Using Spatial Statistics to Determine the Subsurface Spatial Distribution of Lava Flows in Northern California

Research Question

I am trying to determine potential fluid flow paths based on the spatial distribution of lava flows in the Medicine Lake, Lassen Peak Big Valley Mountain area of Northern California. The final goal of this project is a 3-D subsurface framework of the geology from which we can model fluid and heat flow.

Thus we want to know “How the spatial pattern of the depth of the lava flows attributes of wells is related to the spatial pattern of lava flow depth (B1), which in turn is related to pre-lava-flow topography (B2) and the regional geology (B3), because lava flows follow topography and subside post emplacement at rates that follow basin subsidence rates in the region, and form barriers for/conduits of groundwater (C1).”

Dataset

My data are a series of more than 1500 well logs. Each contain data that pertains to a map coordinate and with information about changes in lithology, or rock type, with respect to depth. Well logs are collected the year the well is made. I have well logs that range from the 1960s to the present. Temporal data is less important for the initial part of my study (Fig 1).

Figure 1: What is a Well Log? A well log is a record of the changes in rock type that occur with changes in depth and a location at the surface of the earth.

I also have data from geologic maps. Geologic maps provide the spatial extent of the surface exposure of a geologic unit, which includes information about its contacts with other rock units in x,y space as well as information about the elevation (Fig 2).

Figure 2: My study area in Northern California, it lies between the Big Valley Mountain, Medicine Lake Volcano and Lassen Peak with the Pit River draining the middle of it. The green dots represent the center of the township and range section that the wells are located in, and the size of the circle indicates the number of wells in that section.

Hypothesis

 

Figure 3: Cross section of a Basalt Column (Lyle 2000). In Volcanic systems, fluid flow is limited to the Vesicular flow tops, the rubbly bases (P.P.C in this diagram) and sedimentary interbeds that lie between vertically stacked flows. These sections of the rock are the only locations with high enough permeability and porosity to allow the movement of water.

This means that if we know where the lava beds lie, and we know their contacts, then we can outline potential zone of flow. Determining the patterns of how lavas flow and emplacement then allows us to determine the lava flow’s spatial extent, and therefore potential flow paths. I expect lavas to follow the laws of physics. They travel as viscous fluids and fill basins, and so I would expect them to be thickest where paleotopography was lowest, they will likely thin out at the edges, and they will be down slope from the volcano or vent that erupted them. Given the regional geology, I would expect the thickest lava flows to lie in the Pit River basin, near the range bounding Big Valley Mountain Fault (Fig 3).

At its simplest, we expect lava flows to follow the geologic principals of original horizontality and of cross cutting relationships.

Approaches

I would like to learn both how to apply variograms and kriging and how they work; plus any new techniques that I am not yet aware of. We can also make the assumption that all our residuals with follow the rules of stationarity. This means that any irregularities in the data represent unacknowledged geologic features.

Expected outcome

My first goal is to create a 3-D subsurface map of the connectivity and contacts of lava flows in the Medicine Lake, Lassen Peak Big Valley Mountain region.  Ideally I would begin the process with Geog 566. I would like to have a few surface I can test in the field by the end of this term, but understanding different methods with which I can make this framework is my first goal.

Relevance

Understanding the distribution of lava flows in the region ties into the regional geology of my study area. As I stated in Question 3, lavas fill basins. Basin morphology, and the amount of space lavas can fill depends on the slip rates and distribution on faults in the Medicine Lake, Lassen Peak Big Valley mountain triangle. By constraining slip rates in the basin, we both build a better picture of the regional geology, and we can make more rigorous checks on the validity of our statistical outputs.

 

Another equally important point is the next step in the project. After we make the 3-D framework, the USGS will use it to model fluid and heat flow in the region. Comprehending potential changes in groundwater flow in the region will allow city manages in the region to better manage water in the future.

 

Preparation

 

Arc-Info Not much, ArcMap, yes
Modelbuilder and/or GIS programming in Python Working knowledge of python outside of GIS programming
R None
Image Processing Working Knowledge
Relevant Software Matlab

 

Sources

Lyle, P. “The Eruption Environment of Multi-Tiered Columnar Basalt Lava Flows.” Journal Of The Geological Society, vol. 157, 2000, pp. 715–722.

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One thought on “Using Spatial Statistics to Determine the Subsurface Spatial Distribution of Lava Flows in Northern California

  1. jonesju

    Marina, this is a nice start. Needs more work on the following: 2) data. Issues with geologic maps – may not be at appropriate scales for the processes you are interested in. Check what the map units are and work on improving your hypothesis to specify particular mechanisms that you can detect from information about the lava flows depicted on the maps. 3) Hypothesis. Hypothesis does not explain anything about well logs. Try rephrasing as “The spatial pattern of XX attributes (depth of certain layers? numbers of different rock types? chemistry of rocks?) of wells is related to the spatial pattern of lava flow depth (B1), which in turn is related to pre-lava-flow topography (B2), because lava flows follow topography, and form barriers for/conduits of groundwater (mechanism C)..” 4) Analyses. For exercise 1, try creating semivariograms of well log data (which properties? Need to make more specific hypothesis). You could also try kriging if the variograms fit spherical models. For Ex. 2, try cross-variograms to see how well data are related to lava flow depth.

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