If we were to survey the universe of seismic sources in use today for production seismic data in the petroleum industry, it would reveal only a few serious contenders. Over the last 80 years or so, many seismic sources have been developed, tested, and tossed into the Darwinian struggle for market survival as a reliable commercial source. At present, there are three sources that account for the vast majority of data acquisition.
In marine seismic applications the airgun is ubiquitous. There are several dispersive effects related to airguns and airgun arrays, including ghosting and radiation patterns. Recall that we are using dispersion in a generalized sense meaning frequency-dependent phenomena, not just seismic velocity variation with frequency. The ghost is an interesting example of dispersion where the physical source interacts with the ocean surface to form a plus-minus dipole that is a strong function of frequency. For a given source depth, the radiated field can have one or several interference notches along certain angular directions away from the source. These show up in the measured seismic data as spectral nulls called a ghost notch. To further complicate the picture, ghosting occurs on both the source and receiver side of acquisition. The radiation pattern associated with an airgun array is an exercise in the theory of antenna design and analysis, again complicated by dipole characteristics due to ghosting.
For land seismic data, there are two major sources in use worldwide: explosives and vibroseis. The explosive source has, in principle, the weakest dependence on frequency. Certainly it has a bandwidth determined by shot characteristics and local geology, but is an approximately impulsive point source. A buried explosive shot will, like the marine airgun, develope a dipole nature due to ghosting. But this is often not as well-developed as in the marine case, likely due to lateral variations in near surface elastic properties and topography.
The other significant land source, vibroseis, has a host of dispersive effects. For a single vibe we can mention two fascinating phenomena, radiation pattern and harmonics. The theory of radiation for a circular disk on an isotropic elastic earth was developed by several investigators in the 1950's, most notably Miller and Pursey. They were able to show the power emmitted in various wave types (P, S, Rayleigh) ultimately depends only on the Poisson ratio. But even though the total power for a single vibe is not a function of frequency, in real world applications it is common to use a source array which will radiate seismic waves in a way that strongly depends on frequency.
A vibroseis unit injects a source signal (sweep) into the earth over the course of several seconds. The sweep is defined by time-frequency (T-F) characteristics and for simplicity we will consider a linear upsweep here (very common in practice). The emitted signal bounces around in the earth and is recorded by a surface sensor, the resulting time series being an uncorrelated seismic trace. Conceptually, when this uncorrelated time trace is transformed into the T-F plane by a suitable spectral decomposition method, we should see a representation of the sweep with a decaying tail of reflection energy. This is observed, but we also commonly see a series of other linear T-F features at frequencies higher than the sweep at any given time. These are vibroseis harmonics. Since the observed uncorrelated seismic trace is the summation of all frequencies in the T-F plane, these harmonics can interfere and distort the weak reflection events we are trying to measure.
The origin of harmonics can be understood in relation to human hearing. As first discussed by Helmoltz in the 1860's, when a sound wave interacts with the human hearing apparatus something very interesting happens. First we need to realize that away from any obstacle, a sound wave proceeds by vibratory motion of the air particles and this motion is symmetric (equal amplitude fore and aft). But when a sound wave encounters the ear it pushes against the eardrum which is a stretched elastic membrane with fluid behind. The amount of power in the sound wave is fixed, and that power will compress the eardrum (due to its elasticity) less than the sound wave will compress air. If we think of, say, a 200 Hz wave as a cosine, this interaction means the deflection will be asymmetric. It will be a waveform that repeats 200 times per second, but it will not be a symmetric cosine wave. How can something repeat 200 times per second and not be a pure 200 Hz wave? Helmoltz found the answer: it must a 200 Hz wave plus a series of harmonics (400 Hz, 800 Hz, etc.). The fact that the material properties of the ear impede the motion due to sound necessarily means that harmonics will be generated.
Now back to the vibroseis case, when the mechanical apparatus of the vibrator pushes down against the earth it is resisted by the elastic nature of the near surface. On the upstroke the motion is unimpeded, asymmetry develops, and harmonics are generated. All this happens despite some pretty amazing engineering in the system. With modern T-F methods, we can think up various ways to remove the harmonics by data processing the uncorrelated data traces. There is also ongoing discussion about how to use the harmonics rather than filter them out.
Next time.... Dispersion and processing
Tuesday, September 15, 2009
Tuesday, September 8, 2009
Seismic dispersion
All of seismology is based on waves and a primary property of any wave is the velocity (v) at which it travels. This is related to wavelength (L) and frequency (f) through v = f L. This shows that as the frequency changes, so does the wavelength in just such a way that their product is preserved as the constant velocity. But it is important to note that velocity itself is not a function of frequency, a situation termed nondispersive wave propagation. As the frequency is ramped up, the wavelength drops, and the waves always travel at the same speed. This is the case with waves in unbounded ideal gases, fluids, and elastic materials.
Porous media is another matter. Wave speed is a function of material properties (matrix and fluid) and environment variables (pressure, temperature, stress). Luckily for us, in the low frequency range (0-100 Hz) of surface seismic data, the velocity does not depend on frequency to within measurable tolerance. However, as frequency ramps up to sonic logging (10-20 KHZ) and bench top rock physics (MHZ) the wave speeds do become dispersive (classic paper is Liu et al., 1976).
This is the classical meaning of the word 'dispersion', velocity is a function of frequency. Here we will take a more general definition that includes any wavefield property, not just speed. Examples will include velocity, of course, but also attenuation, anisotropy, and reflection characteristics. We could also lump all of these things into the name 'frequency-dependance', but 'dispersion' is already out there with respect to velocity and it seems better to go with the shorter, more familiar term.
I am a bit embarrassed to admit that I made a strong point to a colleague (Jack Dvorkin, I believe) a few years ago about his use of 'dispersion' for something other than frequency-dependent velocity. I think he was talking about attenuation. Anyway, my tardy apologies because I have arrived at the same terminology.
It is curious that so much of classical seismology and wave theory is nondispersive: basic theory of P and S waves, Rayleigh waves in a half-space, geometric spreading, reflection and transmission coefficients, head waves, etc. Yet when we look at real data, strong dispersion abounds. The development of spectral decomposition has served to highlight this fact.
We will distinguish two kinds of dispersion. If the effect exists in unbounded media then we will consider it to be 'intrinsic' and thus a rock property that can be directly measured in the lab. On the other hand, if the dispersion only presents itself when layering is present then we will term it 'apparent', this case being responsible for the vast majority of dispersive wave behavior in the lower frequency band of 0-100 Hz.
To make some sense of the seismic dispersion universe, we will break down our survey into the traditional areas of acquisition, processing, and interpretation.
It is a fascinating and sometimes challenging topic. We will not seek out mathematical complexities for their own sake. Rather we will gather up interesting and concise results, presented in a common notation, and dwell more on the physical basis, detection and modeling tools, and especially the meaning of dispersive phenomena.
Reference:
Liu, H.-P., Anderson, D. L., and Kanamori, H., 1976, Velocity dispersion due to anelasticity; implications for seismology and mantle composition, Geophys. J. R. astr. Soc., 47, 41-58.
Porous media is another matter. Wave speed is a function of material properties (matrix and fluid) and environment variables (pressure, temperature, stress). Luckily for us, in the low frequency range (0-100 Hz) of surface seismic data, the velocity does not depend on frequency to within measurable tolerance. However, as frequency ramps up to sonic logging (10-20 KHZ) and bench top rock physics (MHZ) the wave speeds do become dispersive (classic paper is Liu et al., 1976).
This is the classical meaning of the word 'dispersion', velocity is a function of frequency. Here we will take a more general definition that includes any wavefield property, not just speed. Examples will include velocity, of course, but also attenuation, anisotropy, and reflection characteristics. We could also lump all of these things into the name 'frequency-dependance', but 'dispersion' is already out there with respect to velocity and it seems better to go with the shorter, more familiar term.
I am a bit embarrassed to admit that I made a strong point to a colleague (Jack Dvorkin, I believe) a few years ago about his use of 'dispersion' for something other than frequency-dependent velocity. I think he was talking about attenuation. Anyway, my tardy apologies because I have arrived at the same terminology.
It is curious that so much of classical seismology and wave theory is nondispersive: basic theory of P and S waves, Rayleigh waves in a half-space, geometric spreading, reflection and transmission coefficients, head waves, etc. Yet when we look at real data, strong dispersion abounds. The development of spectral decomposition has served to highlight this fact.
We will distinguish two kinds of dispersion. If the effect exists in unbounded media then we will consider it to be 'intrinsic' and thus a rock property that can be directly measured in the lab. On the other hand, if the dispersion only presents itself when layering is present then we will term it 'apparent', this case being responsible for the vast majority of dispersive wave behavior in the lower frequency band of 0-100 Hz.
To make some sense of the seismic dispersion universe, we will break down our survey into the traditional areas of acquisition, processing, and interpretation.
It is a fascinating and sometimes challenging topic. We will not seek out mathematical complexities for their own sake. Rather we will gather up interesting and concise results, presented in a common notation, and dwell more on the physical basis, detection and modeling tools, and especially the meaning of dispersive phenomena.
Reference:
Liu, H.-P., Anderson, D. L., and Kanamori, H., 1976, Velocity dispersion due to anelasticity; implications for seismology and mantle composition, Geophys. J. R. astr. Soc., 47, 41-58.
Monday, September 7, 2009
Comeback, DISC, and SMT depth conversion
After a hiatus of about 9 months, I am dusting off the Seismos blog. A few things have helped me come to this decision.
First, I set up a blog for my wife Dolores, former SEG assistant editor for The Leading Edge. If you are interested, here is the link: Proubasta Reader The experience of setting up and customizing her blog gave me some good ideas about how to maintain my own. Back in January 2009, I was just playing around with the blog and found it onerous to come up with daily or even weekly entries. Now I see the point is not to wait for big things to write about, but say a few words as things come up. Closer to a postcard than a book chapter.
Another push came from my being nominated for SEG Distinguished Instructor Short Course (DISC) for 2012. It still requires approval of the SEG/EAGE Executive Committees in about 6 weeks at the SEG convention here in Houston, which brings me to another push. For this approval meeting, I need to supply the DISC committee chairman, Tad Smith, with a 2 page summary of what I have in mind for my DISC. What better place for this to develop than on the blog, leading to a Seismos column in TLE (which will surely have to be published after the convention due to editorial backlog).
And finally, assuming I am approved the DISC instructor must write a book that is used as notes whenever the 1-day short course is given. So as I get the book in shape over the next few months I can track progress and interesting topics on the blog.
Enough for now about the comeback and DISC.
************************ SMT depth conversion note ******************
I'm teaching a graduate 3D seismic interpretation class this semester at U Houston (GEOL6390). The software used for this class is Seismic MicroTechnology's (SMT) Kingdom software (v.8.4). We have a generous and important 30-seat license donation that makes this popular class possible. This semester we have 26 students, limited by good hardware seats and optimum instructor-student interaction.
I am also principal investigator for a DOE-funded CO2 sequestration characterization project in the Dickman field of Ness County, Kansas.
In both cases, the issue of depth conversion comes up. For the class we have 3 assignments, the last of which is prospect generation in the Gulf of Mexico using data donated by Fairfield Industries (thank you very much John Smythe). There is one well in the project that allows for depth control. For the Dickman project we have 135+ wells and a 3D seismic volume, so a more ambitious integrated depth map is in order.
But just today I was testing various ways to track and depth convert the Mississippian horizon at Dickman. First I carefully did 2D picking in each direction, keeping an eye on the event as it passed through each well with a Miss formation top pick. Using a shared time-depth (TD) curve all the wells lined up nicely with the seismic event. Next came 3D infill picking that did a good job.
But how to convert the time structure horizon to depth? I created grids to infill a few small tracking holes due to noise and weak amplitude. It seemed logical to then depth convert the time-structure grid to depth using the shared TD curve. But strangely, this did not let me constrain to an existing polygon. Further, it required some additional gridding parameters, even though you would think it just needs to look up each already gridded time value and find the associated depth from the TD curve. I was also hoping for the ability to cross-plot the seismic gridded depth values at all wells that have a Miss formation top picked. From the cross-plot there is enough information to generate a v(x,y) velocity field, extending the v(z) time-depth curve, so that all known tops are matched exactly and some kind of interpolation happens between known points. No can do, as far as I can see.
Finally, it would be nice to be able to plot the TD curve as a simple time-depth crossplot, and do this with several TD curves to investigate lateral variability.
A different, perhaps better, approach is to depth convert the seismic data directly using the TD curve (TracePAK) and then re-track the Miss event through the depth volume. SMT does not allow the tracked time horizon to be extracted through the depth volume, again strange since the TD curve is known.
The jury is still out on this one. Perhaps you have a better idea....
First, I set up a blog for my wife Dolores, former SEG assistant editor for The Leading Edge. If you are interested, here is the link: Proubasta Reader The experience of setting up and customizing her blog gave me some good ideas about how to maintain my own. Back in January 2009, I was just playing around with the blog and found it onerous to come up with daily or even weekly entries. Now I see the point is not to wait for big things to write about, but say a few words as things come up. Closer to a postcard than a book chapter.
Another push came from my being nominated for SEG Distinguished Instructor Short Course (DISC) for 2012. It still requires approval of the SEG/EAGE Executive Committees in about 6 weeks at the SEG convention here in Houston, which brings me to another push. For this approval meeting, I need to supply the DISC committee chairman, Tad Smith, with a 2 page summary of what I have in mind for my DISC. What better place for this to develop than on the blog, leading to a Seismos column in TLE (which will surely have to be published after the convention due to editorial backlog).
And finally, assuming I am approved the DISC instructor must write a book that is used as notes whenever the 1-day short course is given. So as I get the book in shape over the next few months I can track progress and interesting topics on the blog.
Enough for now about the comeback and DISC.
************************ SMT depth conversion note ******************
I'm teaching a graduate 3D seismic interpretation class this semester at U Houston (GEOL6390). The software used for this class is Seismic MicroTechnology's (SMT) Kingdom software (v.8.4). We have a generous and important 30-seat license donation that makes this popular class possible. This semester we have 26 students, limited by good hardware seats and optimum instructor-student interaction.
I am also principal investigator for a DOE-funded CO2 sequestration characterization project in the Dickman field of Ness County, Kansas.
In both cases, the issue of depth conversion comes up. For the class we have 3 assignments, the last of which is prospect generation in the Gulf of Mexico using data donated by Fairfield Industries (thank you very much John Smythe). There is one well in the project that allows for depth control. For the Dickman project we have 135+ wells and a 3D seismic volume, so a more ambitious integrated depth map is in order.
But just today I was testing various ways to track and depth convert the Mississippian horizon at Dickman. First I carefully did 2D picking in each direction, keeping an eye on the event as it passed through each well with a Miss formation top pick. Using a shared time-depth (TD) curve all the wells lined up nicely with the seismic event. Next came 3D infill picking that did a good job.
But how to convert the time structure horizon to depth? I created grids to infill a few small tracking holes due to noise and weak amplitude. It seemed logical to then depth convert the time-structure grid to depth using the shared TD curve. But strangely, this did not let me constrain to an existing polygon. Further, it required some additional gridding parameters, even though you would think it just needs to look up each already gridded time value and find the associated depth from the TD curve. I was also hoping for the ability to cross-plot the seismic gridded depth values at all wells that have a Miss formation top picked. From the cross-plot there is enough information to generate a v(x,y) velocity field, extending the v(z) time-depth curve, so that all known tops are matched exactly and some kind of interpolation happens between known points. No can do, as far as I can see.
Finally, it would be nice to be able to plot the TD curve as a simple time-depth crossplot, and do this with several TD curves to investigate lateral variability.
A different, perhaps better, approach is to depth convert the seismic data directly using the TD curve (TracePAK) and then re-track the Miss event through the depth volume. SMT does not allow the tracked time horizon to be extracted through the depth volume, again strange since the TD curve is known.
The jury is still out on this one. Perhaps you have a better idea....