LAMB

Program LAMB computes a solution to Lamb's problem. This solution includes surface and body waves that radiate from a vertical impact on a half-space medium. The code is specific to a single medium property where the P- to S-wave velocity is fixed, $V_p/V_s = \sqrt{3}$ (Lamb, 1904). For additional theory, see Mooney (1974). The command line arguments are:

   lamb  xmin dx np tmax fsamin vs den itype sfrq sdamp gfrq gdamp pol stab  
  xmin = minimum geophone offset (m) 
  dx    = spacing of geophones (m)
  np    = number of geophones 
  tmax1 = maximum time for seismogram (s) 
  fsamin= sample interval (seconds) 
  vs    = shear wave velocity (m/s) 
  den   = mass density (kg/m3) 
  itype = type of traces output 
       1= ground displacement, step function source  
       2= ground particle velocity, step function source 
          (or ground displacement, impulse source)
       3= ground displacement, source wavelet=damped resonator
       4= ground particle velocity, source wavelet=damped resonator
       5= geophone displacement with source wavelet 
       6= geophone particle velocity with source wavelet (geophone voltage)
       7= source wavelet displacement (at source)
       8= source wavelet velocity (at source)
       9= source wavelet geophone displacement (at source)
      10= source wavelet geophone velocity (at source)
  sfrq  = source wavelet high-cut frequency (hz)
  sdamp = source damping (fraction of critical, example .7)
  gfrq  = geophone resonant frequency (hz) 
  gdamp = geophone damping (fraction of critical, example .7) 
  pol   = polarity switch
      -1= SEG Sign Convention (up motion = negative = trough)  
       0= TEST MODE, for display of normalized solution, NO 1/R etc. 
      +1= REVERSE SEG Sign Convention (up motion = positive = peak 
  stab  = stability factor, for derivative, moves pole off unit circle 
          (not generally needed except for itype=8 (try stab=.16)  
           since most other outputs have enough low-pass filtering) 
           See function deriv for more

The code computes both vertical and horizontal motion (files lambv.seg and lambh.seg). The itype parameter selects the type of output signal.

**Figure 46:** LAMB:Ground particle velocity solution for Lamb's problem, .
$\includegraphics[scale=0.8]{FigureLambPV.pdf}$

**Figure 47:** LAMB: Geophone (10 Hz, 0.7 damping) response, .
$\includegraphics[scale=0.8]{FigureLambGPV.pdf}$

The LAMB command corresponding to Figure 46 ( $itype=4$ ).

lamb 1 1. 12 .5 .0001 100. 1700. 4 70 .2 10. .7 -1 .2

The above command computes the ground particle velocity for offsets 1 to 12 meters, .5 second record, sample interval of 0.1 msec, $V_s=~~100 m/s$ , density $1700 ~~kg/m^3$ .

LAMB was re-run to compute the particle velocity of the geophone element (which corresponds to geophone voltage) by changing itype to 6. This is shown in Figure 47.

lamb 1 1. 12 .5 .0001 100. 1700. 6 70 .2 10. .7 -1 .2