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{
  "Purpose of lisousi\n"
  "==================\n"
  "\n"
  "Line-source simulation: Transform field data to apparent line-source generated\n"
  "waveforms in preparation for Cartesian 2D full-waveform inversion.\n"
  "\n"
  "Seismic field data is excited by point sources (e.g. hammer blows).\n"
  "Full waveform inversion (FWI) approaches which make use of Cartesian 2D\n"
  "forward modeling implicitly use a line source to fit the observed data.\n"
  "Therefore recorded waveforms must be transformed to simulate equivalent\n"
  "line-source generated data prior to application of 2D FWI.\n"
  "\n"
  "lisousi offers several single-trace approaches for vertical component and\n"
  "radial component data excited by vertical hammer blows or explosions.\n"
  "Single-trace approaches can be applied to each seismic trace individually in\n"
  "contrast to integral transform approaches, which require data from a complete\n"
  "profile. Single-trace approaches have the benefit, that they are independent\n"
  "of survey layout and that they perform reasonably well for data recorded on\n"
  "laterally heterogeneous structures. On the downside they must estimate the\n"
  "wave number from sample time and receiver offset. They inherently are\n"
  "approximations, most of them being derived from the acoustic wave Green's\n"
  "function. Nevertheless, they perform surprisingly well on data from\n"
  "visco-elastic wave propagation in heterogeneous structures.\n"
  "\n"
  "For shallow seismic data we recommend a simple but effective procedure:\n"
  "\n"
  " 1. scale waveform by r*sqrt(2)    (offset times square root of 2)\n"
  " 2. convolve with 1/sqrt(t)        (fractional half integration)\n"
  " 3. taper samples with 1/sqrt(t)\n"
  "\n"
  "Where r is source-to-receiver offset and t is sample time.\n"
  "We call this \"direct-wave transformation\".\n"
  "\n"
  "Theory of operation\n"
  "===================\n"
  "\n"
  "Lisousi in particular offers the following approaches as defined by Forbriger\n"
  "et al. (2014, section 5) and tested by Schäfer et al. (2014, see definition in\n"
  "section 2.2):\n"
  " - Single-velocity transformation\n"
  " - Direct-wave transformation\n"
  " - Reflected-wave transformation\n"
  " - Hybrid transformation\n"
  "\n"
  "All approaches are based on the ratio of the 2D and the 3D Green's function\n"
  "in the frequency domain (Forbriger et al. 2014, eq. 51). This ratio can be\n"
  "understood as a convolution with 1/sqrt(t) in the time domain and appropriate\n"
  "scaling (tapering) of the samples in the time domain (Forbriger et al. 2014,\n"
  "eq. 52). The appropriate scaling factor depends on wave travel time and wave\n"
  "travel distance, where only travel time can be deduced immediately from the\n"
  "data.\n"
  "\n"
  "Single-velocity transformation\n"
  "------------------------------\n"
  "  This approach is appropriate for wave propagation in homogeneous full space,\n"
  "  where travel distance equals source to receiver offset and the average wave\n"
  "  speed equals the actual (constant) wave speed. In this case the amplitude\n"
  "  factor is taken to be (Forbriger et al. 2014, eq. 52)\n"
  "\n"
  "    F = sqrt(2*r*v),\n"
  "\n"
  "  where r is taken as the source to receiver offset (as provided in the data\n"
  "  files) and v is the propagation velocity taken from the argument to option\n"
  "  -velocity or its default value.\n"
  "\n"
  "Direct-wave transformation\n"
  "--------------------------\n"
  "  This approach is appropriate for shallow seismic data, where sources as well\n"
  "  as receivers are close to the free surface and data are dominated by direct\n"
  "  waves or surface waves. In this case the amplitude factor is taken to be\n"
  "  (Forbriger et al. 2014, eq. 58)\n"
  "\n"
  "    F = r*sqrt(2/t),\n"
  "\n"
  "  where r is taken as the source to receiver offset (as provided in the data\n"
  "  files) and t is the travel time of the wave (which equals the sample time in\n"
  "  the data files).\n"
  "\n"
  "Reflected-wave transformation\n"
  "-----------------------------\n"
  "  This approach is appropriate for body waves which are reflected at deep\n"
  "  reflectors in structures where propagation velocity varies only weakly (when\n"
  "  compared to shallow structures). In this case the amplitude factor is taken\n"
  "  to be (Forbriger et al. 2014, eq. 56)\n"
  "\n"
  "    F = v*sqrt(2*t),\n"
  "\n"
  "  where v is the average propagation velocity taken from the argument to\n"
  "  option -velocity or its default value and t is the travel time of the wave\n"
  "  (which equals the sample time in the data files).\n"
  "\n"
  "Hybrid transformation\n"
  "---------------------\n"
  "  This approch is a variant of the direct-wave transformation, where the \n"
  "  single-velocity transformation is used as a replacement at small offsets\n"
  "  (Forbriger et al. 2014, sec. 6.2). This is necessary in cases, where the\n"
  "  amplitude taper, which becomes singular at zero offset for the direct-wave\n"
  "  transformation, otherwise would result in artefacts. The one is replaced by\n"
  "  the other gradually over a given offset range.\n"
  "\n"
  "The program offers options to select different ways of constructing the\n"
  "1/sqrt(t) filter and the way this filter is applied. Application of the filter\n"
  "(convolution with 1/sqrt(t)) and the application of the scaling (tapering with\n"
  "1/sqrt(t)) are not commutative in a mathematical sense and the results may\n"
  "differ for a different order of the application. However, residuals have not\n"
  "yet been observed at a significant level in practical application. Some of the\n"
  "options are not really of practical relevance due to more efficient and\n"
  "equally accurate alternatives. For instance a time domain convolution is not\n"
  "recommended. These options are primarily provided for experimental purposes.\n"
  "\n"
  "Application of program control parameters\n"
  "=========================================\n"
  "\n"
  "Direct-wave transformation and reflected-wave transformation\n"
  "------------------------------------------------------------\n"
  "The default (with no option selected) is the \"direct-wave transformation\". Use\n"
  "the option -sqrttaper to select the \"reflected-wave transformation\". Both\n"
  "approaches convolve the seismograms with 1/sqrt(t) and are different with\n"
  "respect to the time domain taper applied to the waveform data. Both operations\n"
  "can be controlled by command line options.\n"
  "\n"
  "  Application of filter (convolution with 1/sqrt(t)):\n"
  "    1) Frequency domain application:\n"
  "       recommended approach\n"
  "       default; fastest approach\n"
  "       Convolution with the 1/sqrt(t) filter response is done in the\n"
  "       Fourier domain by multiplication with the analytically derived\n"
  "       Fourier coefficients of the filter response function.\n"
  "\n"
  "    2) Frequency domain application of dicrete Fourier transform:\n"
  "       select option: -fdfilter\n"
  "       The 1/sqrt(t) filter response is constructed in the time\n"
  "       domain. Convolution with the time series is done in the\n"
  "       frequency domain after FFT.\n"
  "\n"
  "    3) Time domain application:\n"
  "       slowest approach\n"
  "       select option: -tdfilter\n"
  "       The 1/sqrt(t) filter response is constructed in the time\n"
  "       domain. Convolution with the time series is done in the\n"
  "       time domain by discrete convolution.\n"
  "\n"
  "    Options:\n"
  "      For the frequency domain applications (1 and 2) the following\n"
  "      options are available:\n"
  "        -pad n    padding of time series\n"
  "\n"
  "      The 1/sqrt(t) filter response becomes singular for t=0. This\n"
  "      requires special measures for the approaches which construct\n"
  "      the filter response in the time domain (2 and 3) in order to\n"
  "      create a response which behaves equivalent to its analytical\n"
  "      counterpart. The following options are available:\n"
  "        -integshift t\n"
  "        -notinteg\n"
  "      If -nointeg is selected, the following options are available:\n"
  "        -tshift f\n"
  "        -tlim f\n"
  "        -tfac f\n"
  "\n"
  "  Application of the taper:\n"
  "    By default 1/sqrt(t) is applied to the seismograms as a time-domain taper\n"
  "    and the signals are scaled by r*sqrt(2). This is called the \"direct-wave\n"
  "    transformation\".\n"
  "\n"
  "    Option -sqrttaper selects sqrt(t) as taper function and scales\n"
  "    seismograms additionally by a factor sqrt(2)*velocity. This is called the\n"
  "    \"reflected-wave transformation\".\n"
  "\n"
  "    Tapers are applied prior to filtering by default. Option -taperlast\n"
  "    selects to taper the time series after filtering.\n"
  "\n"
  "    Tapers are always constructed in the time domain. The default\n"
  "    1/sqrt(t) taper is singular at t=0. This requires special\n"
  "    measures to set up the taper appropriately, such that it behaves\n"
  "    equivalent to its analytical counterpart. The following options\n"
  "    are available:\n"
  "        -integshift t\n"
  "        -nointeg\n"
  "    If -nointeg is selected, the following additional options are available:\n"
  "      -tshift f\n"
  "      -tlim f\n"
  "      -tfac f\n"
  "    They have a lesser (or even unnoticeable) impact when compared to their\n"
  "    impact when constructing the filter resonse. This is because the portion\n"
  "    of the time series (close to t=0) which would be affected by the\n"
  "    close-to-singular taper usually is of small or vanishing amplitude.\n"
  "\n"
  "    Sampling time is taken as travel time in order to determine the\n"
  "    appropriate scaling (taper) factor. Since a finite bandwidth wavelet\n"
  "    appears slightly after the ray-theoretical arrival in the seismogram,\n"
  "    scaling factors are typically too small for near offset traces, where\n"
  "    pulse duration is close to pulse travel time. The program offers the\n"
  "    option -tapdel to apply a correction for this effect. -tapslo can be used\n"
  "    to set an upper limit for tapdel at small offsets.\n"
  "\n"
  "Single-velocity transformation\n"
  "------------------------------\n"
  "  select by option: -fredomain\n"
  "  additional options:\n"
  "    -velocity v\n"
  "    -pad n\n"
  "\n"
  "  Operation:\n"
  "  A Fourier transform of the waveform is divided by the Fourier transform of\n"
  "  the 3D Greens function and multiplied by the 2D Greens function. This\n"
  "  approach works only for waves of a single given wave velocity. It is hence\n"
  "  only appropriate for the impulse response in homogeneous full space, but\n"
  "  also performs surprisingly well when applied to dispersive wavefields.\n"
  "\n"
  "Hybrid transformation\n"
  "---------------------\n"
  "  select by option: -transition\n"
  "\n"
  "Step-by-step examples\n"
  "=====================\n"
  "  Step-by-step examples are provided with the source code. See\n"
  "  https://git.scc.kit.edu/Seitosh/Seitosh/blob/master/src/ts/lisousi/examples/README\n"
  "\n"
  "References\n"
  "==========\n"
  "\n"
  "Forbriger, T., Groos, L. and Schäfer, M., 2013. Appropriate line source\n"
  "  simulation procedure for shallow seismic field data. 73rd Annual Meeting of\n"
  "  the German Geophysical Society (DGG), Leipzig. \n"
  "  (http://www.opentoast.de/Data_analysis_code_246.php)\n"
  "\n"
  "Forbriger, T., 2014. Line source simulation.\n"
  "  http://www.opentoast.de/Data_analysis_code_lisousi.php\n"
  "\n"
  "Forbriger, T., L. Groos, M. Schäfer, 2014. Line-source simulation for\n"
  "  shallow-seismic data. Part 1: theoretical background. Geophys. J. Int.,\n"
  "  198(3), 1387-1404. (doi:10.1093/gji/ggu199)\n"
  "        \n"
  "Schäfer, T., M., L. Groos, T. Forbriger, T. Bohlen, 2014. Line-source\n"
  "  simulation for shallow-seismic data. Part 2: full-waveform inversion \n"
  "  — a synthetic 2-D case study. Geophys. J. Int., 198(3), 1405-1418.\n"
  "  (doi:10.1093/gji/ggu171)\n"
};