Elastodynamic Solution Near and Far Field (bnfd)

The program bnfd computes synthetic seismograms for a point source in a whole space. While limited in terms of practical applications (most problems of interest are in more complicated media), the solution does provide insight into radiation patterns and issues related to the transition from near to far field. The computation is taken directly from Aki and Richards (1) (equation 4.23, page 73). The program has 9 command line arguments which are documented in the man pages and the online help. Users are encouraged to review the documentation. The man page is viewed by typing

man bnfd

and the online help is viewed with the command,

bnfd -h.

The program allows the user to restrict the terms included in the computation, as well as select a specific component of motion to display. The source is represented by a single equivalent force applied within the medium. The waves are computed relative to that point where the source is applied. The wavelet (scalar source moment) is an exponentially decaying sinusoid

$$X_{o}(t)=\exp\left(-\alpha t\right)\cdot\sin\left(2\pi f_{c}\right),$$ (47)

where $f_{c}$ is the center frequency of the source spectrum. The near-field integral is evaluated by Simpson's rule. For the convenience of the reader, equation 4.23 is repeated below

$$u_{i}(x,t)= \begin{array}{c} \frac{1}{4\pi\rho}\left(3\gamma_... ...ht) \frac{1}{r}X_{o}\left(t-\frac{r}{\beta}\right) \end{array},$$ (48)

where the P-wave velocity is $\alpha$ , the S-wave velocity is $\beta$ , the distance from the source point to the observer is r, the direction cosines are the $\gamma_{i}=\frac{x_{i}}{r}$ , density is $\rho$ , time is t, particle displacement in the i-direction is $u_{i}$ , x is the position vector, and $\delta_{ij}$ is the delta function. The first term in equation (48) is the near-field term, the second, the far-field P-wave motion, and the last, the far-field S-wave.