In Volcanic Regions fluid flow paths are limited to the rubbley bases and flow tops of lava flows where permeability promotes transitivity.

Hypothesis:

The depths to first water will corresponds to depths located near lava flows.

Definitions:

Contact: location on the surface, or at depth where two different rock types touch.

Depth to first water: the depth from a particular well log where water was first noted, this is not always listed.

Depth to first lava: the depth at which the first lava is noted in a particular well log. There can be multiple contacts to a lava in a well log, which is why I specified first.

Figure 1: Block diagram of what well log depicts. The green and red planes represent contacts between the two rock types. Well (grey) and well logs record these contacts as depths from the surface (brown).

Question:

Does the depth to first water correspond to the depth to first lava in my data set?

Tool:

Cross Variogram and Kriging

Like the variogram, the cross variogram is a tool that allows you to compare spatial data at multiple scales. Unlike the variogram, the cross variogram compares one data set to another data set at multiple scales.

Kriging uses the variogram to interpolate a surface.

Brief Description:

In order to use both the variogram and the cross variogram you must normalize the data you are working with. Otherwise the semivariance values can range from 0 to infinity. Normalizing the data allows you to distinguish data that are correlated (semivariance<1) from data that have no correlation with eachother (semivariance>1).

In order to use the R function gstat, I had to turn the data into a spatial data frame.

The function gstat allows you to simultaneously create variograms for each of the induvidal data sets you are working with and compares them with each other. In this case I just compared the depth to first lava with the depth to first water.

I used Arc GIS kriging formula (ordinary) to krige a surface that represented the difference between between the depth to first lava and the depth to first water. In other words I subtracted the depth to first lava from the depth to first water and kriged that “surface”. I wanted to see if there was a spatial distribution around which those difference were low. I tried to use R to krige, but did not have the time to work out the krige function.

Results:

My results were strange, though ultimately unsurprising.

Figure 2: Variograms of my two variables water1 and lava1 as well as the cross variogram that comes from comparing the two. Note that the water1lava1 cross variogram has negative values for the semivariance.

Figure 3: Plot of well log data with the difference between first lava and first water plotted on top of its kriged surface.

The strangest thing to resolve from this exercise are the negative semivariance values for the cross variogram. Semivariance is a squared values and therefore should not have negative values. I have no idea what is happening here. I need to ruminate upon it. Either way, the data does not appear to be well correlates, or at the very least, I am not comfortable making conclusions about it with the negative semivariance values.

The ordinary Kriged surface interpolated from the difference between lava and water lets me know that the highest Kriged surface (Fig 3, white) between water and contact lies in the middle of the study area . In geographic and geologic space this corresponds to a basin filled with sediment and inter-fingered with lava. Many of the well logs in the region are not deep, they don’t have to be because the water here is near the surface, and close to some of these buried basalt flows. The data at the far edges of the map are spatial outlies, and thus we can’t look at any of the map that lies far from the main cluster of data points.

From physically looking at the well logs I know that while the well logs do often correspond to a lava flow, it is almost never the first lava flow. I am not surprised that the semivariance indicates that the data are not correlated.

Critique of the method:

what was useful, what was not?

It was not particularly useful, because it told me what I already know and left me with more questions than answers. However, I did walk away with some considerations. The cross variogram (and variogram) might work at a smaller scale.

In other words, if I broke my field area up in regions where I think the lava layers might source from the same place (Lassen Peak or Medicine Lake Volcano) I would be able to make the assumption that lava layers that are at similar depths in the well log correspond to the same lava flow in space. If we consider figure 1, in a small area we would be able to link the green layer to other locals where the green layers lies at depth, and would be able to spatially autocorrelate them with the variogram.

The next step, one I narrowed down my area, would be to correlate the depth to water with the depth to every lava flow I found in the well log. This would allow me to see which lava layer best corresponds to the depth to first water.

One of the things I discussed with my partner was trying to figure out what the negative values meant in my variogram. As I stated above, I still need to think about this, or figure out what I did wrong. I also discussed taking data out of lat-long space and into UTM space; that is something I am also still thinking about.

One final note: At the moment my data is both clustered around certain spots, and I do not have much of it. Every time I add a few data points, the shape of the variogram changes.  Some of the spikiness I am seeing is likely from that.