Seismic Shifts from Regulations: Spatial Trade-offs in Marine Mammals and the Value of Information from Hydrocarbon Seismic Surveying

Abstract

Seismic surveys can improve estimates of net private benefits from uncertain hydrocarbon deposits. The Value-of-Information (VOI) can capture these gains. At the same time, seismic surveys impose uncertain damages from noise pollution on marine life. Arctic waters are increasingly attractive exploration locales, but ice cover temporally constrains both surveying and marine mammal species. Thus, damage mitigation requires both temporal and spatial planning. We develop a spatially explicit bio-economic model through which we can calculate the VOI from seismic surveying options alongside potential marine mammal displacements. We demonstrate the model using hydrocarbon exploration opportunities off the Western Greenlandic coast. Lacking estimates for marine mammal sound habitat conservation benefits, we use cost-effectiveness (CEA) as an alternative to weakly informed cost–benefit analysis to identify implicit thresholds as a function of regulatory choices based on different relative spatial values of marine mammal habitat conservation. We check robustness using Monte Carlo (MC) simulations. We illustrate how the combined use of VOI, CEA and MC can ease decision making when uncertainties are compounded and cost–benefit analysis is not feasible.

Appendices

Appendix I: Derivation of the VOI

The derivation of the VOI here is based on Bratvold et al. (2009) and Howard and Abbas (2016). In each cell i there is a prior probability that oil is present: $p\left({X}_{i}=1\right),$ and we know both the probability of true positive (sensitivity) of the test $p\left(\left.{Y}_{i}=1\right|{X}_{i}=1\right)$, and the probability of true negative (specificity) of the test $p\left(\left.{Y}_{i}=0\right|{X}_{i}=0\right)$. Moreover, if oil is present the net private benefits of extraction are v_i.

Before deciding to carry out a survey the situation is as illustrated in the left panel of Fig. 

Fig. 5

Assessed and inferential form of the decision to survey a cell

5 that displays the assessed form, where $p\left({X}_{i}=0\right)$, $p\left(\left.{Y}_{i}=0\right|{X}_{i}=1\right)$ and $p\left(\left.{Y}_{i}=1\right|{X}_{i}=0\right)$ can be calculated as the complements of the known prior probability of oil, the sensitivity and specificity, respectively. The inversion of this diagram to its inferential form is displayed in the right hand panel of Fig. 5; this allows us to calculate the posterior from these probabilities.

If one surveys the cell in question and gets a positive signal the expected payoff of drilling cell i is:

$$p\left({X}_{i}=1|{Y}_{i}=1\right)\left({v}_{i}-{c}^{d}\right)+\left(1-p\left({X}_{i}=1|{Y}_{i}=1\right)\right)\left(-{c}^{d}\right)={p\left(\left.{X}_{i}=1\right|{Y}_{i}=1\right)v}_{i}-{c}^{d}$$

One would only drill if this value is positive and therefore the value of this cell in case of a positive signal is:

$$\mathrm{max}\left(\left({p\left(\left.{X}_{i}=1\right|{Y}_{i}=1\right)v}_{i}-{c}^{d}\right),0\right)$$

If one gets a negative signal, one may decide to drill anyway, and the expected payoff of drilling in such a case is:

$$p\left({X}_{i}=1|{Y}_{i}=0\right)\left({v}_{i}-{c}^{d}\right)+\left(1-p\left({X}_{i}=1|{Y}_{i}=0\right)\right)\left(-{c}^{d}\right)={p\left(\left.{X}_{i}=1\right|{Y}_{i}=0\right)v}_{i}-{c}^{d}$$

One would only drill if this value is positive and therefore the value of this cell in case of a negative signal is:

$$\mathrm{max}\left(\left({p\left(\left.{X}_{i}=1\right|{Y}_{i}=0\right)v}_{i}-{c}^{d}\right),0\right)$$

Weighting these values in case of a positive or negative signal by their respective probabilities of occurrence we can calculate the expected value of the cell with updated information from the survey ${\pi }_{i}^{\mathrm{posterior}}$:

$${\pi }_{i}^{\mathrm{posterior}}=p\left({Y}_{i}=1\right)\mathrm{max}\left(\left({p\left(\left.{X}_{i}=1\right|{Y}_{i}=1\right)v}_{i}-{c}^{d}\right),0\right)+p\left({Y}_{i}=0\right)\mathrm{max}\left(\left(p\left(\left.{X}_{i}=1\right|{Y}_{i}=0\right){v}_{i}-{c}^{d}\right),0\right)$$

The value of information is the difference between the certainty equivalents of the value of a cell with and without the information from the survey. In the case of a risk-neutral decision maker this simplifies to the expected values and hence the value of the information W_i in cell i is:

$${W}_{i}=p\left({Y}_{i}=1\right)\mathrm{max}\left(\left({p\left(\left.{X}_{i}=1\right|{Y}_{i}=1\right)v}_{i}-{c}^{d}\right),0\right)+p\left({Y}_{i}=0\right)\mathrm{max}\left(\left(p\left(\left.{X}_{i}=1\right|{Y}_{i}=0\right){v}_{i}-{c}^{d}\right),0\right)-\mathrm{max}\left(p\left({X}_{i}=1\right){v}_{i}-{c}^{d},0\right),$$

where the last max operator accounts for the fact that the prior might be negative, in which case the owner would decide not to drill. The expected net private benefits Z_i of a survey in cell i are the value of information in that cell minus the cost of the survey c^s:

$${Z}_{i}={W}_{i}-{c}^{s}$$

As shown here the calculation of the VOI and its associated net private benefits is relatively straightforward for a single cell and a risk neutral decision maker. However, it becomes increasingly difficult if multiple prospects are to be surveyed, especially in the presence of budget constraints, spatial correlation or sequential decision making.

Appendix II: Seismic Surveys and Damages to Marine Mammals from Anthropogenic Noise

Seismic surveys usually consist of a ship pulling a series of air guns, which are cylinders that release a sound pulse in a timed manner under a fixed angle. The ship also pulls a number of recorders that record the echo of these sound pulses. The echo provides information that can be used to make inferences about the surface and geological composition of the seafloor, and the presence of oil (Deffenbaugh 2002; Laws and Hedgeland 2008).

Erbe (2012: Figure 1) confirms that, amongst hydrocarbon exploration techniques including surveying and exploratory drilling, typical air gun arrays create the greatest potential impact on marine mammals as they have the highest power spectrum density. The power spectrum density is the power in the signal per unit of frequency (in dB re 1 μPa²/Hz @1 m)¹³ from relevant anthropogenic noises at any frequency (Hz) from 10 to 10,000. Air gun arrays’ densities (~ 150–210 dB) are consistently higher than pile-driving activities (~ 145–190), with more than 40 dB difference at lower frequencies, and average about 60 dB higher than drilling caisson activities (~ 105–145). As dB is a logarithmic scale, the environmental costs of the survey in terms of noise pollution are higher than those of drilling would be.

Gordon et al. (2003) classify the effects of anthropogenic noise, and of seismic surveys in particular, on marine mammals in three types: (1) Physical, (2) Perceptual (masking) and (3) Behavioral effects. Physical effects are direct effects on the animals, such as tissue damage and hearing loss. Perceptual effects are effects caused by changed perceptions, such as the masking of sounds by noise. Behavioral effects are changes in behavior by the sounds, such as startle reactions, diving or switching between behavior types (Gordon et al. 2003).

The anticipated damages become worse if they are cumulative, such as with multiple surveys in a short time span near each other. This is because animals must move away from ideal habitat multiple times or stay away longer. Firms should find longer surveying to become more attractive with increased adoption of 4D surveying, a tool that may be most attractive in new exploration (wildcat) areas where little is known of reservoir conditions or behavior. Similarly, if surveys take place near mating grounds, masking the mating calls, the breeding grounds lose their function. Moreover, if a single survey typically takes place over several weeks (e.g. the survey described in Johnson et al. 2007 took 8–10 weeks), then the noise pollution is even more likely to have cumulative effects.

Directly measuring the effects of seismic surveys is typically infeasible and the effects of surveys must be inferred from observational field studies, modeling, and extrapolation from data on either a few captive individuals or other species (Gordon et al. 2003; Southall et al. 2007c). Potential effects are therefore often highly uncertain. While there is no direct evidence of physical effects of seismic surveys on marine mammals, Southall et al. (2007b) use models, data from captive animals, terrestrial species and threshold levels in humans to determine the criteria for the most widely considered, those of hearing loss damages; their results are summarized in Table 7, second column.

Table 5 Sensitivity of groups marine mammals to seismic surveys

A second dimension of damages is the potential masking of marine mammals’ signals. Marine mammals use sound for a variety of purposes, among others echolocation and communication. The signal masking becomes problematic if it results in reduced fitness of the individuals. The evidence of how animals respond to masking is mixed. It is certainly clear that the frequency of surveys and the frequencies used by baleen whales (such as the blue whale) overlap. Di Iorio and Clark (2010) found that blue whales increase their vocalization rate in the presence of surveys, most likely to compensate for the masking. However, reactions such as no changes or cessation of singing have also been observed (e.g. Castellote et al. 2012; Madsen et al. 2002).

The final concern is that of behavioral changes. These changes are among the most variable ones and therefore the net effects on fitness and survival are uncertain. In general whales seem to try to avoid loud noises but the range where effects are observed depends very much on the species (Gordon et al. 2003). Table 7, third column gives a general overview of the sensitivity of broad species groups to seismic surveys.

Appendix III: Sensitivity Analysis of Parameters

We present several alternative outcomes for relevant scenarios under different parameter values. We show the effect of the survey precision on net private benefits in the economic scenario, and the effect of the connectivity parameter on the outcomes in the population and spatial restriction scenarios.

3.1 Varying the Precision of the Survey

See Fig. 6.

Fig. 6

Net private benefits of the surveys in the economic scenario as a function of the precision of the positive signal (p(X_i = 1|Y_i = 1)) and the precision of the negative signal p(X_i = 0|Y_i = 0). The kinks in the line represent additional cells that are surveyed

Table 6 Varying the sensitivity of habitat quality to surveys

3.2 Monte Carlo Analysis over Priors and Prospects

We carried out a Monte Carlo analysis over the priors and prospects. We drew 1500*5 prospect values from a normal distribution with μ = 150 million $ and σ = 50 million $ and combined this with another 1500*5 draws of priors from a triangular distribution, where we used a minimum of 10% a maximum of 50% and a mode of 25% for Qamut and Napu, and a minimum of 30%, a maximum of 50% and a mode of 40% for the others. The different prior generators reflect the different probability spaces for the locations (see Fig. 2).

We calculated the solutions for all 4 different scenarios, and below we report the mean values, standard deviation and 95% confidence intervals of the Average Cost Effectiveness Ratios (ACERs) and ICERs for each scenario over all draws (see Table 8).

Table 7 Mean, standard deviation and 95% confidence intervals of ACERs and ICERs

The ICERs are far from normally distributed, resulting in large standard deviations and confidence intervals. This is illustrated in Fig. 7. These extremes are typically draws where the restrictions and/or parameter values allow one survey only, with a high value of information in Tooq and a low one in Anu. Moving from one scenario to the other corresponds with moving the survey from Tooq to Anu, resulting in a large loss of valuable information in Tooq, and gaining only little in Anu, whereas the corresponding overall increase in whale population associated with moving the survey is very small.

Fig. 7

Distribution of ICERs across 1500 MC draws

The lower sample sizes for the spatial and combined scenario are a result of domination (n = 53 for the spatial scenario) or non-existence because two scenarios generate the same solution (n = 145 for the spatial scenario and n = 1255 for the combined scenario).

Appendix IV: Results from the Four Scenarios Including CERs

Table 8 CER calculations for the four scenarios

The ΔVOI is calculated as the difference in net private benefits between the no restriction scenario and the restricted scenario. Similarly, ΔPopulation is calculated as the difference in population between the restricted scenario and the no restrictions scenario. The ICER is then calculated by ordering the options by cost and then: $\mathrm{ICER}=\frac{\Delta VOI}{\Delta Population}*1000$ where the changes in VOI and population are between the next most costly alternative and the option itself As the spatial restrictions scenario in this case has fewer whales conserved for more money, it is a dominated alternative and dropped from the ICER calculations.