Example - if k = 1500 years/m calculate sediment age at depths of 1m, 2m and 5.3m. Repeat for k =3000 years/m 1m 2m 5.3m Age = 1500 years Age = 3000 years Age = 7950 years For k = 3000years/m Age = 3000 years Age = 6000 years Age = years

The geologist’s use of math often turns out to be a periodic and necessary endeavor. As time goes by you may find yourself scratching your head pondering once- mastered concepts that you suddenly find a need for. This is often the fate of basic power rules. Evaluate the following x a x b = x a / x b = (x a ) b = x a+b x a-b x ab

Question 1.2a Simplify and where possible evaluate the following expressions - i) 3 2 x 3 4 ii) (4 2 ) 2+2 iii) g i. g k iv) D 1.5. D 2

Exponential notation is a useful way to represent really big numbers in a small space and also for making rapid computations involving large numbers - for example, the mass of the earth is kg the mass of the moon is kg Express the mass of the earth in terms of the lunar mass.

Can you write the following numbers in exponential notation (powers of 10)? Density of the earth’s core is kg/m 3 The volume of the earth’s crust is m 3 The mass of the earth’s crust is kg Differences in the acceleration of gravity on the earth’s surface (and elsewhere) are often reported in milligals. 1 milligal =10 -5 meters/second 2. Express the acceleration due to gravity of the earth (9.8m/s 2 ) in milligals.

The North Atlantic Ocean is getting wider at the average rate v s of 4 x m/y and has width w of approximately 5 x 10 6 meters. 1. Write an expression giving the age, A, of the North Atlantic in terms of v s and w. 2. Evaluate your expression. When did the North Atlantic begin to form?

Here is another polynomial which again attempts to fit the near-surface 100km. Notice that this 4 th order equation (redline plotted in graph) has three bends or turns.

In sections 2.5 and 2.6 Waltham reviews negative and fractional powers. The graph below illustrates the set of curves that result as the exponent p in Is varied from 2 to -2 in steps, and a 0 equals 0. Note that the negative powers rise quickly up along the y axis for values of x less than 1 and that y rises quickly with increasing x for p greater than 1.

Power Laws - A power law relationship relevant to geology describes the variations of ocean floor depth as a function of distance from a spreading ridge (x). What physical process do you think might be responsible for this pattern of seafloor subsidence away from the spreading ridges?

This equation assumes that the initial porosity (0.6) decreases by 1/2 from one kilometer of depth to the next. Thus the porosity (  ) at 1 kilometer is 2 -1 or 1/2 that at the surface (i.e. 0.3),  (2)=1/2 of  (1)=0.15 (I.e.  =0.6 x 2 -2 or 1/4th of the initial porosity of 0.6. Equations of the type Are referred to as allometric growth laws or exponential functions.

In the equation a = ? b = ? c = ? The constant b is referred to as a base. Recall relationships like y=10 a. a is the power to which the base 10 is raised in order to get y.

By definition, we also say that x is the log of y, and can write So the powers of the base are logs. “log” can be thought of as an operator like x and  which yields a certain result. Unless otherwise noted, the operator “log” is assumed to represent log base 10. So when asked what is We assume that we are asking for x such that

Sometimes you will see specific reference to the base and the question is written as leaves no room for doubt that we are specifically interested in the log for a base of 10. One of the confusing things about logarithms is the word itself. What does it mean? You might read log 10 y to say - ”What is the power that 10 must be raised to to get y?” How about this operator? - The power of base 10 that yields (  ) y

Observational data for earthquake magnitude (m) and frequency (N, number of earthquakes per year) What would this plot look like if we plotted the log of N versus m?

The Gutenberg-Richter Relation -b is the slope and c is the intercept.

In general, or Try the following on your own