Velocities in Reflection Seismology
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Contents:
To further characterize these events, we estimate their slowness spectra using the FDB algorithm. The horizontal velocity c hor is defined as. It shows frequency as a function of the apparent wave number , where. The black dashed triangle indicates the area where we would expect the surface wave energy from the panel.
Since the surface wave noise is generated by cars along the road, the surface wave energy in this panel could have been generated by several cars at various distances away from the line. This appears to have been the case when this panel was recorded. Hence, on an FK spectrum, these could easily be misinterpreted for body waves. This can be resolved by forming a slowness spectrum using the areal array.
The wavenumber response of the array along the receiver line is a sinc function with its first zero at twice the Nyquist wavenumber for sampling at the station spacing.
If aliased noise is strong, then the attenuation achieved by the geophone pattern may not be sufficiently strong to prevent the retrieval at small wavenumbers. We determine the individual FK spectra for small frequency bins and sum the individual spectra to produce the output slowness spectrum. This is a body wave which, depending on the distance to its source, could contribute to the retrieval of reflections from the noise.
We only pick the dominant slowness from each slowness spectrum of a particular panel. These secondary peaks may be due to reflections, different phases from the same sources or wavefields from another source being captured at the same time as the dominant wavefield. Hence, there could be more events with different slownesses present in the data.
This slowness corresponds for the larger part to a train of fairly strong events coming from the same direction in the time span of a few consecutive records. With the current equipment, it is not possible to identify any clear phases in the events. The latter may have been caused by electromagnetic noise due to the power lines that were feeding the equipment, and thus, these peaks do not carry information of the subsurface.
On the other hand, the noise sources might be emitting energy with different strength at different times. Because of this, the noise in some panels might happen to be magnitudes stronger than in others. In the summation process after crosscorrelation, such panels would give by far a dominant contribution, and this would effectively mean using a much lower number of summed correlated noise panels. To prevent this, as a third step in our processing, we apply per noise panel normalization to each of the traces by dividing over the trace's energy energy normalization.
The difference is that we use the root mean square of the energy of each trace to normalize the amplitudes in this trace. In this way, the relative amplitudes in each trace are kept the same, while among traces, the amplitudes are equalized. This is repeated for all noise panels. To compensate for this, Bensen et al. Then we use the spectrum of this time window to divide by the spectrum of the result from the fifth step.
Note that the processing we propose of energy normalization before correlation and wavelet deconvolution for the source function after correlation is akin to the utilization of the coherence function [see, e. This means that some parts of the Green's function might be retrieved only at positive times, while others only at negative times. For one horizontal layer in the subsurface, the relation between the traveltime t a reflected wave will take to propagate between a source and a receiver, the offset y between the source and the receiver, and the velocity c down to the layer is , where t 0 is the traveltime at zero offset.
The traveltime difference between two offsets is called moveout. For these measurements, the active vibrator sources were placed The active wavelet is obtained from a correlation of the raw recorded data with the vibrator sweep; the ANSI wavelet comes from a sum of correlations. By again taking a filter that rejects slightly higher velocities, we suppress most such arrivals. Because the FK filter becomes very short at low frequencies, it will create in both the active and passive data linear artifacts that would appear to propagate in both directions.
We therefore conclude that at short offsets, these retrieved events correspond to the apexes of the reflection hyperbolas in the active data. The first thing that is seen is that the data retrieved from ANSI contains many events that do not correspond to physical arrivals in the active data. We can see that in the proximity of the road, the lateral coherency of the apexes and the tails of the retrieved reflections disappears. This means that even though we did our best to suppress the remnants of the surface waves, they are still present and dominant at recording stations closer to the road.
This has the advantage that the wavefield components found in these panels are expected to contribute to retrieval of reflections. Another significant advantage of this approach is that it minimizes the absolute amount of interference from the attenuated but not fully removed aliased surface waves and other arrivals with higher wave numbers.
Knowing the illumination characteristics of the noise allows application of steps 6 and 7 to the individual correlated noise panels.
References
The deconvolution step 6 can be applied by assuming that each event noise panel contains arrivals from only one source of body waves. Deconvolving per noise panel could potentially increase the overall resolution of the retrieved results, as there would be no need to assume that the power spectra of the noise sources in the different noise panels are the same.
On the other hand, by applying the deconvolution for the autocorrelation of the source function after the summation over the correlated noise panels when all noise panels are used , we do not have to assume that we have only one source per noise panel. We know from the active data that the subsurface is close to horizontally layered.
In such a case, cross correlation of an incoming train of dipping plane waves would also result in a retrieved train of plane waves with the same dip in both causal and acausal times. For an apparent dip toward the bigger x values along the lines, we sum the opposite parts. For details of this technique, see Ruigrok et al. In the previous section, we showed that we have retrieved reflection arrivals from ANSI at several places along Line L4.
Obtaining a stacked section of the subsurface would also show whether reflections are retrieved at more places along the line. To extract velocity and structural information, we follow a standard processing scheme [ Claerbout , ; Yilmaz , ] and compare the results with information extracted from the active data.
In field measurements, the first seismic arrival to be detected at shorter offsets is the direct P wave arrival, while at longer offsets, refracted waves arrive first. This means that all events in the retrieved CMP gathers appearing earlier than these arrivals are not physical. The picking is performed by fitting hyperbolic curves through the retrieved CMP gathers [ Taner and Koehler , ].
The analysis is performed by plotting the ratio of the square of summed amplitudes of the time samples fitted by calculated hyperbolic curves and of the summed squared amplitudes of the same time samples. Both the nominator and the denominator are smoothed by performing extra summation over time in a short time window centered at the time sample for which the velocity stacks are computed.
In the resulting panel, we look for the maxima in the velocity range.
Although considera bIe efforts are now being made to find new sources of energy , alI the experts are agreed that hydrocarbons will have to provide the greater. Interval Velocities from Seismic Reflection Time Measurements. Authors: Peter Hubral; and Pages: Publisher: Society of Exploration Geophysicists.
The picking should be done at the apexes of reflection events and thus is done in combination with the corresponding CMP gather, which shows where the reflection apexes are. As we mentioned above, one is looking for the maxima in the velocity range in the resulting velocity plot.
EARTHQUAKE SEISMOLOGY I
It can be seen that the lines do not strictly follow the maxima. There are two reasons for this. Such events do not form parts of hyperbolic arrivals.
The traces in a flattened CMP gather are then stacked together, and the obtained stacked trace is assigned to the position of the midpoint of this gather. This is true only for uncorrelated noise. In our case, the stacking process may not be that efficient as the traces to be stacked are themselves the result of a correlation process and much of the noise that did not contribute to the retrieved reflections is not uncorrelated such as the remaining aliased surface waves.
During the stacking process, this would lead to a reduced number of stacked individual traces contributing to a reflection, but also to an increased noise level between the reflections. The green curves enclose the Earth's surface.
A Simple Guide to Seismic Depth Conversion I
As these imaged events are obtained from retrieved reflections and because they coincide very well in traveltime sense with imaged reflectors in the active data, we conclude that they are imaged reflectors. Using incorrect stacking velocities results in smearing of the reflections during the stacking process.
This might also have contributed to the obtained lower frequencies of the retrieved images. Such retrieved events containing higher frequencies can be observed only relatively close to the place where the road intersects the line, and even though they are also present in the part of the section with x values lower than the x value of the road, there they do not form laterally continuous features.
Subsurface Models. Preview Abstract Three factors influence the accuracy with which subsurface parameters can be obtained— measurement accuracy, aptness of the model , and completeness of the theory. In exploration seisinology, as in all other geophysical methods concerned with solving Seismic Wave Velocities. Preview Abstract This brief chapter is included prior to embarking on the central theme so as to remind us of the physical rock properties which ultimately govern all seismic wave propagation. Seismic wave velocity pertains to the speed of a seismic disturbance Ray Theory. Preview Abstract Suppose that the layers of the model in Figure are inhomogeneous and isotropic; then both P - and S -wave velocities are functions of space coordinates but are independent of the direction of wave propagation.
Anisotropic media, in which velocities Preview Abstract The ray-theoretical concepts as presented in chapter 4 are little tailored to the demands of recording techniques now standard in the seismic reflection method. All ray-theoretical considerations from this chapter on will be put in the context of the Preview Abstract So long as layer interfaces in the earth's subsurface have only moderate curvature, CDP reflections for primaries and symmetric multiples fall upon symmetric CDP reflection time curves that, for small offsets, are approximately hyperbolic. In contrast, Time Migration. Preview Abstract Exploration seismologists base their interpretation, skill, and judgment largely on the study of primary reflections for selected key horizons on time sections.
These horizons are normally available in either CDP-stacked i. Preview Abstract Traveltimes of CDP-stacked or time-migrated reflections tempt seismic interpreters to associate them directly with shapes of the reflecting horizons in depth. Such an association is certainly justified in areas of moderate geologic complexity.
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Computation of Interval Velocity.