3-D Geological Mapping of Rocks Potentially Suitable for Capturing Carbon Dioxide from the Atmosphere

Introduction

During most of the past 800,000 years, global atmospheric CO2 concentration value was fluctuating between about 200 and 300 ppm. However, at the beginning of the Anthropocene in about 1850, it began its increasingly rapid increase to approximately 422 ppm. This increase is the main reason that global surface temperature became enlarged by about 1.2 oC. It is well-known that CO2 in air and mean global temperature are linked because the Earth’s heat radiation is intercepted by “greenhouse gases”, primarily CO2 (but also methane and nitrous oxide). As documented in the latest (2022) Assessment Report of the International Panel on Climate Change, the average global temperature increase has resulted in many adverse climate conditions. Weather is the short-term manifestation of climate. Multifractal theory offers new insights into the relationship between weather and climate [1]. Currently, various efforts are being made to reduce further annual increases in the mean ambient air CO2 concentration value. A one-page summary of some material covered in this paper has been published as a Viewpoint [2].

Global atmospheric CO2 concentration value has fluctuated significantly during the Phanerozoic that commenced 539 million years ago. It was relatively low (< 500 ppm) during the Earth’s two periods of widespread continental glaciation and relatively high (>1000 ppm) during warmer periods. Esmeray-Senlet [3] has identified three major Phanerozoic climate-related mass extinctions: Late Ordovician (445 Ma), Late Devonian (372 Ma) and end-Triassic (201 Ma) (ages from [4]; also see [5]). These three events were accompanied by significant atmospheric CO$_2$ increases. According to Royer [6], global atmospheric CO$_2$ concentration value reached about 3000 ppm at the Triassic-Jurassic boundary. Recently, Song [7] has published a seawater temperature variation curve for the Phanerozoic accompanied by a post-Silurian CO$_2$ variation curve. Rapid CO$_2$ emissions resulting from basaltic volcanism may have been the cause of other worldwide Phanerozoic discontinuities as well. Such events can reoccur in future. Atmospheric oxygenation history analysis may be a new technique to help predict sudden CO$_2$ emissions of this type (cf. [8]).

With CO$_2$ concentration values more than a hundred times greater at the Triassic-Jurassic and Silurian-Devonian boundary ages, global surface temperatures probably also greatly exceeded its currently low Anthropocene value of about 14$^\circ$ Celsius. In the geologic past, higher temperatures on Earth were primarily reduced by absorption of CO$_2$ from the air by vegetation. The rapid Anthropocene CO$_2$ increase of about 120 ppm is unusual because it has taken place over such a short period of geologic time.

Large-scale ambient air CO$_2$ concentration reduction technologies would involve expensive major changes in the management of natural resources in the upper parts of the Earth’s crust. Nevertheless, there already exist several ways in which the current average global atmospheric CO$_2$ concentration value of 422 ppm could be reduced. An example is Lackner’s [9] method to capture CO$_2$ from ambient air. The CO$_2$ collection rate described by this author significantly exceeds those of trees and other photosynthesizing organisms that in the geologic past were primarily responsible for decreasing the air’s CO$_2$ content. Another promising technique is to capture CO$_2$ in water and injecting it under high pressure into basaltic rocks. At the Hellisheidi Carbix site in Iceland this process results in the formation of stable, CO$_2$-free, carbonate minerals (mainly calcite) in less than 2 years [10]. The calcite is dissolved in water to form bicarbonate ions (HCO$_3^-$) that subsequently are incorporated into carbonate minerals for shells and skeletons in the ocean (Encyclopedia Britannica, 2020).

Other methods to reduce atmospheric CO$_2$ by capturing it in the form of carbonates (primarily dolomite) are also becoming increasingly effective. Chemical engineers are actively working to improve existing methods for this purpose, especially by carbonization of rocks rich in olivine or in serpentine derived from olivine. Geoscientists can help by 3-dimensional mapping of the upper part of the Earth’s crust, outlining the shapes and compositions of rock units suitable for the capture and retainment of ambient CO$_2$. Potential widespread usage of peridotites and serpentinites for this purpose will be discussed later in this paper. First, new theory on the relationship between weather and climate will be discussed in some detail.

Weather and Climate

Weather is a short-term random manifestation of long-term climate. During the past 10 years significant progress has been made in understanding the relationship between weather and climate. Lovejoy and Schertzer [1] use the following approach. In their 3-parameter $\alpha$-model, $\alpha$ represents the Lévy index that, together with the “codimension” $C_1$ and the “deviation from conservation” $H$, characterizes a universal multifractal field $\rho_\lambda$ that can be a flux or density characterized by its probability distribution

$$P(\rho_\lambda \lambda^\gamma \propto \lambda^{-C_1(\gamma)}) \text{ with statistical moments } E(\rho_\lambda^q) \propto \lambda^{K(\gamma)};$$

$\lambda = L/\epsilon$ is the so-called scale ratio with $L$ representing the largest scale that can be set equal to 1 without loss of generality as shown by Cheng and Agterberg [11]. The relations between $K(q)$, $C_1(\gamma)$ and the field order $\gamma$ are:

$$K(q) = \max_{\gamma} \{q \gamma - C_1(\gamma)\}; \quad C_1(\gamma) = \max_{\gamma} \{q \gamma - K(q)\}$$

Detailed explanations of these concepts are provided elsewhere [1]. Time series for temperature and other variables associated with weather and climate have characteristic features involving chaotic events. The approach taken here is an example of non-linear modeling of extreme events in the geosciences as defined by Cheng [12, 13]; also see Agterberg [14], and advocated in geophysics by Lovejoy et al. [15].

Weather, which typically has a duration of about one week only and is clearly full of chaotic events, is followed by a relatively long period with relatively few chaotic events that can last as long as 50 years depending on geographic location. After this quiet period called “macroweather” by Lovejoy and Schertzer [1], the “climate” sees a renewal of the occurrence of reactively many chaotic events. Weather and climate have positive values of $H$, whereas $H$ is negative for the interval between weather and climate. The parameter $H$ is named after Hurst [16], an early climatologist who discovered that average number of consecutive years $m(t)$ of plentiful water in the river Nile reaching Egypt is not constant as had been assumed previously but proportional to $t^{n}$, where $t$ is time and $H > 1$ instead of $H = 1$. Before $H$ was termed the multifractal “deviation from conservation” by Lovejoy and Schertzer and can become negative, it was called “fractal dimension” with the property $H > 0$ by Mandelbrot [17].

As mentioned before, Lovejoy and Schertzer [1] have shown that what is commonly called “climate” covers two separate time-domains. The first of these two domains is much less chaotic than both the short-term weather and the long-term climate. One of their examples is a Greenland dataset of 17,551 points of GRIP (summit) ice-core $\delta^{18}$(O) (a temperature proxy) location data spanning the period from the present to 91,000 years ago. These authors prefer to use the power spectrum for statistical analysis with Log10 E(ω) plotted against Log10 ω in the frequency domain where E denotes mathematical expectation and ω is a measure of frequency, A major advantage of this approach is that regimes of events that take place at the same time occupy separate, consecutive domains along the frequency axis. The resulting log-log spectrum for the GRIP example as shown in Lovejoy and Schertzer [1] Fig. 1.9c consists of approximately three consecutive straight-line segments with slopes βw ≈ 2, βmw ≈ 0.2, and βc ≈ 1.4, where the subscripts w, mw and c denote weather, macroweather and climate, respectively. The Log10 ω values separating these domains are 1.5 and slightly less than 2. It is noted that the macroweather slope (βmw ≈ 0.2) in the power spectrum for the GRIP example is close to zero. A horizontal macroweather line would correspond to a signal-plus-noise model [18] for variations of the original measurements along the ice core. The signal would then be according to a smooth, continuous curve without the possibility of discontinuous, chaotic interruptions as can occur when β > 0.

Each slope parameter satisfies the equation β=1+2H-K(2) that is mainly determined by the value of H, which is positive during weather and climate but negative during the macroweather period. For a simple explanation of positive versus negative value of H (see Fig. 2.10 in [17]). Macroweather value of H depends strongly on geographic location. It is close to zero in the tropics and close to -0.5 in the Arctic, where macroweather variability would be according to a signal-plus-noise model without the possibility of catastrophic events (cf., Fig. 5.5) [19]. Statistical methods to estimate H include the one developed by Ramanathan [20] for rainfall scenarios in parts of France. Clearly, the preceding 3-stage approach to weather and climate differs from the commonly used 2-stage approach. The likelihood of re-occurrence of major chaotic events after the relative calm post-weather period from about 10 to 50 years that is generally believed to constitute “climate” deserves further study. Post-macroweather climate would signify the re-emergence of new types of chaotic events associated with the Late Anthropocene increases in atmospheric CO2. concentration value and global temperature. The recent excessive rain fall event in Pakistan (September, 2022) could be an example of a chaotic event of this type, although it might also constitute a chaotic weather or macroweather event amplified by the Anthropocene rise in global surface temperature of 1.2o.

Concluding Remarks

During the Anthropocene there has been rapid increase in global surface temperature by about 1.2 oC, primarily due to increase of the atmospheric CO2 concentration value. This process has already resulted in numerous undesirable climate and weather changes. Multifractal weather-climate modeling indicates that short-term weather is followed by “macroweather” representing a 10-50 year long period of relative stability with fewer chaotic events before long-term climate sets in with re-occurrences of major chaotic events. These three periods take place simultaneously anywhere on Earth. Currently, geoscientists and chemical engineers are developing promising, increasingly less expensive methods of atmospheric CO2 concentration value reduction that would reduce the occurrence of both short-term and long- term chaotic events. These important contemporaneous efforts will probably be intensified as weather and climate continue to worsen. In the 19th century geology’s subscience of stratigraphy and the invention of geologic maps helped to find coal and, subsequently, hydrocarbon deposits. Geoscientists may now intensify efforts to identify and describe rock units potentially favorable for carbonization by 3-D mapping and compositional data analysis of Mantle- derived rocks.