Complex trace attributes were introduced into geophysics by the paper

Taner, M. T., F. Koehler, and R. E. Sheriff, 1979, Complex seismic trace analysis: Geophysics, 44, 1041-1063.

If $s(t)$ is the input seismic trace, then the analytical trace is defined as the complex-valued signal $a(t) = s(t)+i h(t)$, where $h(t)$ is the Hilbert transform of $s(t)$

$$h(t) =\displaystyle \frac{1}{\pi} \int \frac{s(\tau)}{t-\tau} d\tau\;.$$

The signal envelope is the positive signal $e(t)=\sqrt{s^2(t)+h^2(t)}$. A phase-rotated seismic signal is $p(t)=s(t)\,\cos{\phi} +h(t)\,\sin{\phi}$ where $\phi$ is the phase of rotation. By default, sfenvelope computes the signal envelope. It can also produce a phase-rotated signal if given hilb=y and phase=. If phase=90 (the default value), the phase-rotated signal will be simply the Hilbert transform of the input.

The following figure from book/rsf/rsf/sfenvelope illustrates an application of sfenvelope:

Computing the discrete Hilbert transform is not a trivial task. In the Fourier domain, the continuous Hilbert transform is given by

$$\displaystyle H(\omega) = i\,\operatorname{sgn}(\omega)\,S(\omega)$$

where $\operatorname{sgn}$ is the sign function. The discontinuity of the sign function in the frequency domain at $\omega=0$ is related to the slow $1/t$ decay of the filter impulse response in the time domain. The discontinuity at the Nyquist frequency creates additional oscillations. Different practical implementations shorten the filter impulse response by effectively smoothing the Fourier-domain discontinuities. The Madagascar implementation of the discrete Hilbert transform follows the algorithm described in

Pei, S.-C., and P.-H. Wang, 2001, Closed-form design of maximally flat FIR Hilbert transformers, differentiators, and fractional delayers by power series expansion: IEEE Trans. on Circuits and Systems, v. 48, No. 4, 389-398.

The accuracy/cost trade-off is controlled by two parameters: order= and ref=. The following figures frombook/rsf/rsf/sfenvelope illustrate the effect of the order= parameter:

The Seismic Unix implementation (suhilb program) applies a Hamming window in the time domain. For some reason, it has the filter polarity reversed:

A multidimensional analog of the Hilbert transform is the Riesz transform. It is implemented in the sfriesz program.

sfagc implements Automatic Gain Control, a popular technique for normalizing signal amplitudes.
The algorithm is simple: divide the signal by its smoothed absolute value. The smoothing is controlled by rect#= and repeat= parameters, similar to the ones used by sfsmooth.
The following example from rsf/rsf/sfagc illustrates the application of sfagc in comparison with the application of sfpow, which applies a gain based on a power of time. The gains are applied to a shot gather from Alaska from the collection of shot gathers by Yilmaz and Cumro. A similar example appears on page 236 in Jon Claerbout’s Imaging the Earth’s Interior.

For a more accurate algorithm, try sfshapeagc, which computes the gain function using shaping regularization.

sfclip is very simple yet very useful program. It “clips” the data to the specified maximum by the absolute value.

Here is a simple test. First, let us make some data.

bash$ sfmath n1=10 output="sin(x1)" > data.rsf
bash$ < data.rsf sfdisfil
   0:             0       0.8415       0.9093       0.1411      -0.7568
   5:       -0.9589      -0.2794        0.657       0.9894       0.4121

Now clip it to 0.5 by maximum absolute value.

bash$ < data.rsf sfclip clip=0.5 > clip.rsf
bash$ < clip.rsf sfdisfil
   0:           0.5          0.5          0.5       0.1411         -0.5
   5:          -0.5      -0.2794          0.5          0.5       0.4121 

What if you need to clip the data not by the maximum value but to a specified range? Use sfclip2.

bash$ < data.rsf sfclip2 lower=0 upper=0.9 > clip2.rsf
bash$ < clip2.rsf sfdisfil
   0:             0       0.8415          0.9       0.1411            0
   5:             0            0        0.657          0.9       0.4121

sfclip should handle correctly infinite values, for example those resulting from division by zero.

bash$ sfmath n1=10 output=1/x1 > data.rsf
bash$ < data.rsf sfdisfil
   0:           inf            1          0.5       0.3333         0.25
   5:           0.2       0.1667       0.1429        0.125       0.1111
bash$ < data.rsf sfclip clip=0.3 > clip.rsf
bash$ < clip.rsf sfdisfil
   0:           0.3          0.3          0.3          0.3         0.25
   5:           0.2       0.1667       0.1429        0.125       0.1111

A prototype of sfclip is used as an example in Guide to madagascar API. The actual program is a little different.