Theory of measurements

These pages provide you the theory of the measurements.

Seismic reflection profiling is used for making 2-D or 3-D cross-sections of underground structures. The principle behind reflection seismics is the same as with underwater echo-ranging. A typical reflection campaign utilizes the near-normal reflections of compressional waves (P-waves) from buried interfaces.

The seismic source can be impulsive (explosion) or vibratory (Vibroseis), and to get the best results, it is important to optimize the frequency content and the type of the source signal. For simplicity, all types of source events may be called 'shots' even if Vibroseis was used and no actual explosion was involved.

Explosions generally have a wide frequency spectrum but the precise frequency distribution is difficult to control. In the Vibroseis method, the source is a sweep from low to high frequencies or vice versa. The sweep parameters can be chosen quite arbitrarily, and different sweeps may be tested in the target area before starting the actual field work.


Seismic reflection profiling can only discern those interfaces that have the sufficient acoustic contrast.

The seismic characteristics of a medium are described with the acoustic impedance, i.e. the product of density and propagation velocity (ρc). Typically a 5 per cent difference in acoustic impedance is required for an interface to be "seen" by the reflection seismic method.

In Fennoscandia, reflections can be due to stacking and thrusting of bedrock blocks, deep detachment faulting, metasomatism, or the contacts between e.g. layered mafic dykes and their surrounding lithologies. Weak reflectivity indicates e.g. sedimentary basins, intrusions, and old crustal pieces whose internal structure has been destroyed. (Korja and Heikkinen, 2005)

Other factors influencing the resolution of reflection seismic profiling include the effect of the acquisition geometry, noise contamination, source frequency, and the size and shape of so-called Fresnel zones.


The Vibroseis acquisition may be performed on-road to avoid the clearing of forest. A typical measurement configuration comprises source trucks and a string of geophones with a predetermined number of receiver channels (some dozens or hundreds) that is progressively moved along the road.

The midpoint of each source and receiver (CMP) represents (approximately) the point under which the reflection has occurred. The CMP spacing is two times less than the geophone spacing. The fold of the acquisition tells how many times the same CMP is involved in different source-to-receiver settings, that is, how many times each reflector should theoretically have been observed.


The processing of reflection seismic data starts with data collection, correlation and de-multiplexing. In these stages, the complicated source signature (sweep) is removed and reduced to an impulsive source, and the data is converted to a more useful format such as SEG-Y. The shot gathers (all traces relevant to one shot) are visualized and their resolution is improved by correcting for overburden thickness (field statics) and spherical divergence, and by performing filtering and deconvolution.

In subsequent stages, the data is projected on a CMP line which is a smoother version of the original survey geometry and passes through the cloud of all surface-receiver midpoints. Then the data is sorted into CMP gathers (all traces relevant to one CMP, i.e. all traces describing reflections off the same depth-point).    

Reflections normally appear as parabolae in CMP gathers so next, adjacent channels are compared for such features. Having a large fold ensures that genuine reflections are more easily distinguished from other interferences and diffractions. The reflection parabolae are unwrapped with moveout corrections (see below) and each CMP gather is summed or stacked into one zero-offset trace. This process theoretically packs the data down to (1 / fold) of its original size.

Two types of moveout are normally distinguished. In normal moveout (NMO) it is assumed that the reflecting surfaces are horizontal so that the reflector parabolae are symmetrical about the time axis. In dip moveout (DMO), eventual tilts in the interfaces are considered since they shift the parabolae off the time axis. DMO stacking is better at bringing out steep dips, but it is useful only near the surface.


The resulting stacks are balanced and the reflectors are migrated (repositioned) to their right places. Before this, the stacks may need to be lowpass filtered and resampled to spare computing resources.

Mathematically we can describe the unmigrated stacks to be (via the 2-D FFT) in (kx, ω) -domain, where the horizontal dimension represents distance but the vertical dimension represents two-way travel time (TWT). This doesn't yet guarantee that the geometry of the stack represents the actual geometry observed in nature.

Migration is used to convert the data into (kx, ky) -domain. This reduces dips and removes artefacts from the data such as bow-tie shapes and diffraction parabolae. The conventional technique for this is the Stolt migration, which, however, requires as its basis a 1-D velocity model from earlier wide-angle studies. The Stolt stretch factor W can be estimated with the approach of Fomel & Vaillant (2001).

After migration, time-to-depth conversion is performed. As a rule of thumb, the depth can be estimated from the TWT by multiplying it by three (e.g. a travel time of 5.0 seconds corresponds to a 15-kilometer depth), but this approximation breaks down for two-way travel times more than 15 seconds (50 kilometres). A refined 1-D velocity model should be used for this conversion as well.


The migrated and depth-converted sections are visualized as shaded wiggle plots, envelope sections or automated line drawings

The shaded wiggle plot is the classical way to visualize traces. In OpenFIRE, coherence filtering and high-amplitude clipping are used with it to enhance reflective events and bring out smaller details.

In envelope sections, each trace is replaced by the instantaneous amplitude (envelope) of the corresponding analytical trace, and the data is smoothed by averaging it to e.g. a 500-meter resolution. Each average gets represented by a pixel whose colour is picked from a logarithmic grayscale or colour gradient.

The wiggle plot and envelope section can be overlaid with one another, producing a 'two-attribute' picture. This representation is typically used for near-surface data.

Line drawings are produced by algorithms that extract the strongest reflection events from the data, automatically determine their dips, and assign a small tilted line segment to each reflection event. Line drawings have been produced for parts of FIRE and published in articles but they are not included in the OpenFIRE collection.

A Matlab script for plotting envelope sections from stacked .su data can be found in the OpenFIRE tools GitHub repository.


Fomel, S., & Vaillant, L. (2001). Evaluating the stolt-stretch parameter. Journal of Seismic Exploration, 9(4), 319-335.

Korja, A. & Heikkinen, P. (2005). The accretionary Svecofennian orogen—insight from the BABEL profiles. Precambrian Research, 136(3–4), 241–268.