June 2007

Virtual sources can yield real results

A virtual source can be any seismic sensor that, through some simple mathematics, is then moved around in new ways to get interesting results.

Vol. 228 No. 6  


Virtual sources can yield real results

 What is a virtual source? It’s any seismic sensor that, through some simple mathematics, can then be “moved around” in new ways to get interesting results. 

Rodney Calvert, Shell, Houston

The Virtual Source (VS) idea is to reconsider receivers of wave energy as virtual sources with a known and controllable output waveform and radiation pattern for a wide range of conditions. This idea allows us to improve what we can do with physical sources and leads to many new possibilities, some described below, and many more to explore.

Acoustic waves going through a receiver are measured and recorded in various ways. These measured signals may be filtered to a desired waveform and selectively weighted and summed. This allows us to mathematically build a virtual source with the known desired waveform radiating from our illuminated receiver, Fig. 1.

Fig. 1

Fig. 1. The virtual source method focuses surface energy to a point, as a pulse with a desired waveform at time zero. 

Properly designed downhole geophone configurations allow wave energy to pass through the virtual source receiver to the target and scatter back wave energy to this and other receivers. With this in mind, we can mathematically create a source that is as unobtrusive and cheap as a geophone, yet as powerful as any physical source we can use, and with the unique property of having a known and controllable wave-field in the medium.

To image targets with virtual sources only requires determination of the velocity model between the geophones and target. We do not need to know the velocity or other properties of the earth or medium between the physical energy sources and our virtual source geophone; similarly we do not need to worry about scattering and reverberation or attenuation. Nor do we need to know the physical source waveform, its timing or coupling; we measure the composite result of all these effects at our virtual source receiver.

This approach enables us to recast and solve many imaging problems by surveying targets between suitably placed receivers. This has obvious applications in seismic problem areas, where we can place geophones under troublesome overburden and make high-fidelity measurements below them, without having to model or consider the overburden complexity. We will see that the more scattering the overburden, the easier it is to make good wide-aperture virtual sources, conditions that would ruin conventional imaging from surface.

The algorithm is general. We may use it for making P-wave virtual sources. We may also make shear and elastic virtual sources of given polarizations radiating in particular directions.


This is surprisingly easy, as illustrated in Fig. 2. In many cases, we shoot conventionally as for a 3D VSP. We effectively deconvolve the downward traveling energy arriving at a designated VS geophone to a desired pulse as follows.

Fig. 2

Fig. 2. The down-going part of a VSP recorded at a virtual source geophone is time reversed and convolved (correlated) with itself, and amplitude deconvolved and shaped for each shot, yielding a desired pulse waveform. The combined filters to do this for each shot are then applied to the records of other geophones and summed, yielding the virtual source geophone, firing with the chosen pulse, into the other geophones. 

Consider the acquisition geometry illustrated in the left panel of Fig. 2. It shows a series of real surface shots, Si, detected by a single downhole geophone, Rj. Each shot into the geophone is measured and results in a series of seismic traces, Tij, as seen in the second panel. The down-going signal for each trace, in this case selected by windowing, is then time reversed as shown in the left-middle panel. If we then convolve each Tij trace with its time-reversed counterpart, we obtain the next panel. This has filtered our Tij so that shots Si all appear to arrive at the geophone at zero time with different but symmetrical wavelets.

We now apply an amplitude deconvolution to equalize these wavelets as suggested at the right panel of Fig. 2. This is no more than a spectral balancing filter to create a desired wavelet within the available bandwidth. We now have our virtual source radiating a consistent known wavelet in its illuminating directions. Directional control of the radiation pattern may be applied by weighting. These same correlations, filters and weights are applied shot-by-shot to the upcoming signals Tik received at the other receivers Rk and the results summed. The signal Tjk received at Rk from the virtual source Rj may be estimated as

Equation 1 
where Fij is the spectral balancing filter for shot Si into virtual source Rj, and denotes correlation, or time reversal and convolution, and * denotes convolution.

This may be formally shown to be equivalent to time reversing the reciprocal experiment of a desired upward radiating source at the VS location, illuminating receivers at the physical source locations. If we repeat this for each geophone, in turn, as a virtual source, then we have re-datummed the survey from shots at surface to a survey with known downward radiating sources at each geophone location. However, instead of the conventional processing approach of having to estimate the re-datuming operator, approximated as Kirchhoff operator time shifts, we have created an operator from downhole measurements that takes out all the complexities of the illumination from above.

Of course, we cannot perform magic. We can only produce a virtual source within the physical illumination bandwidth and the physical illumination aperture. However, we can do a perfect phase deconvolution and use the higher frequency coda arrivals from multi-path illumination that are not available with surface imaging, which is subject to scattering attenuation. This adds to the VSP bandwidth advantages available on the receiver side to the source leg, giving better bandwidth than is available from surface or conventional VSP approaches. These advantages will be greatest for scattering overburden.

Another strength is that the concept is simple and does not require a genius to apply it. The geometries may be designed using simple ray-tracing ideas, and the processing and software steps required to generate virtual sources are available in all signal-processing packages and could almost be hardwired and applied in the field. We can expect easy, wide proper use and benefits.


The virtual source idea has ancestors and relations. A 1D version, using natural noise as source energy and auto-correlation of surface records, was developed by Shell’s Charles Weller of the then Bellaire Research Center in the 1960s and published with results by Weller and Padhi in 1970. Jon Claerbout published similar work under name of Daylight Imaging in 1968 and 1976, and academia has been an intermittent participant since then.

Jerry Schuster and others are working on various cross-correlation methods under the name of interferometry. Shell has joint research with Roel Snieder of the Colorado School of Mines. There is a strong community lead by Matthias Fink doing exciting things with time-reversed acoustics, in which the recorded waves may be physically time reversed and sent back into a medium to be focused, for example, to break up gall stones in a patient’s body.

The virtual source idea is very general and potentially useful for many applications, probably wherever there is wave energy. The ability to use two or more detectors (subject to wave illumination) to determine the impulse response from one to the other has as many applications as we can imagine. Expect some of these applications to spawn a whole new industry of integrity monitoring.

This technique is being used commercially; interest is building and results are encouraging. Shell has used it for tar sand extraction monitoring, for looking below salt and for ocean-bottom seismic. Some applications are now patented.

In the deep subsurface. The principle application of the Virtual Source technique is in using buried geophones to better image the subsurface.1 These applications greatly enhance the ability to image beneath a complex overburden, and to do this repeatably even when the overburden changes. This gives us unprecedented sensitivity in monitoring subsurface changes due to production or injection. The generality of the virtual source idea of making receivers into ideal sources offers many more applications than these. If we can place geophones suitably under salt, basalt, karsts or other problematic overburden, we can image through heterogeneous and scattering overburden.

There are particular advantages for repeatable 4D monitoring. With permanent receivers downhole, or as OBC on the seabed, we have the ability to make repeat surveys with exactly the same geometry, with the same virtual source waveform, even if the near surface, physical sources and coupling change. These are the ideal conditions for high-repeatability yielding measures of real 4D differences in the subsuface.1

With fixed, buried geophones, the repeat surveys may be performed quickly and cheaply. This makes the method attractive for frequent monitoring and real-time control for oil recovery optimization. Some suitable basic geometries for 3D coverage are shown in Fig. 3. This significant capability may share downhole arrays with micro-seismic monitoring.

Fig. 3

Fig. 3. Geophone layouts for virtual source 3D coverage. 

If we place our receivers in our reservoir and it is a low-velocity wave-guide, then we may still make useful virtual sources using natural noise from production, noise from tube waves or long-offset surface sources. These will enable well-to-well tomography as shown in Fig. 4.

Fig. 4

Fig. 4. Reservoir-level receivers may still make useful virtual sources, enabling well-to-well tomography using natural noise from production, noise from tube waves or long offset surface sources. 

We may also try to simulate well-to-well tomography in the vertical plane. This may be useful to get higher resolution images from wells piercing some seismic barrier such as salt, multiple ridden or scattering overburden, as shown in Fig. 5. Another application would be imaging and monitoring steeply dipping reservoirs from vertical wells, as illustrated in Fig. 6.

Fig. 5

Fig. 5. Well-to-well virtual sources with physical sources located on surface with receivers downhole in two or more wells. 


Fig. 6

Fig. 6. Steep dips may be imaged from vertical wells. 

What is the catch? This may all sound too good to be true and beg the question, “Why are we not heavily using the idea?” The answer is because our industry has not yet widely adopted the practice of instrumenting observation wells above targets for imaging. The extent of the required geophone arrays also becomes an issue considering that they should cover both the required source and receiver imaging-aperture aprons extending outside the target area.

Nevertheless, the economic case for action on valuable assets seems very appealing. A modest Middle East oilfield with, say, 100 m of oil column has a potential 100% recovery worth $4.8 billion per km2 at $50/bbl. These fields are difficult to image, and conventional seismic data is not considered good enough for 4D monitoring. If enhanced virtual-source monitoring could increase recovery 1%, we could spend $48 million per km2 and still break even. Observation wells for virtual source coverage would be much less than this and, with high-resolution, highly repeatable monitoring and tracking water floods, we could expect much better than a 1% recovery gain.

It is quite possible that onshore sub-horizontal observation wells could be drilled for as little as $100k per km and instrumented for the same or less. Some possible geometries for suitable 3D coverage are shown in Fig. 3.

There is more work to be done before we have a general capability that can take advantage of “free” passive noise sources.

Non-invasive shallow surface seismic. Near-surface imaging usually requires dense sampling of sources and receivers, and it can be both expensive and invasive. By making our receivers virtual sources, we may be able to use dense receivers and sparser shots. The virtual sources would be illuminated by upcoming energy that would normally give rise to surface multiples. Thus, for sensitive areas such as nature reserves, breeding grounds, glass houses, stately homes and other places where seismic sources would not be welcome, we may replace source locations with virtual source geophones, provided we can suitably illuminate them.

This may be useful for work where dense source access for shallow 3D imaging would not be permitted or affordable. In our industry, monitoring shallow reservoirs such as coalbed methane, or tar sands, shallow heavy oil or monitoring surface contamination remediation might be made attractively affordable. This could also create benefits of 3D seismic imaging for activities such as mining exploration, mine monitoring and archeology.

Non-oily uses. As water becomes a more precious resource, we could expect simple receiver arrays could be used to image and monitor water table changes and help water management. This could be an essentially passive monitoring illuminated by noise from local traffic.

The VS idea has potential applications for measuring and monitoring the structural integrity of various structures subject to vibration, impact, storms or other trauma - such as buildings in earthquake and storm zones, dams, bridges, offshore platforms, ships, aircraft airframes and wings, railway lines, yacht rigging, etc. We can monitor any structure subject to elastic waves and determine a diagnostic impulse response between receivers. This has been nicely illustrated by Prof. Roel Snieder of the Colorado School of Mines with whom we have productive collaboration.2

Non-contact seismic. An interesting example of this has been demonstrated by Kasper van Wijk at the Physical Acoustics Laboratory (PAL) at the Colorado School of Mines.3 He has produced surface virtual source seismograms accurately reproducing direct physical responses measured in a slab of granite just over one inch thick. The comparison of the PAL virtual source result and a conventional measurement is shown in Fig. 7. This demonstrates that the method will work with surface virtual sources powered by energy coming to surface, and that the method is applicable over a wide range of scales.

Fig. 7

Fig. 7. Surface virtual source and physical source surface shot compared. 

The PAL measurement has added interest in that the seismic detection was performed by laser Doppler interferometry. The setup is diagrammed in Fig. 8. The laser light scattered by the surface has its frequency changed by the moving surface subject to seismic waves. With the fast control and stability of lasers now available, van Wijk can measure many receiver locations in real time up to frequencies in the kHz range. He used the heat shock wave from the pulse of a power laser as a seismic source. The PAL thus has the capability to perform rapid 3D surveys over locations or objects without even touching them. This is being investigated as a good way for shallow mine detection. It remains to be seen whether the virtual source approach will add to the efficiency of their methods. It may be that there are locations that should not be zapped by energetic laser pulses.

Fig. 8

Fig. 8. Experimental set-up used to measure data for Fig. 7. 

Interestingly, Shell used to have the controlling patent on laser Doppler seismic detection. However, development was stifled by rapid growth in 3D seismic systems and their high channel counts. The laser Doppler approach still looks attractive for Arctic and desert terrain with sparse vegetation, particularly for shallow targets, even detecting anomalies as shallow as land mines.


The virtual source idea need not be restricted to seismic waves. The method could be used for electro-magnetic and other waves, such as surface waves or sound waves in air.

The sound we hear over public address systems in many places is very distorted. With the virtual source algorithm we could measure the filter response between the transmitting speaker and a reception point. This filter response could be inverted so that we could hear messages more clearly. This has general application for improving signal or data transmission through complex media.


Before long, we can expect to hear of many interesting developments using impulse response or Green’s function estimates using the virtual source idea. Some of these should be quite important and valuable. Others may not be needed and will only be advanced by marketing. WO  



1 Bakulin, A. and R. Calvert, “Virtual source: A new method for imaging and 4D below complex overburden,” Expanded abstracts of the 2004 SEG Annual Conference pp. 2477-2480.
2 Snieder, R. and E. Safak, “Extracting the building response using seismic interferometry: Theory and application to the Millikan library in Pasadena, California,” Bull. Seismol. Soc. Am., 96:586-589, 2006.
3 Wijk, K. van, “On estimating the impulse response between receivers in an ultrasonic experiment,” Geophysics, 71(4), SI79-SI84, 2006.


Bakulin, A., Mateeva, A., Calvert, R., P. Jorgensen and J. Lopez. “Virtual shear source makes shear waves with air guns.” Geophysics, Vol. 72, No 2, A7-A11;2007.
Calvert, R. W., Bakulin, A. and T. C. Jones. “Virtual Sources, a new way to overburden problems,” Expanded abstracts of the 2004 EAGE Annual Conference.



Rodney Calvert started his first time-lapse work measuring continental drift in Iceland as part of a PhD, earned during 1966-‘69. He joined Shell in The Hague as a seismic processor, and then became a processing manager for Shell Malaysia. He was heavily involved with Shell’s early 3D efforts in the North Sea. He held several research and management positions in geophysics and integrated reservoir characterisation before returning to 4D. In 2005 he was sponsored by the SEG to conduct a 26-stop world lecturing tour as part of their Distinguished Instructor Series. Rodney is based in Houston and serves as chief scientist geophysics.


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