/*!
Initialize the stress calculation by setting initial block slip and stresses
then calculating the stress in the whole system.
*/
void UpdateBlockStress::init(SimFramework *_sim) {
BlockList::iterator nt;
BlockID gid;
int lid;
double stress_drop, norm_velocity;
sim = static_cast<Simulation *>(_sim);
tmpBuffer = new double[sim->numGlobalBlocks()];
// All processes need the friction values for all blocks, so we set rhogd here
// and transfer stress drop values between nodes later
for (lid=0; lid<sim->numLocalBlocks(); ++lid) {
double rho = 5.515e3; // density of rock in kg m^-3
double g = 9.81; // force of gravity in m s^-2
double depth = -sim->getBlock(gid).center()[2]; // depth of block center in m
gid = sim->getGlobalBID(lid);
sim->setRhogd(gid, rho*g*depth); // kg m^-3 * m s^-2 * m = kg m^-1 * s^-2 = Pa
sim->setDynamicVal(gid, sim->getDynamic());
sim->setFailed(gid, false);
// Set stresses to their specified initial values
sim->setShearStress(gid, sim->getInitShearStress(gid));
sim->setNormalStress(gid, sim->getInitNormalStress(gid));
// Set the stress drop based on the Greens function calculations
stress_drop = 0;
norm_velocity = sim->getBlock(gid).slip_rate();
for (nt=sim->begin(); nt!=sim->end(); ++nt) {
stress_drop += (nt->slip_rate()/norm_velocity)*sim->getGreenShear(gid, nt->getBlockID());
}
sim->setStressDrop(gid, sim->getBlock(gid).max_slip()*stress_drop);
// noise in the range [1-a, 1+a)
sim->setSlipDeficit(gid, 0);
if (sim->isLocalBlockID(gid)) {
sim->decompressNormalRow(gid);
//sim->setGreenNormal(bid, bid, 0.0); // Erase diagonal for normal Greens matrix
sim->compressNormalRow(gid, 0.7);
}
}
#ifdef MPI_C_FOUND
// Transfer stress drop values between nodes
// This is needed for normal stress Green's calculations
for (gid=0; gid<sim->numGlobalBlocks(); ++gid) {
double stress_drop;
if (sim->isLocalBlockID(gid)) {
stress_drop = sim->getStressDrop(gid);
}
MPI_Bcast(&stress_drop, 1, MPI_DOUBLE, sim->getBlockNode(gid), MPI_COMM_WORLD);
if (!sim->isLocalBlockID(gid)) {
sim->setStressDrop(gid, stress_drop);
}
}
#endif
// Compute initial stress on all blocks
stressRecompute();
}
/*!
Determine the next time step in the simulation when a failure occurs.
Return the block ID of the block responsible for the failure and the timestep until the failure.
*/
void UpdateBlockStress::nextTimeStep(BlockVal &fail_time) {
BlockList::iterator it;
BlockVal temp_block_fail;
double ts;
VCEvent new_event;
BlockID gid;
int lid;
quakelib::Conversion convert;
// Set up the temporary buffer and update field
for(it=sim->begin();it!=sim->end();++it) {
tmpBuffer[it->getBlockID()] = 0.0;
// Set the update field to be the slip rate of each block
sim->setUpdateField(it->getBlockID(), it->slip_rate());
}
// update the temporary buffer with the Greens function applied to the block slip rates
sim->matrixVectorMultiplyAccum(tmpBuffer,
sim->greenShear(),
sim->getUpdateFieldPtr(),
true);
if (sim->doNormalStress()) {
for(it=sim->begin();it!=sim->end();++it) {
sim->setUpdateField(it->getBlockID(), -it->friction()*it->slip_rate());
}
sim->matrixVectorMultiplyAccum(tmpBuffer,
sim->greenNormal(),
sim->getUpdateFieldPtr(),
true);
}
// Go through the blocks and find which one will fail first
temp_block_fail.val = DBL_MAX;
temp_block_fail.block_id = UNDEFINED_BLOCK_ID;
for(lid=0;lid<sim->numLocalBlocks();++lid) {
gid = sim->getGlobalBID(lid);
Block &block = sim->getBlock(gid);
// Calculate the time until this block will fail
// If the block has aseismic slip, the calculation is the exact solution of the
// differential equation d(cff)/dt = rate_of_stress_change + cff*aseismic_frac*self_shear/recurrence
if (block.aseismic() > 0) {
double A, B, K;
A = -tmpBuffer[gid];
B = -block.aseismic()*block.getSelfStresses()/block.getRecurrence();
K = -log(A+B*block.getCFF())/B;
ts = K + log(A)/B;
} else {
ts = convert.sec2year(block.getCFF()/tmpBuffer[gid]);
}
// Blocks with negative timesteps are skipped. These effectively mean the block
// should have failed already but didn't. This can happen in the starting phase
// of a simulation due to initial stresses. These blocks will fail anyway in the
// event propagation section, so we can safely ignore them here. However, negative
// timesteps should not happen after the simulation has progressed for a while.
if (ts <= 0) continue;
// If the time to slip is less than the current shortest time, record the block
if(ts < temp_block_fail.val) {
temp_block_fail.block_id = gid;
temp_block_fail.val = ts;
}
}
// Each node now has the time before the first failure among its blocks
// Determine the time to first failure over all nodes
sim->allReduceBlockVal(temp_block_fail, fail_time, BLOCK_VAL_MIN);
// If we didn't find any blocks that slipped, abort the simulation
assertThrow(fail_time.val < DBL_MAX, "System stuck, no blocks to move.");
// Setup the current event to have the trigger block ID and time
new_event.setEventTriggerOnThisNode(fail_time.block_id==temp_block_fail.block_id);
new_event.setEventTrigger(fail_time.block_id);
new_event.setEventYear(sim->getYear()+fail_time.val);
new_event.setEventNumber(sim->getEventCount());
sim->addEvent(new_event);
}
/*!
Determine the next time step in the simulation when a failure occurs.
Return the block ID of the block responsible for the failure and the timestep until the failure.
*/
void UpdateBlockStress::nextStaticFailure(BlockVal &next_static_fail) {
BlockList::iterator it;
double ts;
BlockID gid;
int lid;
quakelib::Conversion convert;
// Set up the temporary buffer and update field
for (it=sim->begin(); it!=sim->end(); ++it) {
tmpBuffer[it->getBlockID()] = 0.0;
// Set the update field to be the slip rate of each block
sim->setUpdateField(it->getBlockID(), it->slip_rate());
}
// update the temporary buffer with the Greens function applied to the block slip rates
sim->matrixVectorMultiplyAccum(tmpBuffer,
sim->greenShear(),
sim->getUpdateFieldPtr(),
true);
if (sim->doNormalStress()) {
for (it=sim->begin(); it!=sim->end(); ++it) {
BlockID gid = it->getBlockID();
sim->setUpdateField(gid, -sim->getFriction(gid)*it->slip_rate());
}
sim->matrixVectorMultiplyAccum(tmpBuffer,
sim->greenNormal(),
sim->getUpdateFieldPtr(),
true);
}
// Go through the blocks and find which one will fail first
next_static_fail.val = DBL_MAX;
next_static_fail.block_id = UNDEFINED_ELEMENT_ID;
for (lid=0; lid<sim->numLocalBlocks(); ++lid) {
gid = sim->getGlobalBID(lid);
Block &block = sim->getBlock(gid);
// Calculate the time until this block will fail
// If the block has aseismic slip, the calculation is the exact solution of the
// differential equation d(cff)/dt = rate_of_stress_change + cff*aseismic_frac*self_shear/recurrence
if (block.aseismic() > 0) {
double A, B, K;
A = -tmpBuffer[gid];
B = -block.aseismic()*sim->getSelfStresses(gid)/sim->getRecurrence(gid);
K = -log(A+B*sim->getCFF(gid))/B;
ts = K + log(A)/B;
} else {
ts = convert.sec2year(sim->getCFF(gid)/tmpBuffer[gid]);
}
// Blocks with negative timesteps are skipped. These effectively mean the block
// should have failed already but didn't. This can happen in the starting phase
// of a simulation due to initial stresses. These blocks will fail anyway in the
// event propagation section, so we can safely ignore them here. However, negative
// timesteps should not happen after the simulation has progressed for a while.
if (ts <= 0) continue;
// If the time to slip is less than the current shortest time, record the block
// To ensure reproducibility with multiple processes, if multiple blocks fail
// at the same time then we choose the block with the lowest ID over all the processes
if (ts < next_static_fail.val) {
next_static_fail.block_id = gid;
next_static_fail.val = ts;
} else if (ts == next_static_fail.val) {
next_static_fail.block_id = (gid < next_static_fail.block_id ? gid : next_static_fail.block_id);
}
}
}