sfdip estimates a local slope (dip) using the plane-wave destruction algorithm.

The dip is measured in time samples. If $\alpha$ is the dip angle, then the output of sfdip corresponds to the dimensionless quantity $p=\tan{\alpha}$.

The following example from jsg/flat/flat shows an input synthetic dataset and an estimated dip field

When applied to 3-D data, sfdip outputs a 4-D file with n4=2 and two dips (inline and crossline). To compute only the inline dip, use n4=0. To compute only the crossline dip, use n4=1. The following example from sep/plane/qint shows an input synthetic 3-D dataset and the two dip components calculated from it.

The algorithm consists of a number of non-linear Gauss-Newton iterations (specified by niter=) with a number of linear CG-shaping iterations (specified by liter=) inside each non-linear cycle. The convergence depends on the initial dip values, which can be specified either as constants (p0= and q0=) or as auxiliary input files (idip= and xdip=). If it is necessary to constrain the range of dip values, it can be controlled by specifying minimum or maximum parameters (pmin=, pmax= and qmin=, qmax=). The smoothness of the dip is assured by shaping regularization and controled by the smoothing radii rect1=, rect2=, rect3=.

With default parameters, the dip estimate is accurate only up to 45 degrees. To estimate steeper (aliased) dips, increase the order= parameter. The order of the filter corresponds to the maximum dip. Alternatively, one can use the technique of filter stretching (interlacing), explained by Claerbout; the stretching parameters are nj1= and nj2=. The following examples from sep/pwd/alias show aliased data interpolation using (a) order=12 (b) order=3 nj1=4.

For a faster version, with only one non-linear iteration but with fewer options, try sffdip. To estimate two interfering dips, try sftwodip2. To estimate a number of constant dips, try sfdips.

10 previous programs of the month

• sfderiv
• sfgrey3
• sfspectra
• sfnoise
• sfgraph
• sfclip
• sfagc
• sfenvelope
• sfcontour
• sfsmooth

sfderiv applies the first derivative filter.

The algorithm implemented in this program is described in the paper

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.

It is based on the Taylor expansion of the inverse sine function
$$\arcsin{x} = \displaystyle \sum_{n=0}^{\infty} \frac{(2n)!}{4^n\,(n!)^2\,(2n+1)}\,x^{2n+1}$$
which turns into an expansion of the ideal derivative filter into a chain of digital filters. The order= parameter controls the order of the expansion and the accuracy-efficiency trade-off. The following example from rsf/rsf/sfderiv shows the frequency responses and the impulse responses for differentiators of different orders

An alternative is sfigrad, which implements a simple first-order derivative. igrad is more efficient and adequate when computing derivatives of smooth functions.

Previous programs of the month

• sfgrey3
• sfspectra
• sfnoise
• sfgraph
• sfclip
• sfagc
• sfenvelope
• sfcontour
• sfsmooth

sfgrey3 generates “cube” plots from 3-D data. A cube plot displays sections from a 3-D cube as faces of the cube.

Some of the options specific to this kind of display are:

• flat= The flat parameter tells sfgrey3 whether to display the cube as a flat image or in a 3-D projection. The default is flat=y. The following example from bei/fld/cube displays the same input data with both options:

• frame1=, frame2=, frame3= The frame parameters select the slices from the cube to be displayed in the plot. The default is to take the first slice from the vertical and the out-of-plane axis (frame1=0 frame3=0) and the last slice from the horizontal axis (frame2=n2-1). In the following example from geo384w/hw3/gulf, the data size is n1=1000 n2=250 n3=48 and the frame parameters are frame1=500 frame2=160 frame3=10:

• point1=, point2= The point1= and point2= parameters control the aspect ratio of the cube by specifying the ratio (from 0 and 1) that the front face of the cube takes from the plot in the vertical and the horizontal dimension, respectively. The default is point1=0.5 point2=0.5. The following example from sep/plane/qint has point1=0.85 point2=0.74:

• movie= The movie parameter allows the user to create a movie looping over slices in a cube instead of a static picture. The value of the parameter (from 1 to 3) indicates the axis for looping or 0 (the default) for no movie. The frame increment in the movie is controled by dframe=. The following example from cwp/geo2009TTIModeSeparation/tti3 uses movie=1 to loop over the vertical axis:

To generate a movie out of 4-D data, you can use sfgrey4. Here is an example:

Previous programs of the month:

• sfspectra
• sfnoise
• sfgraph
• sfclip
• sfagc
• sfenvelope
• sfcontour
• sfsmooth