Tips on using dromochrones applied to seismic tomography

The dromochrone or travel-time curves are plots in which the arrival times of seismic waves are represented as a function of distance from the source. They find their use in localizing the position of earthquakes, in reflection and refraction seismic surveys. In this post we will address their use in refraction seismic and how they are also useful in traveltime-based refraction seismic tomography.

The dromochrone graph is a diagram in which one axis reports the position of the receivers (or the distance from the source) and on the other axis is indicated the time taken to reach the receivers by a given type of seismic wave.

image showing the propagation of seimic waves in a two layer model.
Diagram showing wavefronts propagating from t0 and incident at critical angle ic at the interface between layer 1 and 2; internal refraction occurs and new wavefronts refracted at angle ic towards the surface originate.

The seismic waves when they meet materials characterized by different velocities give origin to refraction and reflection phenomena. When they hit an interface characterized by increasing speed with depth (V2 > V1) with an angle equal to arcsin(V1/V2) called critical angle, the waves travel parallel to the interface and for the principle of Hyugens part of the energy returns to the surface giving rise to the head waves, represented in purple in the diagram above. Measuring the arrival time of the waves at different distances and representing them on a graph we obtain the following plot.

Traveltimes curves from the model above;

In a model with two uniform horizontal layers where the underlying layer has a velocity V2 > V1 the dromochrone graph is represented by two straight segments. The graph is represented on the plane defined by the distance and time axes so the inverse of the slope of the segment represents the apparent velocity of the crossed layers, i.e.:

(1)   \begin{equation*}V = \frac{ \Delta X } { \Delta T}\end{equation*}

Where X is the position between the receivers or between a receiver and the source while time T is the time required to reach the receivers.

For example, in the image below, the first layer identified by the arrivals between an X equal to 3 and an X equal to 9 corresponding to arrival times of about 3 ms and 23 ms. The speed of the first layer will consequently be

(2)   \begin{equation*}V_1 = \frac{ (9-3) m } { (23-3) ms} = 0,3 m/ms = 300 m/s\end{equation*}

After the X = 9 coordinate, the dromochrone changes slope and indicates that the waves generating the first arrivals have encountered a faster layer and have undergone refraction at a critical angle.

For the interpretation of refraction seismic with the intercept time technique it is necessary to determine the slope of the dromochrone, the crossover point and the intercept time. On the contrary, for tomographic processing only the travel time is important but, of course, refraction must be present, i.e. increasing the distance from the energization position must change the dromochrone slope indicating an increase in velocity. The dromochrone, as in the case of the following image, will be more flattened at greater distances.

Dromochrone of a 2 layers model with V2>V1.

Situations in which dromochrone flexural point does not occur i.e., does not contain a refraction, cannot be interpreted with refraction tomography. Flexion can occur with a sharp inflection point or in a softer manner but must be present. A sharp inflection point may indicate a well-defined interface (e.g., the cover placed on the non-altered bedrock) while a progressive increase in velocity with depth is detected with softer dromochrone flexure.

The following image, represents dromocores that do not show the correct bending, indicating instead an increase in arrival times with increasing distance.
This dromochrone arrangement does not fit the interpretation with the refraction technique. Using SmartTomo the resulting profile would often be just a row of cells whose velocity would try to optimize arrival times through direct waves only.

This situation should be identified already in the campaign to understand if it could be due to acquisition problems (e.g., poorly evident first arrivals) or to actual characteristics of the site and therefore the need to perform different surveys.

Traveltimes curves that show no refraction and may leads to a wrong tomographic profile

An introduction to seismic refraction tomography (SRT)

Seismic tomography allows the reconstruction of an image of the subsoil distribution of seismic wave velocity and its anomalies with high resolving power. In detail, refraction seismic survey is an indirect, active seismic survey that uses refracted waves generated by contrasts of waves velocity to reconstruct subsurface characteristics. The velocity of seismic waves depends on the density and elastic properties of the material crossed, i.e., properties attributable to the lithological characteristics of the substrate investigated. The direction of propagation of the waves in depth follows Snell’s law and at each interface there are phenomena of refraction, reflection and diffraction. In refraction surveys, as the name implies, only refracted waves will be considered. Refraction seismic tomography allows to obtain a picture of the velocity distribution in the subsurface highlighting the continuous changes in velocity rather than a layered model typical of refraction surveys ( Intercept, delaytime, plus minus, GRM).

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Seismic Refraction Tomography: how to gather data

The setting of data acquisition to perform the tomographic processing is similar to the one used for the refraction seismic surveys, for example applying the G.R.M. method (Palmer, 1980).

Esempio di schema per l'acquisizione di una prova sismica tomografica a rifrazione con quattro energizzazioni esterne e tre interne.
Example of a scheme for the recording of a refraction tomographic seismic survey with four external and three internal shots.

The geophones must be placed in line, normally with a constant spacing that depends on the horizontal resolution to be obtained, while the length of the line determines the maximum depth of investigation that can be achieved.

The energizations are placed in line with the geophones line both internally and externally. If to acquire data in a refraction survey can be sufficient, at the limit, only 5 energizations, 4 external (2 per side) and one central, for seismic tomography it is necessary to perform more shots inside the line. We suggest to energize at least every 4-5 geophones.

The signal of a refraction test, performed using a hammer as energization typically has a frequency between 50 and 100Hz. The sampling frequency must therefore be higher than 200Hz. Since you want to have a good time resolution of the signal you can set as acquisition parameter a sampling rate of at least 5000Hz.

Esempio di acquisizione di una prova a rifrazione eccessivamente lunga. Il segnale è schiacciato nella parte alta della vista.
Example of acquisition of a signal that is too long in time. The signal is flattened at the top of the view.
Esempio di acquisizione idonea per la prova a rifrazione. I primi arrivi non risultano schiacciati nella parte alta ed il segnale ha una frequenza di campionamento tale da non generare alias
Example of acquisition suitable for refraction analysis. The first arrivals are not squeezed in the upper part and the signal has a sampling frequency that does not generate alias

Refraction seismic tomography uses the time of first arrivals to calculate the profile in the same way as refraction survey processing using methods such as GRM, time delay, or intercept. The recording of the signal must be long enough to detect the arrivals on all geophones. Usually for 50 meters long seisimic line it is enough to record for a time interval of 500ms. The needed recording time may vary depending on the subsoil conditions we are investigating and the type of wave we are measuring. P waves will be almost twice as fast as S waves in many stratigraphics contexts.
For example, with the average speed of 1000 m/s, the first break takes 50 ms to reach a receiver located 50 meters from the source.

SmartTomo quick start manual

This guide introduces the fundamental steps to process seismic refraction tomography with smartTomo software. The demo version is distributed with a pre-loaded dataset. The characteristics of the dataset are described in this article (Demo version).
At startup the following screen appears reminding you that this is a demo version and it shows the list of files that will be loaded.

Avviso che si tratta di una versione demo del software smarttomo

After pressing OK, the dialog box will be displayed and the can set the geometry of both shots and geophones.
On the left side of the window the positions of the shots are listed while the summary of the locations of the geophones are shown on the left. It is possible that for the same processing there are several groups of geophones, for example when performing an acquisition with a work-away configuration.

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Screenshots

Seismic profile processed using SmartTomo
Tomographic profile computed using SmartTomo software for seismic processing
Filtering signal
SmartTomo dialog to set receivers geometry
Traveltimes plot for a 100 geophones and 101 shots dataset
SmartTomo traveltimes plot

Performance

smartTomo 2018.0 has been tested to verify the speed of execution as the number of nodes increases. A synthetic dataset of 12 shots recorded with 96 channels was used for the test.

Mobirise

The test was conducted by decreasing the size of the cells and, for each dimension, using both 6 and 11 nodes per side.
The test has been performed on a MacbookPro configured as follows:
Processor name: Intel Core i5
Processor speed: 2.9 GHz
Number of processors: 1
Total number of Core: 2
Cache L2 (for Core): 256 KB
Cache L3: 3 MB
Memory: 16 GB

smartTomo 2018.0 has shown to have a linear behavior with respect to the increase in the number of nodes both for the execution time and for the memory used.

The graph on the left shows oscillations due to the number of nodes per cell side. Increasing the number of nodes per side improves the definition of seismic rays but complicates some calculation steps.

Concluding, for a section 212 meters long, 25 meters deep with a resolution of 0.5 meters and 11 nodes per cell side (407541 nodes) it takes 51 seconds for 5 iterations and 4.55GB of ram, obtaining a maximum error on time of first break less than 5%.