Microbially assisted recording of the Earth's magnetic field in sediment

Sediments continuously record variations of the Earth's magnetic field and thus provide an important archive for studying the geodynamo. The recording process occurs as magnetic grains partially align with the geomagnetic field during and after sediment deposition, generating a depositional remanent magnetization (DRM) or post-DRM (PDRM). (P)DRM acquisition mechanisms have been investigated for over 50 years, yet many aspects remain unclear. A key issue concerns the controversial role of bioturbation, that is, the mechanical disturbance of sediment by benthic organisms, during PDRM acquisition. A recent theory on bioturbation-driven PDRM appears to solve many inconsistencies between laboratory experiments and palaeomagnetic records, yet it lacks experimental proof. Here we fill this gap by documenting the important role of bioturbation-induced rotational diffusion for (P)DRM acquisition, including the control exerted on the recorded inclination and intensity, as determined by the equilibrium between aligning and perturbing torques acting on magnetic particles.


Supplementary Note 1 PDRM acquisition kinetics
The magnetization acquired during PDRM experiments is controlled by the statistical distribution , , p t ( )   of magnetic grain orientations at time t , where orientations are expressed in spherical coordinates by the angle  between magnetic moment vector and applied field direction, and the azimuthal angle  . This distribution obeys the Debye-Smoluchowski equation: where D is the rotational diffusion coefficient, Γ is the rotational viscous drag coefficient (e.g.
for spheres with radius a immersed in a fluid with dynamic viscosity  ), and V is a potential whose gradient defines a torque V = - τ that adds to the random torques associated with diffusion 1 . The potential V is the sum of (1) a systematic term cos i m B - , which yields the magnetic torque experienced by a particle with magnetic moment i m in the applied field B , and (2) a random "holding potential" i U that accounts for mechanical interaction forces between particles. The general solution of equation (1) at equilibrium (i.e., where 0 p is a constant ensuring that the total probability associated with eq p is 1. The overall effect of the holding potential is equivalent to an increase of the viscous drag 1 . Therefore, cos V mB = - can be identified with the effective total potential if Γ is corrected for the effect of holding torques, and equation (1) can be rewritten as 2 1 1 sin sin sin where mB D  = /( ) Γ is the so-called Boltzmann factor. Upon substituting cos x =  and t ¢ = D t we obtain the dimensionless form where 0 M is the magnetization corresponding to fully aligned magnetic moments.
A general analytical solution of equation (4) where l P are Legendre polynomials of order l, and l c are coefficients determined by the initial distribution 0, p( )  . Insertion of this solution into equation (5) Accordingly, any initial magnetization decays exponentially in zero field, regardless of how it was acquired (i.e. regardless of the initial distribution of magnetic moment orientations).
On the other hand, PDRM acquisition curves can be obtained only by numerical solution of equation (4). Acquisition curves originating from a fully randomized initial state (i.e. 0, p( )=  1 4 /  ) have been calculated with Wolfram Mathematica ® using the following command: where coth 1 ( )= -/ L    is the Langevin function. Equation (8) is affected by a maximum error of 0.03 as long as 1 £  . Above this limit, magnetizations are acquired faster than their decay in zero field, due to the increasingly strong aligning torques associated with 1 >  (Supplementary Figure 1).
In the case of PDRM acquired in weak fields (i.e. 1 <  ), the following relationship holds between the acquisition curve a M and the zero-field decay curve d M : where f eq s M M = / is the fraction of eq M reached at the end of the acquisition time. This parameter is estimated using an appropriate model of acquisition/decay curves based on a distribution of rotational diffusion coefficients.

Modelling PDRM acquisition/decay curves
As shown above, weak-field PDRM acquisition and decay curves inside a mixed sediment layer characterized by a rotational diffusion coefficient D are given by: where eq M is the magnetization at equilibrium with the applied field. Because D is controlled by several factors, including particle size, bioturbated sediment is modelled by a distribution of D values defined by a probability density function r p D ( ). Accordingly, each magnetized grain is subjected to its own rotational diffusion process characterized by an exponential acquisition and decay curve of the form given by equation (11). Integration of where  is a real parameter chosen to avoid singularities of d f in the complex plane.
In principle, equations (14-16) can be used to reconstruct r p from a set of PDRM acquisition/ decay experiments, provided that r p D ( ) does not change significantly over the experiment duration. In order to test the validity of this condition, acquisition and decay curves are fitted independently using a suitable parameterized approximation  and median D . This probability function yields the decay curve