# Predicting rock type from seismic processing

In reflection seismology, we create a source with an airgun and then use receivers to register acoustic waves (an approximation) at the surface. From these measurements, we can predict a velocity field $$c=c(x)$$. This can be seen in the figure below taken from a research group Karlsruhe Institute of Technology at this link.

The 2D model pictured here shows (the red, yellow, and black colorbar) shows a model of P-wave velocity. This picture shows you the geometry of material interfaces of the subsurface. However, it does not directly tell you anything directly about rock composition. Table 5.4a at this link suggests that it would be hard to tell the difference between limestone and sandstone at 30% porosity. This would make predicting a P-wave velocity field possibly less useful than a direct map of the rock type.

Motivated by the discussion above, my questions are below.

(1) Is rock type not that important and geometry all that matters for the purpose of exploration geophysics? For reservoir modeling, is knowing the rock type important?

(2) If I get a core out of just one spot and map rock type with depth, can I then infer rock type over the whole field? For example, in this image, if I saw the black part correlates with, say, limestone, can I just blindly say "okay everywhere else in this image where I see black is probably limestone" (of course, this may lead to errors but seems a reasonable approach to me)?

(3) If I am able to extract a porosity, permeability field, an S-wave velocity field, and possibly many other fields, can I infer the rock type or at least, decrease my uncertainty in predicting rock type?

(4) In light of (1)-(3), I imagine that on large projects, geophysicists give their images to people more experienced with stratigraphy and the like. What kinds of questions can geophysicists answered with reasonable confidence? What kinds of questions can stratigraphers answer with/without given images from a geophysicist?

NOTE: I identify as an applied mathematician, so feel free to over-explain any geology.

• Fellow applied mathematician, but I've spent a lot of time working in this general area. Reflection seismic surveys are very useful for mapping geologic structure, but not so good at getting parameters like porosity and permeability. The correlation of sesmic data with data from well logs and outcrop studies is critical. May 8, 2022 at 16:06
– Fred
May 8, 2022 at 17:59
• I'm not a seismologist. Something to consider. Hit a piece of steel with a hammer & what type of sound does it make? Use the same hammer & hit a piece of aluminium with the same amount of force & what type of sound does it make? Both pieces of metal will ring with a difference frequency. In seismology is there a difference in response if basalt or granite is pinged by a seismic wave compared to sandstone, shale or limestone? Also, how is the response between basalt & granite different, or sandstone & limestone? Now, go back to the piece of steel & drill it full of holes & then hit it ...
– Fred
May 8, 2022 at 18:11
• ... like it was hit before. Is there a difference in its response?
– Fred
May 8, 2022 at 18:12

This is a ginormous question; a complete answer is probably worth an MSc in exploration geophysics. But I can try to give some pointers for places to find out more.

Preface: in general, considering applied geoscience in the service of natural resource mapping and prediction (petroleum, water, geothermal, etc), we're interested in some specific rock properties. These might be, in very broad strokes and approximate order of usefulness:

• Porosity and permeability.
• Geochemistry (fluid composition, water salinity).
• Other petrophysics (temperature, pressure).
• Lots of other things like lithology (rock type), stratigraphy (rock geometry), geomechanics (stress, fractures, etc).

We're usually only interested in "first-order" (from a seismic point of view) acoustic/elastic properties like P-wave velocity ($$V_\mathrm{P}$$), S-wave velocity ($$V_\mathrm{S}$$) and density ($$\rho$$) insofar as we can use that information to process seismic data or infer porosity, lithology, etc.

The problem is that I am not allowed to measure anything I care about directly. Everything is filtered through the earth (seismic waves) and/or various instruments, and everything is prone to error, bias and uncertainty. Basically, you're looking at just about the hardest inverse problem you can imagine.

Oh right.

1. Rock type is important, because if I know the rock type I can make a lot of pretty good guesses about a lot of things I'm interested in. I know what kinds of porosities sandstones have, and what kind of mineralogy. I know about the A formation and the B formation, so I can correlate them over large distances. I know how old those rocks are and where the sea was at that time, so I know where hydrocarbons might migrate from. You get the idea. (I know that sounds pretty abstract, but eventually this information gets us closer to the list of properties I gave you earlier.)

2. No, velocity and lithology are not correlated like that. If only! Now, in seismic processing, we don't care too much about lithology, because the P and S velocity and the density are all we need to reconstruct the wavefield. But small things — increase porosity, change the pressure, add a tiny amount of natural gas ('fizz gas') — have a large effect on velocity and density. To make things worse, fluids don't sustain S-waves. To make things even worse, wave modes convert between each other at elastic boundaries ('mode conversion'). Then there's dispersion. And attenuation. It's a nightmare, basically. Seismic imaging is a miracle.

By the way, we don't just collect core from boreholes. We also measure a lot of things like velocity, density, and so on. Some of these things are even almost super-useful things like porosity and lithology. This sounds really useful, and it is, but remember that all of those measurements are broken in various ways (the borehole walls are rugged, the rock is invaded by drilling mud, and so on.).

3. You definitely can. In general this is called 'seismic inversion' and it's a billion-dollar industry working on decades of research and development. In many ways, along with 'fluid composition', it's the holy grail of seismic analysis. Note that the only fields you can really extract from seismic are $$V_\mathrm{P}$$, $$V_\mathrm{S}$$ and $$\rho$$ — everything else is a second-order property you'll have to predict.

4. Indeed, seismic interpretation is a multidisciplinary activity. Geologists are good at interpreting the geometric properties, such as stratigraphy and fault networks. Geophysicists understand the artifacts better (seismic is a bandlimited wavefield recorded in a natural environment, so there's interference, resonance, diffraction, coloured and coherent noise, echoes (so-called multiples), and so on. Like I said, it's a nightmare.)

### Last thing: offset

From the point of view of inversion, there's something missing from the diagram in your post: 'offset'. As the ship moves, each point in the earth will be imaged in turn by those green receivers, each of which is a difference distance from the source (red). So we don't just get one trace at each location, we get a whole collection of them, all recorded at different reflection angles. Luckily, the nature of the reflected energy changes with offset, eventually going critical at long offsets. At short offsets (small angles), we only get information about $$V_\mathrm{P}$$ and $$\rho$$; the elastic information is contained in the far offsets (large angle of reflection).