f_m(t)=\sin(2\pi(t-t_d)f_c)-0.5\sin(4\pi(t-t_d)f_c) \quad \mbox{if} \quad t\in[t_d,t_d+1/fc] \quad \mbox{else} \quad fm(t)=0 \label{eq_fm} $sin^3$ wavelet (QUELLART=4): s3(t)=0.75 \pi f_c \sin(\pi(t+t_d)f_c)^3\quad \mbox{if} \quad t \in[t_d,t_d+1/fc] \quad \mbox{else} \quad s3(t)=0 \label{eq_s3} First derivative of a Gaussian function (QUELLART=5): f(t)= -2.0 a (t-t_s) \exp(-a (t-t_s)^2)\quad \mbox{with} \quad a=\pi^2 f_c^2 \quad \mbox{and} \quad t_s=1.2/f_c \label{eq_deriv_of_gaussian} Delta pulse (QUELLART=6): Lowpass filtered delta pulse. Note, that it is not clear if the lowpass filter used in the current version works correctly for a delta pulse.\\ Source time function from SIGNAL\_FILE in su format (QUELLART=7).\\ In these equations, t denotes time and $f_c=1/TS$ is the center frequency. $t_d$ is a time delay which can be defined for each source position in SOURCE\_FILE. Note that the symmetric (zero phase) Ricker signal is always delayed by $1.0/f_c$, which means that after one period the maximum amplitude is excited at the source location. Three of these 5 source wavelets and the corresponding amplitude spectra for a center frequency of $f_c=50$ Hz and a delay of $t_d=0$ are plotted in Figure \ref{fig_source_wavelets_json}. Note the delay of the Ricker signal described above. The Fuchs-M\"uller wavelet has a slightly higher center frequency and covers a broader frequency range. \begin{figure} \begin{center} \includegraphics[width=8cm,angle=0]{figures/signals.eps} \end{center} \caption{Plot of built-in source wavelets (equations \ref{eq_ricker}, \ref{eq_fm}, \ref{eq_s3}) for a center frequency of $f_c=50$ Hz ($TS=1/f_c=0.02$s): Ricker signal (solid), Fuchs-M\"uller signal (dashed), $sin^3$-signal (dotted). a) Time function, b) amplitude spectrum, c) phase spectrum. } \label{fig_source_wavelets_json} \end{figure} You may also use your own time function as the source wavelet (for instance the signal of the first arrival recorded by a geophone at near offsets). Specify QUELLART=3 and save the samples of your source wavelet in ASCII-format in SIGNAL\_FILE. SIGNAL\_FILE should contain one sample per line. It should thus look like: {\color{blue}{\begin{verbatim} 0.0 0.01 0.03 ... \end{verbatim}}} The time interval between the samples must equal the time step interval (DT) of the FD simulation (see above)! Therefore it might be necessary to resample/interpolate a given source time function with a smaller sample rate. You may use the matlab script mfiles/resamp.m to resample your external source signal to the required sampling interval. \newline It is also possible to read different external source wavelets for each shot. Specify QUELLART=7 and save the wavelets in su format in SIGNAL\_FILE.shot. The wavelets in each su file must equal the time step intervel (DT) and the number of time steps of the FD simulation! \newline The following source types are availabe: explosive sources that excite compressional waves only (QUELLTYP=1), and point forces in the x- and y-direction (QUELLTYP=2,3). The force sources excite both P- and S-waves. The explosive source is located at the same position as the diagonal elements of the stress tensor, i.e. at (i,j) (Figure \ref{fig_cell}). The forces are located at the same position as the corresponding components of particle velocity (Figure \ref{fig_cell}). If (x,y) denotes the position at which the source location is defined in source.dat, then the actual force in x-direction is located at (x+DX/2,y) and the actual force in y-direction is located at (x,y+DY/2). With QUELLTYP=4 a custom directive force can be defined by a force angle between y and x. The angle of the force must be specified in the SOURCE\_FILE after AMP. This force is not aligned along the main directions. The locations of multiple sources must be defined in an external ASCII file (SOURCE\_FILE) that has the following format: {\color{blue}{\begin{verbatim} NSRC % XSRC ZSRC YSRC TD FC AMP SOURCE_AZIMUTH SOURCE_TYPE (NSRC lines) \end{verbatim}}} In the following lines, you can define certain parameters for each source point:\\ The first line must be the overall number of sources (NSRC). XSRC is the x-coordinate of a source point (in meter), YSRC is the y-coordinate of a source point (in meter). ZSRC is the z-coordinate should always be set to 0.0, because DENISE is a 2D code. TD is the excitation time (time-delay) for the source point (in seconds), FC is the center frequency of the source signal (in Hz), and AMP is the maximum amplitude of the source signal. \newline \textbf{Optional parameter:} The SOURCE\_AZIMUTH if SOURCE\_TYPE is 4. The SOURCE\_AZIMUTH is the angle between the y- and x-direction in degree and with SOURCE\_TYPE if SOURCE\_TYPE is set here, the value of SOURCE\_TYPE in the input file is ignored. The SOURCE\_FILE = ./sources/source.dat that defines an explosive source at $x_s=2592.0\;$ m and $y_s=2106.0\;$ m with a center frequency of 5 Hz (no time delay) is {\color{blue}{\begin{verbatim} 2592.0 0.0 2106.0 0.0 5.0 1.0 \end{verbatim}}} If the option RUN\_MULTIPLE\_SHOTS=0 in the parameter file all shot points defined in the SOURCE\_FILE are excitated simultaneously in one simulation. Setting RUN\_MULTIPLE\_SHOTS=1 will start individual model runs from i=1 to i=NSRC with source locations and properties defined at line i of the SOURCE\_FILE. (To apply a full waveform inversion you have to use RUN\_MULTIPLE\_SHOTS=1.) % Instead of a single source or multiple sources specified in the SOURCE\_FILE, you can also specify to excite a plane wave parallel (or tilted by an angle PHI) to the top of the model. This plane wave is approximated by a plane of single sources at every grid point at a depth of PLANE\_WAVE\_DEPTH below. The center source frequency $f_c$ is specified by the inverse of the duration of the source signal TS. QUELLART and QUELLTYP are taken from the parameters as described above. If you choose the plane wave option by specifying a PLANE\_WAVE\_DEPTH$>$0, the parameters SRCREC and SOURCE\_FILE will be ignored. % % This option will not be supported in future releases of DENISE. \newpage \section{Acoustic Modelling} \label{ac_mod} {\color{blue}{\begin{verbatim} "Acoustic Computation" : "comment", "ACOUSTIC" : "1", \end{verbatim}}} {\color{red}{\begin{verbatim} Default value is: ACOUSTIC=0 \end{verbatim}}} With this option pure acoustic modelling and/or inversion can be performed (ACOUSTIC = 1). Only a P-wave and a density model need to be provided. Acoustic modelling and inversion can be a quick estimate especially for marine environments. Acoustic gradients are derived from pressure wavefields, therefore the option QUELLTYPB = 4 has to be used and only the inversion of hydrophone data is possible at the moment. For acoustic modelling the option HESSIAN is not available (GRAD\_METHOD needs to be 1), as well as the option VELOCITY. Only FDORDER = 2 and INVMAT1 = 1 are possible. \section{Model input} \label{gen_of_mod} {\color{blue}{\begin{verbatim} "Model" : "comment", "READMOD" : "0", "MFILE" : "model/test", \end{verbatim}}} If READMOD=1, the P-wave, S-wave, and density model grids are read from external binary files. MFILE defines the basic file name that is expanded by the following extensions: P-wave model: ''.vp'', S-wave model: ''.vs'', density model: ''.rho''. In the example above, the model files thus are: ''model/test.vp'' (P-wave velocity model),''model/test.vs'' (S-wave velocity model), and ''model/test.rho'' (density model). In these files, each material parameter value must be saved as 32 bit (4 byte) native float. Velocities must be in meter/second, density values in kg/m$^3$. The fast dimension is the y direction. See \texttt{src/readmod.c}. The number of samples for the entire model in the x-direction is NX, the number of values in the y-direction is NY. The file size of each model file thus must be NX*NY*4 bytes. You may check the model structure using the SU command ximage: \newline \textit{ximage n1=$<$NY$>$ $<$ model/test.vp} . \newline It is also possible to read Qp, and Qs grid files to allow for spatial variable attenuation. For this you must uncomment a few lines in \texttt{src/readmod.c} and generate the corresponding binary files. If READMOD=0 the model is generated ''on the fly'' by DENISE, i.e. it is generated internally before the time loop starts. See \texttt{genmod/1D\_linear\_gradient\_el.c} for an example function that generates a simple model with a linear vertical gradient ''on the fly''. If READMOD=0 this function is called in \texttt{src/denise.c} and therefore must be specified in \texttt{src/Makefile} (at the top of \texttt{src/Makefile}, see section \ref{compexec}). If you change this file, for example to change the model structure, you need to re-compile DENISE by changing to the src directory and ''make denise''. \section{Free surface} {\color{blue}{\begin{verbatim} "Free Surface" : "comment", "FREE_SURF" : "1", \end{verbatim}}} A plane stress free surface is applied at the top of the global grid if FREE\_SURF!=0 using the imaging method proposed by \cite{levander:88}. Note that the free surface is always located at $y$=0 or at the first grid point, respectively. \section{Boundary conditions} \label{abs} {\color{blue}{\begin{verbatim} "PML Boundary" : "comment", "FW" : "20", "DAMPING" : "600.0", "FPML" : "31.25", "BOUNDARY" : "0", "npower" : "4.0", "k_max_PML" : "8.0", \end{verbatim}}} The boundary conditions are applied on each side face and the bottom face of the model grid. If FREE\_SURF = 0 the boundary conditions are also applied at the top face of the model grid. Note that the absorbing frames are always located INSIDE the model space, i.e. parts of the model structure are covered by the absorbing frame, in which no physically meaningful wavefield propagates. You should therefore consider the frame width when you design the model structure and the acquisition geometry (shot and receivers should certainly be placed outside). A convolutional perfectly matched layer (CPML) boundary condition is used. The PML implementation is based on the following papers \cite{komatitsch:07} and \cite{martin:09}. A width of the absorbing frame of FW=10-20 grid points should be sufficient. For the optimal realization of the PML boundary condition you have to specify the dominant signal frequency FPML occurring during the wave simulation. This is usually the center source frequency FC specified in the source file. DAMPING specifies the attenuation velocity in m/s within the PML. DAMPING should be approximately the propagation velocity of the dominant wave near the model boundaries. In some cases, it is usefull to apply periodic boundary conditions (see section \ref{bound_cond}). IF BOUNDARY=1 no absorbing boundaries are installed at the left/right sides of the grid. Instead, wavefield information is copied from left to right and vice versa. The effect is, for example, that a wave which leaves the model at the left side enters the model again at the right side. \section{Receivers} {\color{blue}{\begin{verbatim} "Receiver" : "comment", "SEISMO" : "1", "READREC" : "1", "REC_FILE" : "./receiver/receiver.dat", "REFRECX, REFRECY" : "0.0 , 0.0", "XREC1, YREC1" : "6.0 , 0.2", "XREC2, YREC2" : "93.0 , 0.2", "NGEOPH" : "80", \end{verbatim}}} If SEISMO$>$0, seismograms are saved on hard disk. If SEISMO equals 1 x- and y-component of particle velocity will be written according to parameters specified in Chapter \ref{seismograms_json}. If SEISMO = 2 pressure (sum of the diagonal components of the stress tensor) recorded at the receiver locations (receivers are hydrophones!) is written. If SEISMO = 3 the curl and divergence are saved. For SEISMO = 4 everthying is saved and for SEISMO = 5 everything except curl and divergence is saved. The curl and divergence of the particle velocities are useful to separate between P- and S-waves in the snapshots of the wavefield. DENISE calculates the divergence and the magnitude of the curl of the particle velocity field according to \cite{dougherty:88}. The motivation for this is as follows. According to Morse and Feshbach \cite{morse:53} the energy of P- and S-wave particle velocities is, respectively, E_p=\left(\lambda + 2 \mu\right) (div(\vec{v}))^2 \quad \mbox{and} \quad E_s=\mu \left|rot(\vec{v})\right|^2 \quad\mbox{.} \label{eq_E} $\lambda$ and $\mu$ are the Lam\{e} parameters, and $\vec{v}$ is the particle velocity vector. The locations of the receivers may either be specified in a separate file REC\_FILE or in this parameter file. If READREC=1 receiver locations are read from the ASCII-file REC\_FILE. Each line contains the coordinates of one receiver, the first two number in each line indicate the horizontal x- and the vertical y-coordinate of each receiver position. To give an example of a receiver file, the following 3 lines specify 3 receivers located at constant depth (2106.0 m). However, the receiver coordinates change in x-direction (starting at 540 m) and therefore lining up along the x-axis. {\color{blue}{\begin{verbatim} 540.0 2106.0 1080.0 2106.0 1620.0 2106.0 \end{verbatim}}} These receiver coordinates in REC\_FILE are shifted by REFREC[1], REFREC[2] into the x- and y-direction, respectively. This allows for completely moving the receiver spread without modifying REC\_FILE. This may be useful for the simulation of moving profiles in reflection seismics. If READREC=0 the receiver locations must be specified in the parameter file. In this case, it is assumed that the receivers are located along a straight line. The first receiver position is defined by (XREC1, YREC1), and the last receiver position by (XREC1, YREC1). The spacing between receivers is NGEOPH grid points. Receivers are always located on full grid indices, i.e. a receiver that is located between two grid points will be shifted by the FD program to the closest next grid point. It is not yet possible to output seismograms for arbitrary receiver locations since this would require a certain wavefield interpolation. \textbf{It is important to note that the actual receiver positions defined in REC\_FILE or in DENISE.json may vary by DH/2 due to the staggered positions of the particle velocities and stress tensor components. } In our example, we specify 100 receiver location. Due to the small size of the model, most of the specified receiver positions will be located inside this absorbing boundary (if ABS=2, see Chapter \ref{abs}). A corresponding warning message will appear. If you choose to read the receiver location from REC\_FILE receiver.dat (READREC=1), only 10 receivers locations are considered. The list of receivers specified in file receiver.dat is equivalent to the parameters in the input file with only a larger distance between adjacent receivers (NGEOPH = 10.) \section{Seismograms} \label{seismograms_json} {\color{blue}{\begin{verbatim} "Seismograms" : "comment", "NDT" : "1", "SEIS_FORMAT" : "1", "SEIS_FILE_VX" : "su/DENISE_x.su", "SEIS_FILE_VY" : "su/DENISE_y.su", "SEIS_FILE_CURL" : "su/DENISE_rot.su", "SEIS_FILE_DIV" : "su/DENISE_div.su", "SEIS_FILE_P" : "su/DENISE_p.su", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: NDT=1 \end{verbatim}}} If SEISMO$>$0 seismograms recorded at the receiver positions are written to the corresponding output files. The sampling rate of the seismograms is NDT*DT seconds. In case of a small time step interval and a high number of time steps, it might be useful to choose a high NDT in order to avoid a unnecessary detailed sampling of the seismograms and consequently large files of seismogram data. Possible output formats of the seismograms are SU, ASCII and BINARY. It is recommended to use SU format for saving the seismograms. The main advantage of this format is that the time step interval (NDT*DT) and the acquisition geometry (shot and receiver locations) are stored in the corresponding SU header words. Also additional header words like offset are set by DENISE. This format thus facilitates a further visualization and processing of the synthetic seismograms. Note, however, that SU cannot handle sampling rates smaller than 1.0e-6 seconds and the number of samples is limited to about 32.000. In such cases, you should increase the sampling rate by increasing NDT. If this is impossible (for example because the Nyquist criterion is violated) you must choose a different output format (ASCII or binary). \section{Q-approximation} {\color{blue}{\begin{verbatim} "Q-approximation", "L" : "0", "FL1" : "50.0", "FL2" : "100.0", "TAU" : "0.00001", "F_REF" : "100", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: L=0 \end{verbatim}}} These lines may be used to define an overall level of intrinsic (viscoelastic) attenuation of seismic waves. In case of L=0, a purely elastic simulation is performed (no absorption). The frequency dependence of the (intrinsic) Quality factor $Q(\omega)$ is defined by the L relaxation frequencies (FL=$f_l=2\pi/\tau_{\sigma l}$) and one value $\tau$ (see equation 5 in \cite{bohlen:02}). For a single relaxation mechanism (L=1) $Q \approx 2/\tau$ \citep{bohlen:98,blanch:95,bohlen:02}. If the model is generated ''on the fly'' the value of TAU can be assigned to all gridpoints for both P- and S-waves. Thus, intrinsic attenuation is homogeneous and equal for P- and S-waves ($Q_p(\omega)=Q_s(\omega)$). However, it is possible to simulate any spatial distribution of absorption by assigning the gridpoints with different Q-values by reading external grid files for $Q_p$ (P-waves) and $Q_s$ (S-waves) (see \texttt{src/readmod.c}) or by generating these files ''on the fly'' (see section \ref{gen_of_mod} or exemplary model function \texttt{genmod/1D\_linear\_gradient\_visc.c}). Small $Q$ values ($Q<50$) may lead to significant amplitude decay and velocity dispersion. Please note, that due to dispersive media properties the viscoelastic velocity model is defined for the reference frequency only. In DENISE, this reference frequency is specified as the center source frequency. With F\_REF one can set the reference frequency manually. At the exact reference frequency, elastic and viscoelastic models are equivalent. As a consequence, slightly smaller and larger minimum and maximum velocity values occure in the viscoelastic model. The frequency dependence of attenuation, i.e. $Q$ and phase velocity as a function of frequency, may be calculated using the Matlab functions in the directory mfiles. \section{Wavefield snapshots} {\color{blue}{\begin{verbatim} "Snapshots" : "comment", "SNAP" : "0", "TSNAP1" : "2.7e-3", "TSNAP2" : "6.0", "TSNAPINC" : "0.12", "IDX" : "1", "IDY" : "1", "SNAP_FORMAT" : "3", "SNAP_FILE" : "./snap/waveform_forward", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: SNAP=0 IDX=1 IDY=1 \end{verbatim}}} If SNAP$>0$, wavefield information (particle velocities (SNAP=1), pressure (SNAP=2), or curl and divergence of particle velocities (SNAP=3), or everything (SNAP=4)) for the entire model is saved on the hard disk (assure that enough free space is on disk!). Each PE is writing his sub-volume to disk. The filenames have the basic filename SNAP\_FILE plus an extension that indicates the PE number in the logical processor array (SNAP\_FILE.). The first snapshot is written at TSNAP1 seconds of seismic wave traveltime to the output files, the second at TSNAP1 + TSNAPINC seconds etc. The last snapshots contains wavefield at TSNAP2 seconds. Note that the file sizes increase during the simulation. The snapshot files might become quite LARGE. It may therefore be necessary to reduce the amount of snapshot data by increasing IDX, IDY and/or TSNAPINC. In order to merge the separate snapshots of each PE after the completion of the wave modeling, you can use the program snapmerge (see Chapter \ref{installation}, section \textbf{src}). The bash command line to merge the snapshot files can look like this: \newline \textit{../bin/snapmerge DENISE.json}. \section{Monitoring the simulation} {\color{blue}{\begin{verbatim} "Monitoring the simulation" : "comment", "LOG_FILE" : "log/2layer.log", "LOG" : "1", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: LOG=1 LOG_FILE="log/LOG_FILE" \end{verbatim}}} DENISE can output a lot of useful information about the modeling parameters and the status of the modeling process etc. The major part of this information is output by PE 0. If LOG=1, PE 0 writes this info to stdout, i.e. on the screen of your shell. This is generally recommended to monitor the modeling process. You may want to save this screen info to an output file by adding ''$>$ DENISE.out'' or ''| tee DENISE.out''. to your starting command. If LOG=1 all other processes with PE number greater than zero will write their information to LOG\_FILE.. If you specify LOG=2 PE 0 will also output information to LOG\_FILE.0. As a consequence only little information is written directly to the screen of your shell. On supercomputers where you submit modeling jobs to a queuing system as batch jobs LOG=2 may be advantageous. In case of LOG=2, you may still watch the simulation by checking the content of LOG\_FILE.0 for example by using the Unix commands more or tail. After finishing the program the timing information is written to the ASCII file log/test.log.0.timings. This feature is useful to benchmark your local PC cluster or supercomputer. If LOG=0 no output from node 0 will be written, neither to stdout nor to an LOG file. There will be also no output of timing information to the ASCII file log/test.log.0.timings. If TIME\_FILT is set to one the log file L2\_LOG.dat contains a 9th column with the corner frequency in Hz used in the iteration step. \newpage \section{General inversion parameters} {\color{blue}{\begin{verbatim} "General inversion parameters" : "comment", "ITERMAX" : "10", "DATA_DIR" : "su/measured_data/DENISE_real", "INVMAT1" : "1", "INVMAT" : "0", % "INVTYPE" : "2", "QUELLTYPB" : "1", "MISFIT_LOG_FILE" : "L2_LOG.dat", "VELOCITY" : "0", "Inversion for ..." : "comment", "INV_RHO_ITER" : "0", "INV_VP_ITER" : "0", "INV_VS_ITER" : "0", % % "Cosine taper" : "comment", % "TAPER" : "0", % "TAPERLENGTH" : "10", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: % INVTYPE=2 MISFIT_LOG_FILE=L2_LOG.dat VELOCITY=0 INV_RHO_ITER=0 INV_VP_ITER=0 INV_VS_ITER=0 % TAPER=0 % TAPERLENGTH=10 \end{verbatim}}} This section covers some general inversion parameters. The maximum number of iterations is defined by ITERMAX. The switch INVMAT controls if only the forward modeling code should be used (INVMAT=10), e.\,g. to calculate synthetic seismograms or a complete FWT run (INVMAT=0). The seismic sections of the real data need to be located in DATA\_DIR and should have the ending \_x.su.shot for the x-component and so on. As noted in section \ref{model parametrizations} the gradients can be expressed for different model parameterizations. The switch INVMAT1 defines which parameterization should be used, seismic velocities and density (Vp,Vs,rho, INVMAT1=1), seismic impedances (Zp,Zs,rho, INVMAT1=2) or Lam$\rm{\acute{e}}$ parameters ($\rm{\lambda,\mu,\rho}$, INVMAT1=3). If models are read from binary files appropriate file extensions are required for the different models (see section \ref{gen_of_mod}). Depending on the data different components of the seismic sections can be backpropagated. For two component data (x- and y-component) set QUELLTYPB=1, only the y-component (QUELLTYPB=2) and only the x-component (QUELLTYPB=3). For acoustic modelling pressure seismograms and QUELLTYPB=4 have to be used.\\ During the inversion the misfit values are saved in a log file specified in MISFIT\_LOG\_FILE. The log file consists of eight or nine columns and each line corresponds to one iteration step. The used step length is written in the first column. In the second to fourth column the three test step lengths used for the step length estimation are saved. The corresponding misfit values for these test step lengthes and the test shots are written to column five to seven. Column eight corresponds to the total misfit for all shots and if you use freqeuncy filtering then the ninth column corresponds to the corner frequency of the lowpass filter used in the inversion step.\\ In general DENISE tries to minimize the misfit in the particle displacement between the observed data and the synthetic data. If you set the switch VELOCITY to 1 the misfit in the particle velocity seismograms is minimized.\\ The parameters INV\_RHO\_ITER, INV\_VP\_ITER and INV\_VS\_ITER define from which inversion step on an inversion for density, Vp and Vs, respectively, is applied. To invert for one parameter from the beginning of an inversion set it to 0 or 1.\\ % The parameters TAPER, TAPERLENGTH and INVTYPE are debug parameters and should not be changed. \section{Output of inversion results} \label{sec:Output_of_inversion_results_json} {\color{blue}{\begin{verbatim} "Output of inverted models" : "comment", "INV_MODELFILE" : "model/model_Test", "nfstart" : "1", "nf" : "1", "Output of gradients" : "comment", "JACOBIAN" : "jacobian/jacobian_Test", "nfstart_jac" : "1", "nf_jac" : "1", \end{verbatim}}} The inverted models are saved in INV\_MODELFILE. The first model that is saved is at iteration step nfstart and then every $\mathrm{nf}^{\mathrm{th}}$ iteration step. Analog the gradients are saved every $\mathrm{nf\_jac}^{\mathrm{th}}$ iteration step from iteration step nftart\_jac on in JACOBIAN. \section{Change optimization method} {\color{blue}{\begin{verbatim} "Hessian and Gradient-Method" : "comment", "HESSIAN" : "0", "FC_HESSIAN" : "100", "ORDER_HESSIAN" : "4", "TSHIFT_back" : "0.0", "GRAD_METHOD" : "1", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: HESSIAN=0 \end{verbatim}}} DENISE contains the option to calculate the diagonal elements of the Hessian (after \cite{sheen:06}) for the starting model. Currently the Hessian is calculated for the Vp- and Vs-model and only for sources with directed forces in y-direction. The Hessian for the density model is not implemented yet.\\ The estimation of the Hessian requires for each shot position the solution of the forward problem with the actual source wavelet and for each receiver position the backpropagation of a spike. The forward and backpropagated wavefields have to be saved in memory and convolved with each other for each shot-receiver combination. This convolution is currently implemented as a multiplication in the frequency domain in \texttt{conv\_fd.c}. Because the time intensive computation of the forward/backpropgated wavefields and the convolution process it is highly recommended to estimate the Hessian only for acquisition geometries with a small number of sources and receivers.\\ To calculate the Hessian the parameter HESSIAN in the input file has to be set to 1 and INVMAT to 0. If HESSIAN is set to 0 and INVMAT to 0 the code runs a standard FWT. If HESSIAN is set to 0 and INVMAT to 10 the code runs a forward modeling only. A few important things to keep in mind, when calculating the Hessian in the current version of DENISE: \begin{enumerate} \item The HESSIAN can currently only be calculated for sources with forces in y-direction. Therefore the parameters QUELLTYP and QUELLTYPB in the input file should be set to 3 and 2 respectively. \item To calculate the impulse response of a spike from the receiver positions a spike wavelet is defined as option in the parameter QUELLART. Due to the limitation of the frequency range by the grid dispersion criterion it is not possible to calculate a true spike response, neither in time or in frequency-domain FD. Therefore, the spike wavelet is low-pass filtered using the parameters FC\_HESSIAN and ORDER\_HESSIAN. Note that in the current version there maybe is a bug in the definition of the spike wavelet. Therefore, one should check the source signal that will be written out using \texttt{output\_source\_signal.c}. The parameter TSHIFT\_back must be given in seconds and causes a timeshift of the delta impulses which are propagated from the receiver positions into the medium. This parameter must be used in cases where the source signal of the forward propagated wavefields does not have its main impulse at t=0 s. \item The estimated Vp-Hessian is written in binary format to JACOBIAN\_hessian.old in the Jacobian directory, the estimated Vs-Hessian to JACOBIAN\_hessian\_u.old, respectively. \item The inversion of the Hessian and the application of a Marquardt-Levenberg regularization can be done with the Matlab script check\_hessian.m, which can be found in the /mfiles directory. With this script the value of the Marquardt factor, the damping function of the Hessian within the PML regions and additional preconditioning operators can be applied on the Hessian. To test the influence of the different parameters on the Hessian it is useful to calculate one FWT iteration and multiply the resulting gradient in check\_hessian.m with the inverse Hessian. When the regularization and preconditioning of the inverse Hessian is satisfying, the inverse Hessian is written in binary format to the file taper.bin. \item To apply the taper (inverse Hessian) defined in taper.bin, on the gradient in DENISE, the parameter SWS\_TAPER\_FILE has to be set to 1 (see section~\ref{sec:Definition_of_gradient_taper_geometry}). Each model parameter requires a taper file which should be located in the /par directory and named as taper.bin for the Vp-model, taper\_u.bin for the Vs-model and taper\_rho.bin for the density model. Because the density-Hessian is not implemented yet, taper\_rho.bin can be simply a copy of taper.bin. \item At each preconditioned conjugate gradient (PCG) iteration the Hessian for the starting model is multiplied by the regularized and preconditioned inverse Hessian. This scaling of the gradient improves the convergence speed of DENISE by approximately a factor 2. However it is not a real Gauss-Newton method, which would require the calculation of the inverse Hessian at each iteration step. The implementation of a quasi-Newton method, the L-BFGS method (see f.e. the book \cite{nocedal:1999}) is currently in development. A pre-alpha version is included in this version. It can be activated by the parameter GRAD\_METHOD, but a bug seem to prevent the convergence of the L-BFGS method. Therefore it is higly recommended to use only the PCG method (GRAD\_METHOD=1) and not the L-BFGS method. \end{enumerate} \section{Misfit definition} {\color{blue}{\begin{verbatim} "Gradient calculation" : "comment", "LNORM" : "2", "NORMALIZE" : "0", "DTINV" : "2", "WATERLEVEL_LNORM8" : "0.0", \end{verbatim}}} With LNORM=2 the L2 norm is used as misfit definition. In this case the misfit is scaled with the energy of the observed seismograms.\\ With LNORM=5 the global correlation is used as misfit function. It was suggested e.\,g. by \cite{choi:2012} and consists of a zero-lag cross correlation of two normalized signals. The misfit is calculated by E = - \sum_i^{ns} \sum_j^{nr} \sum_k^{nc} \frac{\vec{u}_{i,j,k} \cdot \vec{d}_{i,j,k}}{|\vec{u}_{i,j,k}| |\vec{d}_{i,j,k}|} where the sum over $i$ denotes the sum over the sources, the sum over $j$ denotes the sum over the receivers and the sum over $k$ denotes the sum over the components used in the inversion. $\vec{u}$ are the forward modeled data and $\vec{d}$ are the observed data. The misfit is minimized but the misfit function is not yet normalized. Therefore, a perfect fit results in a misfit of $(-1)\cdot ns \cdot nr \cdot nc$.\\ LNORM=1 uses the L1 norm, LNORM=3 the Cauchy norm and LNORM=4 the SECH norm.\\ LNORM=7 uses the normalized L2 norm E=\frac{\sum_i^{ns} \sum_j^{nr} \sum_k^{nc} \left| \frac{\vec{u}_{i,j,k}}{|\vec{u}_{i,j,k}|}-\frac{\vec{d}_{i,j,k}}{|\vec{d}_{i,j,k}|}\right|^2}{\sum_i^{ns} \sum_j^{nr} \sum_k^{nc} \left| \frac{\vec{d}_{i,j,k}}{|\vec{d}_{i,j,k}|}\right|^2} suggested by \cite{choi:2012}. The misfit is scaled with the energy of the observed seismograms.\\ LNORM=8 is based on an envelope-based objective function which compares the difference between the envelopes of observed and synthetic wave fields. The misfit function is defined by E= \frac{1}{2} \sum_i^{ns} \sum_j^{nr} \sum_k^{nc} \int_0^T \left( \text{env}(\vec{u}_{i,j,k}) - \text{env}(\vec{d}_{i,j,k}) \right)^2~\text{d}t. \label{misfit_envelope} At time samples $t$ where the envelope of the synthetics $\text{env}( u)$ becomes small with respect to the noise of the observed data $\text{env}( d)$, the corresponding adjoint source develops a singularity (for $\text{env}( u) \rightarrow 0$). A finite water-level (WATERLEVEL\_LNORM8) is used to keep the division regular. The water-level is estimated about the smallest signal amplitude of the observed data which is considered in the misfit.\\ If NORMALIZE is set to 1, the synthetic data and the measured data will be normalized before calculating the residuals.\\ To reduce the memory requirements during an inversion one can define that only every DTINV time sample is used for the calculation of the gradients. To set this parameter appropriately one has to keep in mind the Nyquist criterion to avoid aliasing effects. \section{Step length estimation} {\color{blue}{\begin{verbatim} "Step length estimation" : "comment", "EPS_SCALE" : "0.01", "STEPMAX" : "4", "SCALEFAC" : "4.0", "TESTSHOT_START , TESTSHOT_END , TESTSHOT_INCR" : "1 , 2 , 1", \end{verbatim}}} For the step length estimation a parabolic line search method proposed by \cite{sourbier:09,sourbier:09b}, \cite{brossier:2009} and \cite{nocedal:1999} is implemented. For this step length estimation only two further test forward modelings are needed. The vector L2t contains the misfit values and the vector epst contains the corresponding step length. During the forward modeling of an iteration step the misfit norm of the data residuals is calculated for the shots defined by TESTSHOT\_START, TESTSHOT\_END and TESTSHOT\_INC. The value L2t(1) then contains the misfit from the forward modeling and the corresponding epst(1) value is 0.0.\\ The step lengths for the different parameters are defined as:\\ EPSILON = EPS\_SCALE * m\_max/grad\_max EPSILON = epst[i] * m\_max/grad\_max\\ where m\_max is the maximum value of the corresponding model parameter in the whole model and grad\_max is the maximum absolute value of the gradient.\\ For a better definition of the parabola the improved line search is now trying to estimate a steplength epst(2) with L2t(2) L2t(2), by increasing the steplength\\ EPS\_SCALE += EPS\_SCALE/SCALEFAC.\\ If a corresponding value epst(3) can be found after STEPMAX forward modellings, DENISE can fit a parabola through the 3 points (L2t(i),epst(i)) and estimates an optimum step length at the minimum of the parabola. If the L2-value L2t(3) after STEPMAX forward models is still smaller than L2t(2) the optimum steplength estimated by parabolic fitting will be not larger than epst(3). \newpage \section{Abort criterion} \label{json:abort_criterion} {\color{blue}{\begin{verbatim} "Termination of the programmme" : "comment", "PRO" : "0.01", \end{verbatim}}} Additionally to the parameter ITERMAX a second abort criterion is implemented in DENISE which is using the relative misfit change within the last two iterations. The relative misfit of the current iteration step and the misfit of the second to last iteration step is calculated with regard to the misfit of the second to last iteration step. If this relative change is smaller than PRO the inversion aborts or in case of using frequency filtering (TIME\_FILT==1) it increases the corner frequency of the low pass filter and therefore switches to next higher bandwidth. \section{Minimum number of iteration per frequency} {\color{blue}{\begin{verbatim} "Minimum number of iteration per frequency" : "comment", "MIN_ITER" : "10", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: MIN_ITER=0 \end{verbatim}}} If you are using frequeny filtering (TIME\_FILT==1) during the inversion, you can set a minimum number of iterations per frequency. Within this minimum number of iteration per frequency the abort criterion PRO will receive no consideration. \section{Definition of the gradient taper geometry} \label{sec:Definition_of_gradient_taper_geometry} {\color{blue}{\begin{verbatim} "Definition of gradient taper geometry" : "comment", "SWS_TAPER_GRAD_VERT" : "0", "SWS_TAPER_GRAD_HOR" : "0", "GRADT1 , GRADT2 , GRADT3 , GRADT4" : "5 , 15 , 490 , 500", "SWS_TAPER_GRAD_SOURCES" : "0", "SWS_TAPER_CIRCULAR_PER_SHOT" : "0", "SRTSHAPE" : "1", "SRTRADIUS" : "5.0", "FILTSIZE" : "1", "SWS_TAPER_FILE" : "0", "SWS_TAPER_FILE_PER_SHOT" : "0", "TAPER_FILE_NAME" : "taper.bin", "TAPER_FILE_NAME_U" : "taper_u.bin", "TAPER_FILE_NAME_RHO" : "taper_rho.bin", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: SWS_TAPER_GRAD_VERT=0 SWS_TAPER_GRAD_HOR=0 SWS_TAPER_GRAD_SOURCES=0 SWS_TAPER_CIRCULAR_PER_SHOT=0 SWS_TAPER_FILE=0 SWS_TAPER_FILE_PER_SHOT=0 \end{verbatim}}} Different preconditioning matrices can be created and applied to the gradients (using the function \texttt{taper\_grad.c}). To apply a vertical taper one has to set the switch SWS\_TAPER\_GRAD\_VERT to one and for a horizontaltaper SWS\_TAPER\_GRAD\_HOR has to be 1. The parameters for the vertical and the horizontal window are defined by the input file paramters GRADT1, GRADT2, GRADT3 and GRADT4. Please have a look at the function \texttt{taper\_grad.c} directly to obtain more information about the actual definition of the tapers. It is also possible to apply cylindrical tapers around the source positions. This can be done by either setting the switch SWS\_TAPER\_GRAD\_SOURCES or SWS\_TAPER\_CIRCULAR\_PER\_SHOT to 1. If one uses SWS\_TAPER\_GRAD\_SOURCES=1 only the final gradients (that means the gradients obtained by the summation of the gradients of each shots) are multiplied with a taper that decreases the gradients at all shot positions. Therefore, one looses the update information at the source positions. To avoid this one can use SWS\_TAPER\_CIRCULAR\_PER\_SHOT=1. In this case the gradients of the single shots are preconditioned with a window that only decreases at the current shot position. This is done before the summation of all gradients to keep model update information also at the shot positions. The actual tapers are generated by the function \texttt{taper\_grad.c} and \texttt{taper\_grad\_shot.c}, respectively. The circular taper around the source positions decrease from a value of one at the edge of the taper to a value of zero at the source position. The shape of the decrease can be defined by an error function (SRTSHAPE=1) or a log-function (SRTSHAPE=2). The radius of the taper is defined in meter by SRTRADIUS. Note, that this radius must be at least 5 gridpoints. With the parameter FILTSIZE one can extend the region where the taper is zero around the source. The taper is set to zero in a square region of (2*FILTSIZE+1 times 2*FILTSIZE+1) gridpoints. All preconditioning matrices that are applied are saved in the par directory with the file names taper\_coeff\_vert.bin, taper\_coeff\_horz.bin and taper\_coeff\_sources.bin.\\ To apply an externally defined taper on the gradients in DENISE, the parameter SWS\_TAPER\_FILE has to be set to 1. Each model parameter requires a taper file which needs to be located in TAPER\_FILE\_NAME for vp, in TAPER\_FILE\_NAME\_U for vs and in TAPER\_FILE\_NAME\_RHO for the density.\\ It is also possible to apply externally defined taper files to the gradients of the single shots before summation of these gradients. This can be done by setting SWS\_TAPER\_FILE\_PER\_SHOT to one. DENISE expects the tapers in TAPER\_FILE\_NAME.shot for the vp gradients, in TAPER\_FILE\_NAME\_U.shot for the vs gradients and in TAPER\_FILE\_NAME\_RHO.shot for the density gradients. \section{Definition of spatial filtering of the gradients} {\color{blue}{\begin{verbatim} "Definition of smoothing (spatial filtering) of the gradients" : "comment", "SPATFILTER" : "0", "SPAT_FILT_SIZE" : "40", "SPAT_FILT_1" : "1", "SPAT_FILT_ITER" : "1", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: SPATFILTER=0 \end{verbatim}}} One can apply a spatial Gaussian filter to the gradients that acts in horizontal direction (SPATFILTER=1). Have a look at the function \texttt{spat\_filt.c} for more information. \section{Smoothing the gradients} {\color{blue}{\begin{verbatim} "Definition of smoothing the gradients with a 2D-Gaussian filter" : "comment", "GRAD_FILTER" : "0", "FILT_SIZE_GRAD" : "5", "GRAD_FILT_WAVELENGTH" : "0", "A" : "0.0", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: GRAD_FILTER=0 GRAD_FILT_WAVELENGTH=0 \end{verbatim}}} If GRAD\_FILTER = 1 the gradients are smoothed with a 2D median filter after every iterationstep. With FILT\_SIZE\_GRAD you can set the filter length in gridpoints.\\ For GRAD\_FILT\_WAVELENGTH = 1 (and TIME\_FILT=1) a new wavelength dependent filter size for smoothing the gradients is calculated by \mbox{FILT\_SIZE\_GRAD} = \frac{V_{s,\text{average}}\cdot \text{A}}{\text{FC}} where FC is the corner frequency of TIME\_FILT and A is a weighting factor. \section{Limits for the model parameters} {\color{blue}{\begin{verbatim} "Upper and lower limits for model parameters" : "comment", "VPUPPERLIM" : "3500", "VPLOWERLIM" : "0", "VSUPPERLIM" : "5000", "VSLOWERLIM" : "0", "RHOUPPERLIM" : "5000", "RHOLOWERLIM" : "0", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: VPUPPERLIM=25000.0 VPLOWERLIM=0.0 VSUPPERLIM=25000.0 VSLOWERLIM=0.0 RHOUPPERLIM=25000.0 RHOLOWERLIM=0.0 \end{verbatim}}} The six limits for the model parameters specify the minimum and maximum values which may be achieved by the inversion. Here, known a priori information can be used. Depending on the choice of the parameter INVMAT1, either vp and vs or lambda and mu is meant. \section{Limited update of model parameters} {\color{blue}{\begin{verbatim} "Limited model update in reference to the starting model" : "comment", "S" : "0", "S_VS" : "0.0", "S_VP" : "0.0", "S_RHO" : "0.0", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: S=0 \end{verbatim}}} For S=1 individual limited updates of the elastic model parameters are considered. S\_VS, S\_VP and S\_RHO are the maximum updates of the model parameters at each grid point (given in \%) in reference to the model parameters of their starting models for S-wave and P-wave velocity as well as density, respectively. For example S\_VS = 30.0 means that the model parameter update of the S-wave velocity model is limited to 30\,\% at each grid point in reference to the starting model of the S-wave velocity model. Zero (S\_VS=0.0, S\_VP=0.0 or S\_RHO=0.0) means that the model parameter won't be updated at all. S\_VS=100.0, S\_VP=100.0 or S\_RHO=100.0 equal to S=0. \section{Vp/Vs ratio} {\color{blue}{\begin{verbatim} "Minimum Vp/Vs-ratio" : "comment", "VP_VS_RATIO" : "1.5", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: VP_VS_RATIO > 1 \end{verbatim}}} With VP\_VS\_RATIO = 1.5 (e.g.) it is possible to ensure a minimum Vp/Vs ratio during the inversion. This is done by checking the Vp/Vs ratio at every grid point after every model update and if it is less than (e.g.) 1.5 the P-wave velocity will be increased. For smaller values than one (1) this criterion is disregarded. \section{Time windowing and damping} {\color{blue}{\begin{verbatim} "Time windowing and damping" : "comment", "TIMEWIN" : "0", "PICKS_FILE" : "./picked_times/picks" "TWLENGTH_PLUS" : "0.01", "TWLENGTH_MINUS" : "0.01", "GAMMA" : "100000", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: TIMEWIN=0 \end{verbatim}}} To apply time windowing in a time series the paramter TIMEWIN must set to 1. A automatic picker routine is not integrated at the moment. The point in time (picked time) for each source must be specified in seperate files. The folder and file name can be set with the parameter PICKS\_FILE. The files must be named like this PICKS\_FILE\_.dat. So the number of sources in (SRCREC) must be equal to the number of files. Each file must contain the picked times for every receiver.\ The parameters TWLENGTH\_PLUS and TWLENGTH\_MINUS specify the length of the time window after (PLUS) and before (MINUS) the picked time. The unit is seconds. The damping factor GAMMA must be set individually. \section{Source wavelet inversion} To remove the contribution of the unknown source time function (STF) from the waveform residuals, it is necessary to design a filter which minimizes the misfit to the field recordings and raw synthetics. Therefore, a second forward simulation is applied. The first one is done with the wavelet specified in QUELLART and the second one with the optimized source wavelet saved in SIGNAL\_FILE (see Section~\ref{sec:sources}). This optimized source wavelet is kept constant within N\_STF or within a frequency range (see below).\\ {\color{blue}{\begin{verbatim} "Definition of inversion for source time function" : "comment", "INV_STF" : "0", "PARA" : "fdlsq:tshift=0.0", "N_STF" : "10", "N_STF_START" : "1", "TRKILL_STF" : "0", "TRKILL_FILE_STF" : "./trace_kill/trace_kill.dat", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: INV_STF=0 \end{verbatim}}} INV\_STF should be switched to 1 if you want to invert for the source time function. %How to construct parameter strings PARA see doxygen documentation. Examples for the parameter PARA are: \begin{itemize} \item To select frequency domain least squares (fdlsq) and shift the returned source time function by 0.4s, pass the following parameter string:\\ \textit{fdlsq:tshift=0.4} \item To select fdlsq, apply offset dependent weights and use a power of two to speed up the FFT\\ \textit{fdlsq:exp=1.4:pow2} \end{itemize} N\_STF is the increment between the iteration steps. N\_STF\_START defines at which iterationstep the inversion for STF should start. This parameter has to be set at least to 1 NOT(!) 0. With TRKILL\_STF = 1 it is possible to apply a trace killing for the estimation of the source wavelet correction filter. \newline Please note: If you additionally switch on frequency filtering during the inversion (TIME\_FILT=1 or TIME\_FILT=2), the parameters N\_STF and N\_STF\_START will be ignored. But the optimal source time function will be inverted for the first iteration and after every change of the frequency range. For more information see \ref{cha:STF-Inversion} \section{Smoothing the models} {\color{blue}{\begin{verbatim} "Definition of smoothing the models vp and vs" : "comment", "MODEL_FILTER" : "0", "FILT_SIZE" : "5", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: MODEL_FILTER=0 \end{verbatim}}} If MODEL\_FILTER = 1 vp- and vs-models are smoothed with a 2D median filter after every iterationstep. With FILT\_SIZE you can set the filter length in gridpoints. \section{Frequency filtering} {\color{blue}{\begin{verbatim} "Frequency filtering during inversion" : "comment", "TIME_FILT" : "0", "F_HP" : "1", "FC_START" : "10.0", "FC_END" : "75.0", "FC_INCR" : "10.0", "ORDER" : "2", "ZERO_PHASE" : "0", "FREQ_FILE" : "freqeuncies.dat"; \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: TIME_FILT=0 ZERO_PHASE=0 \end{verbatim}}} TIME\_FILT = 1 can be set to use frequency filtering. The parameter FC\_START defines the corner frequency of the Butterworth low pass filter at the beginning of the inversion. The parameter FC\_END defines the maximum corner frequency used in the inversion. The parameter FC\_INCR controls in which steps the bandwidth is increased during the inversion. If TIME\_FILT = 2 individual frequencies for each step can be read from FREQ\_FILE. In this file the first entry must be the number of frequencies used for filtering. Each frequency in Hz has to be specified in a row. The example file freqeuncies.dat can be found in \texttt{trunk/par}. The parameter ORDER defines the order of the Butterworth low pass filter. If the variable ZERO\_PHASE is set to one a zero phase filter is applied. It is realized by filtering the the traces in both forward and reverse direction with the defined Butterworth low pass filter. Therefore, the effective order of the low pass filter is doubled. With F\_HP an additional high pass filter can be applied, where F\_HP is the corner frequency in Hz. With the parameter PRO (see~\ref{json:abort_criterion}) one has to adjust the criterion that defines at which points the bandwidth of the signals are increased. \section{Trace killing} {\color{blue}{\begin{verbatim} "Trace killing" : "comment", "TRKILL" : "0", "TRKILL_FILE" : "./trace_kill/trace_kill.dat", \end{verbatim}}} {\color{red}{\begin{verbatim} Default values are: TRKILL=0 \end{verbatim}}} For not using all traces, the parameter TRKILL is introduced. If TRKILL is set to 1, trace killing is in use. The necessary file can be selected with the parameter TRKILL\_FILE. The file should include a kill table, where the number of rows is the number of receivers and the number of columns reflects the number of sources. Now, a 1 (ONE) means, YES, please kill the trace. The trace is NOT used, it should be killed. A 0 (ZERO) means, NO, this trace should NOT be killed. % \newpage % \section{Receiver array} % {\color{blue}{\begin{verbatim} % "Receiver array" : "comment", % "REC_ARRAY" : "0", % "REC_ARRAY_DEPTH" : "70.0", % "REC_ARRAY_DIST" : "40.0", % "DRX" : "4", % \end{verbatim}}} % % {\color{red}{\begin{verbatim} % Default values are: % REC_ARRAY=0 % \end{verbatim}}} % % These options are obsolete. Receiver arrays have to be defined directly in receiver.dat. % % % \section{Checkpointing} % {\color{blue}{\begin{verbatim} % "Checkpoints" : "comment", % "CHECKPTREAD" : "0", % "CHECKPTWRITE" : "0", % "CHECKPTFILE" : "tmp/checkpoint_fdveps", % \end{verbatim}}} % % {\color{red}{\begin{verbatim} % Default values are: % CHECKPTREAD=0 % CHECKPTWRITE=0 % CHECKPTFILE="tmp/checkpoint_fdveps" % \end{verbatim}}} % % These options are obsolete and will not be supported in the current version of DENISE.`